User:Garygo golob/Slovene phonology/sandbox

Dimensionless quantities

Main article: List of dimensionless quantities

Angles

Angles are dimensionless physical quantities that have its own units, depending on how many dimensions the unit n-sphere has. For example, when drawing an angle on paper, it defines an arc on a unit circle, which has two dimensions. In two dimensions, the unit is radian. In three dimensions, a solid angle defines a part of a surface of a sphere, and the unit is radian squared or steradian. On fandom sites and among hobbyists, the angles are extended for higher dimensions.

Scalar quantity	Symbol	Vector-like quantity	Symbol	SI unit	Euclidian space dimension
(plane) angle	φ	angular displacement / angle of rotation	θ	radian (rad)	2
solid angle / realm angle	Ω			steradian (sr), square radian (rad2)	3
flune angle	Ω4			cube radian (rad3)	4
pentrealm angle	Ω5			radian to the fourth power (rad4)	5
⋮
angle in n dimensions	Ωn			radian to the n-th power (radn)	n

Other dimensionless quantities

There are many other dimensionless quantities that arise due to simply counting something (decays, pedestrians, rotations, particles etc.) or are ratios, coefficients, factors or moduli of other quantities and the dimensions cancel out. Examples include coefficient of friction, shear strain, specific gravity, and phase.

There is a specific relation between units that are measured with radians and those that are not. If radians are not included, that means the number of full rotations is counted, and not the angles. The factor between the two is hence τ = 2π. A common example for this are frequency (f; measured in 1/s) and angular speed (ω; measured in rad/s), and the relation between them is ω = 2πf.

Geometry and space measurement

Quantities for measuring space

Vector quantity	Symbol	Scalar quantity	Symbol	Scalar projection quantity	Symbol	SI unit	Euclidian space dimension	Dimension
displacement	x	arc length / edge length	s	distance	d	m	1	L
vector area	S	surface area	A	(planar) area	A	m2	2	L2
vector volume	V	surcell volume	V	volume	V	m3	3	L3
vector bulk		surteron bulk		bulk		m4	4	L4
⋮
breadth in n dimensions						mn	n	Ln

Other quantities

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
altitude	h	Line segment perpendicularly connecting a side of a triangle or its extension to the opposite vertex.	scalar	m	L
amplitude (in length)	u	A measure of its change in a single period.	scalar	m	L
bimedian		Line segment connecting the midpoints of opposite sides in a quadrilateral.	scalar	m	L
breadth		A relatively large width.	scalar	m	L
chord		Line segment connecting two points on a circle or sphere.	scalar	m	L
curvature (by the radius)	κ	The amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane; derived from the radius of a best-fit circle.	scalar	m-1	L-1
curvature (by the arc)	κ	The amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane; derived from the rate of change of angle.	scalar	rad. m-1	L-1
diagonal	d	A line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.	scalar	m	L
diameter	d	Any straight line segment that passes through the centre of the circle or sphere and whose endpoints lie on the circle or sphere.	scalar	m	L
edge	a or b etc.	Line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.	scalar	m	L
face		A flat surface (a planar region) that forms part of the boundary of a solid object	scalar	m2	L2
first moment of area	S	Measure of the spatial distribution of a shape in relation to an axis.	scalar	m3	L3
height and depth	h	Distance perpendicular to gravitational potential lines.	scalar	m	L
hypotenuse	h	Longest side in a right-angle triangle.	scalar	m	L
length	l	Distance along the longest dimension of an object.	scalar	m	L
maltitude		Line segment perpendicularly connecting one side to the midpoint of the opposite side in a quadrilateral.	scalar	m	L
median		Line segment connecting a side's midpoint to the opposite vertex in a triangle.	scalar	m	L
peak amplitude (in length)	û	If the reference is zero, this is the maximum absolute value of the signal.	scalar	m	L
peak-to-peak amplitude (in length)	p-p	the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative).	scalar	m	L
placement		The inverse of distance.	scalar	m-1	L-1
radius	r	Distance from the center to a point on a circle or a sphere.	scalar	m	L
root mean square amplitude (in length)	ûRMS	The square root of the mean over time of the square of the vertical distance of the graph from the rest state.	scalar	m	L
second moment of area / area moment of inertia	I or J	Geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis.	scalar	m4	L4
semi-amplitude (in length)		Half the peak-to-peak amplitude.	scalar	m	L
signed curvature (by the radius)	k	Curvature with the side of curving taken into account.	pseudoscalar	m-1	L-1
signed curvature (by the arc)	k	Curvature with the side of curving taken into account.	pseudoscalar	rad m-1	L-1
width	w	Shorter of the two dimensions of an object.	scalar	m	L

Translational kinematics

Derivatives and antiderivatives of distance and displacement

In the table are given the derivatives and antiderivatives of displacement (vector) and distance (scalar).

Vector quantity	Symbol	Scalar quantity	Symbol	SI unit	Dimension
absut / absput				m s11	L T11
abshot				m s10	L T10
absrop				m s9	L T9
absock				m s8	L T8
absop				m s7	L T7
absrackle				m s6	L T6
absounce				m s5	L T5
abserk	D			m s4	L T4
abseleration	C			m s3	L T3
absity	B			m s2	L T2
absement / absition	A		A	m s	L T
displacement	x	distance	d	m	L
velocity	v	speed	v	m s-1	L T-1
acceleration	a	acceleration and deceleration	a	m s-2	L T-2
jerk/jolt/surge/lurch	j			m s-3	L T-3
jounce/snap	s			m s-4	L T-4
crackle	c			m s-5	L T-5
pop/dork	p			m s-6	L T-6
lock				m s-7	L T-7
drop				m s-8	L T-8
shot				m s-9	L T-9
put				m s-10	L T-10

Antiderivatives of placement

Antiderivatives of placement or reciprocals of derivatives of distance bear the prefix pre- and are only scalar:

Scalar quantity	SI unit	Dimension
presput	m-1 s11	L-1 T11
preshot	m-1 s10	L-1 T10
presrop	m-1 s9	L-1 T9
presock	m-1 s8	L-1 T8
presop	m-1 s7	L-1 T7
presackle	m-1 s6	L-1 T6
presounce	m-1 s5	L-1 T5
preserk	m-1 s4	L-1 T4
preseleration	m-1 s3	L-1 T3
presity	m-1 s2	L-1 T2
presement / pace	m-1 s	L-1 T
placement	m-1	L-1

Other quantities

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
duration	Δt	Time needed to accomplish something.	scalar	s	T
gravity	g	Acceleration due to weight.	vector	m s-2	L T-2
pace		Inverse of velocity or speed.	vector or scalar	m-1 s	L-1 T
relative velocity	vB|A	Velocity in relation to another (moving) object.	vector	m s-1	L T-1
terminal velocity	vt	Highest velocity attainable by a free falling object.	vector	m s-1	L T-1

Angular kinematics & acoustics

Time derivatives and antiderivatives of angle

Pseudovector quantity	Symbol	Scalar quantity	Symbol	SI unit	Dimension
angular absut/absput				rad s11	T11
angular abshot				rad s10	T10
angular absrop				rad s9	T9
angular absock				rad s8	T8
angular absop				rad s7	T7
angular absrackle				rad s6	T6
angular absounce				rad s5	T5
angular abserk				rad s4	T4
angular abseleration				rad s3	T3
angular absity				rad s2	T2
angular absement / anglement				rad s	T
angular displacement	θ	angle	φ	rad	1
angular velocity	ω	angular speed	ω	rad s-1	T-1
angular acceleration	α	angular chirpyness	γ	rad s-2	T-2
angular jerk/jolt/surge/lurch	ζ			rad s-3	T-3
angular jounce/snap	ψ			rad s-4	T-4
angular crackle				rad s-5	T-5
angular pop/dork				rad s-6	T-6
angular lock				rad s-7	T-7
angular drop				rad s-8	T-8
angular shot				rad s-9	T-9
angular put				rad s-10	T-10

Time derivatives and antiderivatives of no. of rotations

Pseudovector quantity	Symbol	Scalar quantity	Symbol	SI unit	Dimension
rotational absut/absput				s11	T11
rotational abshot				s10	T10
rotational absrop				s9	T9
rotational absock				s8	T8
rotational absop				s7	T7
rotational absrackle				s6	T6
rotational absounce				s5	T5
rotational abserk				s4	T4
rotational abseleration				s3	T3
rotational absity				s2	T2
rotational absement				s	T
rotational displacement	N	no. of rotations	N		1
rotational velocity	ν	rotational speed / rotational frequency	ν	s-1	T-1
rotational acceleration		ordinary chirpyness	c	s-2	T-2
rotational jerk/jolt/surge/lurch				s-3	T-3
rotational jounce/snap				s-4	T-4
rotational crackle				s-5	T-5
rotational pop/dork				s-6	T-6
rotational lock				s-7	T-7
rotational drop				s-8	T-8
rotational shot				s-9	T-9
rotational put				s-10	T-10

Other quantities

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
acoustic admittance	Y	Inverse of acoustic impedance.	scalar	Pa-1 s-1 m3	M-1 L4 T1
acoustic conductance	G	Real part of acoustic admittance.	scalar	Pa-1 s-1 m3	M-1 L4 T1
acoustic impedance	Z	Measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system.	scalar	Pa s m-3	M L-4 T-1
acoustic reactance	X	Imaginary part of acoustic impedance.	scalar	Pa s m-3	M L-4 T-1
acoustic resistance	R	Real part of acoustic impedance.	scalar	Pa s m-3	M L-4 T-1
acoustic susceptance	B	Imaginary part of acoustic admittance.	scalar	Pa-1 s-1 m3	M-1 L4 T1
acoustic volume flow rate	Q	Flow rate due to longitudinal waves.	scalar	m3 s-1	L3 T-1
amplitude (in length)	u	A measure of its change in a single period.	scalar	m	L
amplitude (in pressure)	u	A measure of its change in a single period. Used for longitudinal waves.	scalar	Pa	M L-1 T-2
angular wavelength / reduced wavelength	ƛ	Wavelength divided by 2π.	scalar	m rad-1	L
angular wavenumber	k	Wavenumber divided by 2π.	scalar	rad m-1	L-1
audio frequency		A periodic vibration whose frequency is audible to the average human.	scalar	Hz	T-1
bandwith	B	The difference between the upper and lower frequencies in a continuous band of frequencies.	scalar	Hz	T-1
capacitive acoustic reactance	XC	Negative part of acoustic reactance.	scalar	Pa s m-3	M L-4 T-1
cenrifugal acceleration		Acceleration due to centrifugal force.	vector	m s-2	L T-2
centripetal acceleration	ac	Acceleration due to centripetal force.	vector	m s-2	L T-2
Coriolis acceleration		Acceleration due to Coriolis force.	vector	m s-2	L T-2
Coriolis frequency	f	Frequency of inertial oscillation resulting from Coriolis effect.	scalar	Hz	T-1
duration	Δt	Time needed to accomplish something.	scalar	s	T
Euler acceleration	aEuler	Part of the absolute acceleration that is caused by the variation in the angular velocity of the reference frame.	vector	m s-2	L T-2
frequency	f	Number of oscillations per unit time.	scalar	Hz	T-1
frequency drift		Offset of an oscillator from its nominal frequency.	scalar	Hz s-1	T-2
front velocity	vf	The speed at which the first rise of a pulse above zero moves forward.	vector	m s-2	L T-2
group velocity	vg	The velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.	vector	m s-2	L T-2
inductive acoustic reactance	XL	Positive part of acoustic reactance.	scalar	Pa s m-3	M L-4 T-1
longitudinal modulus / P-wave modulus	M	A relation between the density of a material and the speed of P-waves traveling through it.	scalar	Pa	M L-1 T-2
mechanical wave energy		Energy due to the oscillations within a material (longitudinal or transverse).	scalar	J	M L2 T-2
mechanical wave energy density		Mechanical wave energy per unit volume.	scalar	J m-3	M L-1 T-2
mechanical wave intensity	I	The power carried by mechanical waves per unit area in a direction perpendicular to that area.	scalar	W m-2	M T-3
mechanical wave power		Power due to the oscillations within a material (longitudinal or transverse).	scalar	W	M L2 T-3
mechanical wave pressure		The local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a mechanical wave.	scalar	Pa	M L-1 T-2
peak amplitude (in length)	û	If the reference is zero, this is the maximum absolute value of the wave.	scalar	m	L
peak amplitude (in pressure)		If the reference is zero, this is the maximum absolute value of the wave. Used for longitudinal waves.	scalar	Pa	M L-1 T-2
peak-to-peak amplitude (in length)	p-p	the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative).	scalar	m	L
peak-to-peak amplitude (in pressure)	p-p	the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative). Used for longitudinal waves.	scalar	Pa	M L-1 T-2
phase velocity	vp	The rate at which the wave propagates in any medium.	vector	m s-1	L T-1
pulse wave velocity	PWV	The velocity at which a pulse travels through a medium.	vector	m s-1	L T-1
radius of gyration	r	The radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there. Usually includes different powers of radians to cancel out, e.g. rad-1 to convert from angular velocity to velocity and rad-½ to cancel out when multiplying angular velocity and moment of inertia.	scalar	m radx	L
root mean square amplitude (in length)	ûRMS	The square root of the mean over time of the square of the vertical distance of the graph from the rest state.	scalar	m	L
root mean square amplitude (in pressure)	ûRMS	The square root of the mean over time of the square of the vertical distance of the graph from the rest state. Used for longitudinal waves.	scalar	Pa	M L-1 T-2
rotation period	T	The time that the object takes to complete a full rotation.	scalar	s	T
semi-amplitude (in length)		Half the peak-to-peak amplitude.	scalar	m	L
semi-amplitude (in pressure)		Half the peak-to-peak amplitude. Used for longitudinal waves.	scalar	Pa	M L-1 T-2
signal velocity	vs	The speed at which a wave carries information.	vector	m s-1	L T-1
spatial frequency	ξ	The inverse of wavelength.	scalar	m-1	L-1
sound energy		Energy due to a longitudinal wave.	scalar	J	M L2 T-2
sound energy density		Sound energy per unit volume.	scalar	J m-3	M L-1 T-2
sound exposure		The integral, over time, of squared sound pressure.	scalar	Pa2 s	M2 L-2 T-3
sound intensity		The power carried by sound waves per unit area in a direction perpendicular to that area.	scalar	W m-2	M T-3
sound power		Power due to a longitudinal wave.	scalar	W	M L2 T-3
sound pressure		The local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave.	scalar	Pa	M L-1 T-2
specific acoustic admittance	y	Inverse of specific acoustic impedance.	scalar	Pa-1 s-1 m	M-1 L2 T1
specific acoustic conductance	g	Real part of specific acoustic admittance.	scalar	Pa-1 s-1 m	M-1 L2 T1
specific acoustic impedance	z	Measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system.	scalar	Pa s m-1	M L-2 T-1
specific acoustic reactance	x	Imaginary part of specific acoustic impedance.	scalar	Pa s m-1	M L-2 T-1
specific acoustic resistance	r	Real part of specific acoustic impedance.	scalar	Pa s m-1	M L-2 T-1
specific acoustic susceptance	b	Imaginary part of specific acoustic admittance.	scalar	Pa-1 s-1 m	M-1 L2 T1
specific capacitive acoustic reactance	xC	Negative part of specific acoustic reactance.	scalar	Pa s m-1	M L-2 T-1
specific inductive acoustic reactance	xL	Positive part of specific acoustic reactance.	scalar	Pa s m-1	M L-2 T-1
spectral energy density	S̄xx	Energy of a wave per frequency.	scalar	J Hz-1	M L2 T-1
spectral power density	Sxx	Power of a wave per frequency.	scalar	W Hz-1	M L2 T-2
speed of sound	c	The distance travelled per unit of time by a sound wave as it propagates through an elastic medium.	scalar	m s-1	L T-1
tangential acceleration	at	Acceleration perpendicular to the radius of gyration, parallel to the velocity.	vector	m s-2	L T-2
time	t	One of the base units.	scalar	s	T
wave speed		Magnitude of one of the different velocities for measuring waves.	scalar	m s-1	L T-1
wave velocity		One of the different velocities for measuring waves.	scalar	m s-1	L T-1
wavelength	λ	Distance over which the wave's shape repeats.	scalar	m	L
wavenumber / repetancy	ν	The inverse of wavelength, but only limited to waves; elsewhere, spatial frequency is used.	scalar	m-1	L-1

Translational mechanics

Derivatives and antiderivatives of force

Vector / scalar quantity	Symbol		SI unit	Dimension
	Vector	Scalar
momentement			kg m	M L
momentum	p	p	kg m s-1	M L T-1
force	F	F	N	M L T-2
yank	Y	Y	N s-1	M L T-3
tug	T	T	N s-2	M L T-4
snatch	S	S	N s-3	M L T-5
shake	Sh	Sh	N s-4	M L T-6

Derivatives and antiderivatives of energy

Hamiltonian scalar	Symbol	Lagrangian scalar	Symbol	SI unit	Dimension
		integral of action	I	J s2	M L2
actergy		action	S	J s	M L2 T-1
energy			E	J	M L2 T-2
power			P	W	M L2 T-3
power consumption				W s-1	M L2 T-4

Other quantities

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
mass	m	One of the basic quantities.	scalar	kg	M
drag	Fdrag	Force opposing the motion in a fluid.	vector	N	M L T-2
dynamic force	Fd	Component of weight parallel to the slope.	vector	N	M L T-2
dynamic friction		Friction acting on a moving object.	vector	N	M L T-2
elastic potential energy	Eel	Energy due to the deformation of objects.	scalar	J	M L2 T-2
friction	Ff	Force opposing motion.	vector	N	M L T-2
gravitational field work	Wg	Work done by the gravitational field.	scalar	J	M L2 T-2
gravitational force	Fg	Force due to the gravitational attraction.	vector	N	M L T-2
gravitational potential energy	Eg	Energy gained due to the gravitational field work.	scalar	J	M L2 T-2
internal energy	U	Energy inside a system.	scalar	J	M L2 T-2
kinetic energy	Ek	Energy due to movement.	scalar	J	M L2 T-2
normal force	N	The component of a contact force that is perpendicular to the surface that an object contacts.	vector	N	M L T-2
potential energy	Ep	Energy stored (e.g. due to a field or by stretching a material) and can be turned into another form.	scalar	J	M L2 T-2
pressure	p	Force exerted over an area	scalar	Pa	M L-1 T-2
specific force	SF	Quotient of force and mass.	vector or scalar	N kg-1	L T-2
specific power	PWR	Power delivered by unit mass.	scalar	W kg-1	L2 T-3
specific weight	γ (scalar) γ (vector)	Density times gravitational field strength (scalar) or weight per unit volume (vector).	scalar or vector	N m-3	M L-2 T-2
static force	Fs	Component of weight perpendicular to slope.	vector	N	M L T-2
static friction		Friction acting on a stationary object.	vector	N	M L T-2
tension force	Ftension	Collinear shearing forces.	vector	N	M L T-2
virtual displacement	δγ	It shows how the mechanical system's trajectory can hypothetically deviate very slightly from the actual trajectory of the system without violating the system's constraints.	vector	m	L
virtual work	δW	Work done by a force to move a particle along a virtual displacement	scalar	J	M L2 T-2
weight	W (vector) W (scalar)	Force due to the gravitational attraction (vector) or its magnitude (scalar). Usually used for objects with negligible effect on gravitational field. See also gravitational force.	vector or scalar	N	M L T-2
work	W	Energy transferred to an object or from it.	scalar	J	M L2 T-2

Angular mechanics

Torque and its derivatives and antiderivatives

Pseudovector quantity	Symbol	SI unit	Dimension
moment of momentement		N m s2	M L2
angular momentum / moment of momentum	L	N m s	M L2 T-1
torque / moment of force	τ	N m	M L2 T-2
rotatum / moment of yank		N m s-1	M L2 T-3
moment of tug		N m s-2	M L2 T-4
moment of snatch		N m s-3	M L2 T-5
moment of shake		N m s-4	M L2 T-6

Other quantities

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
angular drag coefficient	γ	Coefficient of how much a fluid hinders the rotation of an object.	scalar	kg m2 s-1	M L2 T-1
centrifugal force		Inertial force that appears to act on all objects when viewed in a rotating frame of reference.	vector	N	M L T-2
centripetal force	Fc	Force causing rotation.	vector	N	M L T-2
Coriolis force		An inertial force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame.	vector	N	M L T-2
Euler force	FEuler	The fictitious tangential force that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axes.	vector	N	M L T-2
friction torque		Torque of a frictional force.	vector	N m	M L2 T-2
internal energy	U	Energy inside a system.	scalar	J	M L2 T-2
mass	m	One of the basic quantities.	scalar	kg	M
mechanical energy		Sum of potential and kinetic energies.	scalar	J	M L2 T-2
moment of inertia	I	A quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.	scalar	kg m2	M L2
rotational energy	Er	Energy due to rotation of an object.	scalar	J	M L2 T-2
specific angular momentum	h	Angular momentum per unit mass.	vector	N m s kg-1	L2 T-1
specific torque		Torque per unit mass.	vector	N m kg-1	L2 T-2
specific power	PWR	Power delivered by unit mass.	scalar	W kg-1	L2 T-3
tangential force		Force causing tangential acceleration.	vector	N	M L T-2

Solid mechanics and engineering

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
area density / column density	ρA	Mass per unit area.	scalar	kg m-2	M L-2
area thermal expansion	ΔA	Change in area due to a change in temperature.	scalar	m2	L2
area thermal expansion coefficient	αA	Area thermal expansion per unit temperature.	scalar	K-1	Θ-1
bulk modulus	K	A measure of the resistance of a substance to bulk compression.	scalar	Pa	M L-1 T-2
coefficient of linear thermal expansion	αL	Linear thermal expansion per unit temperature.	scalar	K-1	Θ-1
compressibility (isentropic)	βS	A measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change in an isentropic process.	scalar	Pa-1	M-1 L T2
compressibility (isothermal)	βT	A measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change in an isothermal process.	scalar	Pa-1	M-1 L T2
compressive strength		The capacity of a material or structure to withstand loads tending to reduce size.	scalar	Pa	M L-1 T-2
compressive stress		Stress that causes compression.	scalar	Pa	M L-1 T-2
deflection	w	The degree to which a part of a long structural element (such as beam) is deformed laterally (in the direction transverse to its longitudinal axis) under a load. See also elastic deflection.	scalar	m	L-1
density	ρ	Mass per unit volume.	scalar	kg m-3	M L-3
density change	ρ̇	A measure of density increase or decrease with time.	scalar	kg m-3 s-1	M L-3 T-1
dislocation density (per area)	ρ⟂	Number of dislocations per unit area.	scalar	m-2	L-2
dislocation density (per volume)		Number of dislocations per unit volume.	scalar	m-3	L-3
elastic deflection	δ	Reversible deflection, proportional to the load.	scalar	m	L
elastic modulus	δ	The unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. Exists in many different forms; all but Poisson's ratio have this unit and dimension as listed here.	scalar	Pa	M L-1 T-2
elastic potential energy	Eel	Energy due to the deformation of objects.	scalar	J	M L2 T-2
energy release rate	G	The rate at which energy is transformed as a material undergoes fracture.	scalar	J m-2	M T-2
engineering stress	σe	Stress without taking changes in area due to deformation into account.	scalar	Pa	M L-1 T-2
expansion rate		Rate at which a substance is expanding.	scalar	s-1	T-1
flaw length	a	Half the length of a crack.	scalar	m	L
flexural modulus	Eflex	An intensive property that is computed as the ratio of stress to strain in flexural deformation.	scalar	Pa	M L-1 T-2
flexural strength		The stress in a material just before it yields in a flexure test.	scalar	Pa	M L-1 T-2
fracture stress	σf	Stress at which a structure fails.	scalar	Pa	M L-1 T-2
fracture toughness	Kc	The critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited.	scalar	Pa m½	M L-½ T-2
hardness	H	A measure of the resistance to localized plastic deformation, such as an indentation (over an area) or a scratch (linear), induced mechanically either by pressing or abrasion.	scalar	Pa	M L-1 T-2
J-integral	J	A way to calculate the strain energy release rate, or work (energy) per unit fracture surface area, in a material.	scalar	Pa m½	M L-½ T-2
Lamé's first parameter	λ	Stiffness of a fluid when compressed in one direction and limited in other directions.	scalar	Pa	M L-1 T-2
linear deformation	Δl	Changes in length due to stress.	scalar	m	L
linear (mass) density	λ	Mass per unit length, e.g. of wire.	scalar	kg m-1	M L-1
linear thermal expansion	Δd	Change in length due to a change in temperature.	scalar	m	L
linearly distributed load	q	Load distributed over the distance of an object.	scalar	N m-1	M T-2
load	q	Force(s) causing stress.	scalar	N	M L T-2
longitudinal modulus / P-wave modulus	M	A relation between the density of a material and the speed of P-waves traveling through it.	scalar	Pa	M L-1 T-2
modulus of resilience	Ur	The maximum energy that can be absorbed per unit volume without creating a permanent distortion.	scalar	J m-3 = Pa	M L-1 T-2
modulus of rigidity / shear modulus / Lamé's second parameter	G or μ	A measure of the elastic shear stiffness of a material.	scalar	Pa	M L-1 T-2
plain strain fracture toughness	KIc	The critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. Used for mode I cracks.	scalar	Pa m½	M L-½ T-2
proof resilience		The maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion.	scalar	J	M L2 T-2
proof stress	Rp	The value for this is commonly set at 0.1% or 0.2% plastic strain.	scalar	Pa	M L-1 T-2
proportionality limit stress		Up to this amount of stress, stress is proportional to strain (Hooke's law).	scalar	Pa	M L-1 T-2
reduced modulus	Er	A special relation between the Young's moduli and Poisson's ratios of the sample and the indenter, used for measuring hardness.	scalar	Pa	M L-1 T-2
shear force	Fshear	Unaligned forces acting on one part of a body in a specific direction, and another part of the body in the opposite direction.	vector	N	M L T-2
shear rate	γ̇	The rate at which it is being deformed by progressive shearing without changing its volume.	scalar	s-1	T-1
shear stiffness		The extent to which an object resists deformation in response to applied shear forces.	scalar	N	M L T-2
shear strength		The strength of a material or component against the type of yield or structural failure when the material or component fails in shear.	scalar	Pa	M L-1 T-2
shear stress	τ	The component of stress coplanar with a material cross section.	scalar	Pa	M L-1 T-2
specific area		Area of an object (e.g. textile) per unit mass.	scalar	m2 kg-1	M-1 L2
specific length		Length of an object (e.g. wire) per unit mass.	scalar	m kg-1	M-1 L
specific volume	ν	Volume of an object per unit mass. Inverse of density.	scalar	m3 kg-1	M-1 L3
static moment of area	Q	Property of a shape that is used to predict its resistance to shear stress.	scalar	m3	L3
stiffness / spring constant	k	The extent to which an object resists deformation in response to an applied force.	scalar	N m-1	M T-2
strain energy	U	Elastic potential energy gained by a wire during elongation with a tensile (stretching) or compressive (contractile) force.	scalar	J	M L2 T-2
strain rate	ε̇	Time derivative of strain.	scalar	s-1	T-1
stress	σ	The force across a small boundary per unit area of that boundary, for all orientations of the boundary.	scalar	Pa	M L-1 T-2
stress intensity factor	K	Used to predict the stress state ("stress intensity") near the tip of a crack or notch caused by a remote load or residual stresses.	scalar	Pa m½	M L-½ T-2
surface energy density	γ	Energy per unit area.	scalar	J m-2	M T-2
tangent modulus		The slope of the stress–strain curve at any specified stress or strain, even in the plastic region.	scalar	Pa	M L-1 T-2
tensile strength		The capacity of a material or structure to withstand loads tending to reduce size.	scalar	Pa	M L-1 T-2
tensile stress		Stress that causes elongation.	scalar	Pa	M L-1 T-2
torsion constant	J	It describes a bar's torsional stiffness.	scalar	m4 rad-1	L4
torsion	T	The twisting of an object due to an applied torque.	scalar	Pa	M L-1 T-2
torsional rigidity		Product of shear modulus and torsion constant.	scalar	N m2 rad-1	M L3 T-2
torsional stiffness	τ	The extent to which an object resists deformation in response to an applied torque.	scalar	N m rad-1	M L2 T-2
toughness / deformation energy	UT	The ability of a material to absorb energy and plastically deform without fracturing.	scalar	J m-3 = Pa	M L-1 T-2
true elastic limit		The lowest stress at which dislocations move.	scalar	Pa	M L-1 T-2
ultimate tensile strength	Ftu	The maximum stress that a material can withstand while being stretched or pulled before breaking.	scalar	Pa	M L-1 T-2
volumetric deformation	ΔV	Changes in volume due to stress (expansion and compression due to pressure changes).	scalar	m3	L3
volumetric thermal expansion	ΔV	Change in volume due to a change in temperature.	scalar	m3	L3
volumetric thermal expansion coefficient	αV	Volumetric thermal expansion per unit temperature.	scalar	K-1	Θ-1
yield stress / yield strength		The lowest stress at which permanent deformation can be measured.	scalar	Pa	M L-1 T-2
Young's modulus	E	A mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise.	scalar	Pa	M L-1 T-2

Fluid mechanics

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
apparent thermal expansion		Apparent thermal expansion of a fluid that is partially due to the expansion of a container.	scalar	m3	L3
area density / column density	ρA	Mass per unit area.	scalar	kg m-2	M L-2
buoyancy	Fb	An upward force exerted by a fluid that opposes the weight of a partially or fully immersed object.	vector	N	M L T-2
coefficient of apparent expansion		Apparent expansion of a liquid per unit temperature.	scalar	K-1	Θ-1
compressibility (isentropic)	βS	A measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change in an isentropic process.	scalar	Pa-1	M-1 L T2
compressibility (isothermal)	βT	A measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change in an isothermal process.	scalar	Pa-1	M-1 L T2
compressive strength		The capacity of a material or structure to withstand loads tending to reduce size.	scalar	Pa	M L-1 T-2
compressive stress		Stress that causes compression.	scalar	Pa	M L-1 T-2
density	ρ	Mass per unit volume.	scalar	kg m-3	M L-3
density change	ρ̇	A measure of density increase or decrease with time.	scalar	kg m-3 s-1	M L-3 T-1
drag	Fdrag	Force opposing the motion in a fluid.	vector	N	M L T-2
dynamic modulus	G	The ratio of stress to strain under vibratory conditions.	scalar	Pa	M L-1 T-2
dynamic viscosity / shear viscosity	μ or η	A material property which relates the viscous stresses in a material to the rate of change of a deformation (the strain rate).	scalar	Pa s	M L-1 T-1
electron density	ne	Density of electrons in plasma.	scalar	mol m-3	L-3 N
entropic force	F	An emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale.	vector	N	M L T-2
expansion rate		Rate at which a substance is expanding.	scalar	s-1	T-1
flow velocity gradient		Differences in velocity over distance in a fluid.	scalar	s-1	T-1
force density	f	Force per unit volume.	vector	N m-3	M L-2 T-2
fugacity	f	An effective partial pressure which replaces the mechanical partial pressure in an accurate computation of chemical equilibrium.	scalar	Pa	M L-1 T-2
fugacity capacity	Z	Molar concentration divided by fugacity.	scalar	mol m-3 Pa-1	N M-1 L-2 T2
hydrostatic pressure	p	Pressure in a fluid at a certain depth.	scalar	Pa	M L-1 T-2
hydrostatic pressure gradient		Change of hydrostatic pressure with depth.	scalar	Pa m-1	M L-2 T-2
ion density	ni	Density of ions in plasma.	scalar	mol m-3	L-3 N
kinematic viscosity	ν	Dynamic viscosity divided by the density of a fluid.	scalar	J s kg-1	L2 T-1
linear (mass) density	λ	Mass per unit length.	scalar	kg m-1	M L-1
load		Force(s) causing stress.	scalar	N	M L T-2
longitudinal modulus / P-wave modulus	M	A relation between the density of a material and the speed of P-waves traveling through it.	scalar	Pa	M L-1 T-2
loss modulus	G″	Relation between stress and heat released under vibratory conditions.	scalar	Pa	M L-1 T-2
mass diffusivity	D	Tendency of a substance to diffuse.	scalar	m2 s-1	L2 T-1
mass flow acceleration	m̈	Acceleration of mass flow rate.	scalar	kg s-2	M T-2
mass flow rate	ṁ	Rate of flow in regard to mass.	scalar	kg s-1	M T-1
mass flux	j or J	The rate of mass flow per unit of area.	scalar	kg m-2 s-1	M L-2 T-1
molar volume	Vm	Volume occupied by a unit amount. Used for calculating the thermal expansion of gases.	scalar	m3 mol-1	N-1 L3
neutral density	nn	Density of neutral particles in plasma.	scalar	mol m-3	L-3 N
shear rate	γ̇	The rate at which it is being deformed by progressive shearing without changing its volume.	scalar	s-1	T-1
shear velocity / friction velocity	u	A form by which a shear stress may be re-written in units of velocity.	usually scalar	m s-1	L T-1
specific area		Area of a fluid per unit mass.	scalar	m2 kg-1	M-1 L2
specific length		Length of a fluid per unit mass.	scalar	m kg-1	M-1 L
specific volume	ν	Volume of a fluid per unit mass. Inverse of density.	scalar	m3 kg-1	M-1 L3
storage modulus	G′	Relation between stress and stored energy in vibratory conditions.	scalar	Pa	M L-1 T-2
stress	σ	The force across a small boundary per unit area of that boundary, for all orientations of the boundary.	scalar	Pa	M L-1 T-2
surface tension	γ	the tendency of liquid surfaces at rest to shrink into the minimum surface area possible.	scalar	N m-1	M T-2
vapor concentration (by mass)	C*	Concentration of vapor of a substance in the air.	scalar	kg m-3	M L-3
vapor concentration (by amount)		Concentration of vapor of a substance in the air.	scalar	mol m-3	N L-3
volume viscosity / bulk viscosity	ζ	The irreversible resistance, over and above the reversible resistance caused by isentropic bulk modulus, to a compression or expansion of a fluid.	scalar	Pa s	M L-1 T-1
volumetric deformation	ΔV	Changes in volume due to stress (expansion and compression due to pressure changes).	scalar	m3	L3
volumetric flow acceleration	V̈	Acceleration of volumetric flow rate.	scalar	m3 s-2	L3 T-2
volumetric flow rate	φ	Rate of flow in regard to volume.	scalar	m3 s-1	L3 T-1
volumetric thermal expansion	ΔV	Change in volume due to a change in temperature.	scalar	m3	L3
volumetric thermal expansion coefficient	αV	Absolute thermal expansion per unit temperature.	scalar	K-1	Θ-1

Optics

Radiometry

SI radiometry units

Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol
Radiant energy	Qe	joule	J	M⋅L2⋅T−2	Energy of electromagnetic radiation.
Radiant energy density	we	joule per cubic metre	J/m3	M⋅L−1⋅T−2	Radiant energy per unit volume.
Radiant flux	Φe	watt	W = J/s	M⋅L2⋅T−3	Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called luminosity in Astronomy.
Spectral flux	Φe,ν	watt per hertz	W/Hz	M⋅L2⋅T −2	Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1.
	Φe,λ	watt per metre	W/m	M⋅L⋅T−3
Radiant intensity	Ie,Ω	watt per steradian	W/sr	M⋅L2⋅T−3	Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity.
Spectral intensity	Ie,Ω,ν	watt per steradian per hertz	W⋅sr−1⋅Hz−1	M⋅L2⋅T−2	Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is a directional quantity.
	Ie,Ω,λ	watt per steradian per metre	W⋅sr−1⋅m−1	M⋅L⋅T−3
Radiance	Le,Ω	watt per steradian per square metre	W⋅sr−1⋅m−2	M⋅T−3	Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity".
Spectral radiance Specific intensity	Le,Ω,ν	watt per steradian per square metre per hertz	W⋅sr−1⋅m−2⋅Hz−1	M⋅T−2	Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity".
	Le,Ω,λ	watt per steradian per square metre, per metre	W⋅sr−1⋅m−3	M⋅L−1⋅T−3
Irradiance Flux density	Ee	watt per square metre	W/m2	M⋅T−3	Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral irradiance Spectral flux density	Ee,ν	watt per square metre per hertz	W⋅m−2⋅Hz−1	M⋅T−2	Irradiance of a surface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (1 Jy = 10−26 W⋅m−2⋅Hz−1) and solar flux unit (1 sfu = 10−22 W⋅m−2⋅Hz−1 = 104 Jy).
	Ee,λ	watt per square metre, per metre	W/m3	M⋅L−1⋅T−3
Radiosity	Je	watt per square metre	W/m2	M⋅T−3	Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity".
Spectral radiosity	Je,ν	watt per square metre per hertz	W⋅m−2⋅Hz−1	M⋅T−2	Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity".
	Je,λ	watt per square metre, per metre	W/m3	M⋅L−1⋅T−3
Radiant exitance	Me	watt per square metre	W/m2	M⋅T−3	Radiant flux emitted by a surface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity".
Spectral exitance	Me,ν	watt per square metre per hertz	W⋅m−2⋅Hz−1	M⋅T−2	Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity".
	Me,λ	watt per square metre, per metre	W/m3	M⋅L−1⋅T−3
Radiant exposure	He	joule per square metre	J/m2	M⋅T−2	Radiant energy received by a surface per unit area, or equivalently irradiance of a surface integrated over time of irradiation. This is sometimes also called "radiant fluence".
Spectral exposure	He,ν	joule per square metre per hertz	J⋅m−2⋅Hz−1	M⋅T−1	Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m−2⋅nm−1. This is sometimes also called "spectral fluence".
	He,λ	joule per square metre, per metre	J/m3	M⋅L−1⋅T−2
See also: SI Radiometry Photometry

Photometry

SI photometry quantities

Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol
Luminous energy	Qv	lumen second	lm⋅s	T⋅J	The lumen second is sometimes called the talbot.
Luminous flux, luminous power	Φv	lumen (= candela steradian)	lm (= cd⋅sr)	J	Luminous energy per unit time
Luminous intensity	Iv	candela (= lumen per steradian)	cd (= lm/sr)	J	Luminous flux per unit solid angle
Luminance	Lv	candela per square metre	cd/m2 (= lm/(sr⋅m2))	L−2⋅J	Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit.
Illuminance	Ev	lux (= lumen per square metre)	lx (= lm/m2)	L−2⋅J	Luminous flux incident on a surface
Luminous exitance, luminous emittance	Mv	lumen per square metre	lm/m2	L−2⋅J	Luminous flux emitted from a surface
Luminous exposure	Hv	lux second	lx⋅s	L−2⋅T⋅J	Time-integrated illuminance
Luminous energy density	ωv	lumen second per cubic metre	lm⋅s/m3	L−3⋅T⋅J
Luminous efficacy (of radiation)	K	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	Ratio of luminous flux to radiant flux
Luminous efficacy (of a source)	η	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient	V			1	Luminous efficacy normalized by the maximum possible efficacy
See also: SI Photometry Radiometry

Other quantities

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
absolute air mass	σ	The integral of air density along the light ray.	scalar	kg m-2	M L-2
back focal distance	s′F′	The distance from the vertex of the last optical surface of the system to the rear focal point.	scalar	m	L
circle of confusion	c	An optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source.	scalar	m	L
directional attenuation coefficient	μΩ	Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.	scalar	m-1	L-1
Einstein coefficient A21	A21	Coefficient used in calculation of spontaneous emission.	scalar	s-1	T-1
Einstein coefficient B12	B12	Coefficient used in calculation of photon absorption.	scalar	m3 J-1 s-2	M-1 L
Einstein coefficient B21	B21	Coefficient used in calculation of stimulated emission.	scalar	m3 J-1 s-2	M-1 L
emission coefficient	ε	A coefficient that describes the emission of atomic line radiation at a certain frequency.	scalar	J s-1 m-3 sr-1	M L-1 T-3
(effective) focal length	f	A measure of how strongly the optical system converges or diverges light.	scalar	m	L
fringe spacing	df	Separation between maxima in interference of planar waves.	scalar	m	L
front focal distance	sF	The distance from the front focal point of the system to the vertex of the first optical surface.	scalar	m	L
front focal length	f	The distance from the front focal point to the front principal plane.	scalar	m	L
front velocity	vf	The speed at which the first rise of a pulse above zero moves forward.	vector	m s-2	L T-2
group velocity	vg	The velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.	vector	m s-2	L T-2
group velocity dispersion	GVD	The derivative of the inverse of group velocity of light in a material with respect to angular frequency.	vector	m-1 s2	L-1 T2
hemispherical attenuation coefficient	μ	Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.	scalar	m-1	L-1
hyperfocal distance	H	A distance from a lens beyond which all objects can be brought into an "acceptable" focus.	scalar	m	L
image distance	S2	Distance from a lens to an image produced.	scalar	m	L
intensity	I	The power carried by light per unit area in a direction perpendicular to that area.	scalar	W m-2	M T-3
longitudinal spherical aberration	LSA	Spherical aberration along the optical axis.	scalar	m	L
luminosity	L	An absolute measure of radiated electromagnetic energy (light) per unit time, and is synonymous with the radiant power emitted by a light-emitting object.	scalar	W	M L2 T-3
object distance	S1	Distance from a lens to the object.	scalar	m	L
optical path difference	OPD	Difference of optical path length of two paths.	scalar	m	L
optical path length	OPL	The length that light needs to travel through a vacuum to create the same phase difference as it would have when traveling through a given medium.	scalar	m	L
optical power	P	The degree to which a lens, mirror, or other optical system converges or diverges light.	scalar	dpt	L-1
phase velocity	vp	The rate at which the wave propagates in any medium.	vector	m s-1	L T-1
rear focal length	f′	The distance from the rear principal plane to the rear focal point.	scalar	m	L
recoil energy	Erec	Energy of an atom receiving energy due to the Kapista–Dirac effect.	scalar	J	M L2 T-2
recoil frequency	ωrec	Frequency of an atom receiving energy due to the Kapista–Dirac effect.	scalar	Hz	T-1
resolvable points distance	r	Distance between two points which can be resolved.	scalar	m	L
scattering particle size	x	Size of a particle causing scattering.	scalar	m	L
signal velocity	vs	The speed at which a wave carries information.	vector	m s-1	L T-1
slit width	d	Width of a slit through which light is allowed to pass.	scalar	m	L
spectral directional attenuation coefficient (per frequency)	μΩ,ν	Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.	scalar	m-1	L-1
spectral directional attenuation coefficient (per wavelength)	μΩ,λ	Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.	scalar	m-1	L-1
spectral energy density	S̄xx	Energy emitted as electromagnetic radiation per frequency.	scalar	J Hz-1	M L2 T-1
spectral energy density (per volume)	u	Energy emitted as electromagnetic radiation per unit volume per frequency.	scalar	J m-3 Hz-1	M L-1 T-1
spectral hemispherical attenuation coefficient (per frequency)	μν	Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.	scalar	m-1	L-1
spectral hemispherical attenuation coefficient (per wavelength)	μλ	Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.	scalar	m-1	L-1
spectral power density	Sxx	Energy emitted as electromagnetic radiation per unit time per frequency.	scalar	W Hz-1	M L2 T-2
spectral power density (per volume)		Energy emitted as electromagnetic radiation per unit volume per frequency per unit time.	scalar	W m-3 Hz-1	M L-1 T-2
spectral power distribution	M	The power per unit area per unit wavelength of an illumination (radiant exitance).	scalar	W m-2	M T-3
speed of light in a material	v	Phase speed of electromagnetic radiation as it passes through a medium.	scalar	m s-1	L T-1
thickness of a lens	d	The distance along the lens axis between the two surface vertices.	scalar	m	L
transverse spherical aberration	TSA	Spherical aberration perpendicular to the optical axis; the diameter of focus.	scalar	m	L
wave impedance	Z	The ratio of the transverse components of the electric and magnetic fields.	scalar	Ω	I-2 M L2 T-3

Thermodynamics

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
apparent thermal expansion		Apparent thermal expansion of a fluid that is partially due to the expansion of a container.	scalar	m3	L3
area thermal expansion	ΔA	Change in area due to a change in temperature.	scalar	m2	L2
area thermal expansion coefficient	αA	Area thermal expansion per unit temperature.	scalar	K-1	Θ-1
boiling point	Tb	Temperature at which a substance changes from liquid into vapor.	scalar	K	Θ
boiling point elevation	ΔTb	An increase in the temperature at which a substance boils, caused when a smaller amount of another, non-volatile substance is added.	scalar	K	Θ
chemical energy	Ec	Energy stored in chemical bonds; chemical potential times the number of particles; used in grand potential calculation.	scalar	J	M L2 T-2
chemical potential	μ	The energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition; used in grand potential calculation.	scalar	J	M L2 T-2
coefficient of apparent expansion		Apparent expansion of a liquid per unit temperature.	scalar	K-1	Θ-1
coefficient of linear thermal expansion	αL	Linear thermal expansion per unit temperature.	scalar	K-1	Θ-1
compressibility (isentropic)	βS	A measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change in an isentropic process.	scalar	Pa-1	M-1 L T2
compressibility (isothermal)	βT	A measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change in an isothermal process.	scalar	Pa-1	M-1 L T2
configuration entropy / Boltzmann entropy	SB	The portion of a system's entropy that is related to discrete representative positions of its constituent particles.	scalar	J K-1	Θ-1 M L2 T-2
conformational entropy		The entropy associated with the number of conformations of a molecule.	scalar	J K-1	Θ-1 M L2 T-2
critical point pressure		Pressure where the critical point is situated.	scalar	Pa	M L-1 T-2
critical point temperature		Temperature where the critical point is situated.	scalar	K	Θ
cryoscopic constant	Kf	Ratio of freezing point depression to the molality of a solution.	scalar	K kg mol-1	Θ N-1 M
ebullioscopic constant	Kc	Ratio of boiling point elevation to the molality of a solution.	scalar	K kg mol-1	Θ N-1 M
energy	E	The quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.	scalar	J	M L2 T-2
enthalpy	H	Sum of its internal energy and the product of its pressure and volume.	scalar	J	M L2 T-2
enthalpy of condensation / heat of condensation (per mass)	qc	The change in its enthalpy resulting from providing energy, typically heat, to a unit mass of the substance to change its state from a gas to a liquid.	scalar	J kg-1	L2 T-2
enthalpy of condensation / heat of condensation (per amount)	qc	The change in its enthalpy resulting from providing energy, typically heat, to a unit amount of the substance to change its state from a gas to a liquid.	scalar	J mol-1	N M L2 T-2
enthalpy of deposition / heat of deposition (per mass)	qd	The change in its enthalpy resulting from providing energy, typically heat, to a unit mass of the substance to change its state from a gas to a solid.	scalar	J kg-1	L2 T-2
enthalpy of deposition / heat of deposition (per amount)	qd	The change in its enthalpy resulting from providing energy, typically heat, to a unit amount of the substance to change its state from a gas to a solid.	scalar	J mol-1	N M L2 T-2
enthalpy of fusion / heat of fusion (per mass)	qf	The change in its enthalpy resulting from providing energy, typically heat, to a unit mass of the substance to change its state from a solid to a liquid, at constant pressure.	scalar	J kg-1	L2 T-2
enthalpy of fusion / heat of fusion (per amount)	qf	The change in its enthalpy resulting from providing energy, typically heat, to a unit amount of the substance to change its state from a solid to a liquid, at constant pressure.	scalar	J mol-1	N M L2 T-2
enthalpy of ionization / heat of ionization (per mass)	qi	The change in its enthalpy resulting from providing energy, to a unit mass of the substance to remove a set number of electrons from each atom/ion.	scalar	J kg-1	L2 T-2
enthalpy of ionization / heat of ionization (per amount)	qi	The change in its enthalpy resulting from providing energy, to a unit amount of the substance to remove a set number of electrons from each atom/ion.	scalar	J mol-1	N M L2 T-2
enthalpy of mixing	ΔHmix	The enthalpy liberated or absorbed from a substance upon mixing. When a substance or compound is combined with any other substance or compound, the enthalpy of mixing is the consequence of the new interactions between the two substances or compounds.	scalar	J	M L2 T-2
enthalpy of recombination / heat of recombination (per mass)	qr	The change in its enthalpy resulting from providing energy, to a unit mass of the substance to add a set number of electrons to each atom/ion.	scalar	J kg-1	L2 T-2
enthalpy of recombination / heat of recombination (per amount)	qr	The change in its enthalpy resulting from providing energy, to a unit amount of the substance to add a set number of electrons to each atom/ion.	scalar	J mol-1	N M L2 T-2
enthalpy of solidification / heat of solidification (per mass)	qs	The change in its enthalpy resulting from providing energy, typically heat, to a unit mass of the substance to change its state from a liquid to a solid, at constant pressure.	scalar	J kg-1	L2 T-2
enthalpy of solidification / heat of solidification (per amount)	qs	The change in its enthalpy resulting from providing energy, typically heat, to a unit amount of the substance to change its state from a liquid to a solid, at constant pressure.	scalar	J mol-1	N M L2 T-2
enthalpy of sublimation / heat of sublimation (per mass)	qs	The change in its enthalpy resulting from providing energy, typically heat, to a unit mass of the substance to change its state from a solid to a gas.	scalar	J kg-1	L2 T-2
enthalpy of sublimation / heat of sublimation (per amount)	qs	The change in its enthalpy resulting from providing energy, typically heat, to a unit amount of the substance to change its state from a solid to a gas.	scalar	J mol-1	N M L2 T-2
enthalpy of vaporization / heat of vaporization (per mass)	qv	The change in its enthalpy resulting from providing energy, typically heat, to a unit mass of the substance to change its state from a liquid to a gas.	scalar	J kg-1	L2 T-2
enthalpy of vaporization / heat of vaporization (per amount)	qv	The change in its enthalpy resulting from providing energy, typically heat, to a unit amount of the substance to change its state from a liquid to a gas.	scalar	J mol-1	N M L2 T-2
entropic force	F	An emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale.	vector	N	M L T-2
entropy	S	A scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty.	scalar	J K-1	Θ-1 M L2 T-2
entropy of fusion		Increase in entropy when a solid melts.	scalar	J K-1	Θ-1 M L2 T-2
entropy of ionization		Increase in entropy during ionization of a gas.	scalar	J K-1	Θ-1 M L2 T-2
entropy of mixing		Increase in the total entropy of a compound system after mixing.	scalar	J K-1	Θ-1 M L2 T-2
entropy of vaporization		Increase in entropy during vaporization of a liquid.	scalar	J K-1	Θ-1 M L2 T-2
free entropy		Either Gibbs free entropy or Helmholtz free entropy.	scalar	J K-1	Θ-1 M L2 T-2
freezing-point depression	ΔTf	A drop in the maximum temperature at which a substance freezes, caused when a smaller amount of another, non-volatile substance is added.	scalar	K	Θ
fugacity	f	An effective partial pressure which replaces the mechanical partial pressure in an accurate computation of chemical equilibrium.	scalar	Pa	M L-1 T-2
fugacity capacity	Z	Molar concentration divided by fugacity.	scalar	mol m-3 Pa-1	N M-1 L-2 T2
gas constant / difference in heat capacities	k	Pressure energy per unit absolute temperature; equal to amount times molar gas constant. Not to be confused with molar gas constant or specific gas constant.	scalar	J K-1	Θ-1 M L2 T-2
Gibbs free energy	G	A thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.	scalar	J	M L2 T-2
Gibbs free entropy / Planck potential	Ξ	Negative value of Gibbs free energy divided by temperature.	scalar	J K-1	Θ-1 M L2 T-2
grand potential / Landau free energy	φG or Ω	Helmholtz free energy minus the chemical energy.	scalar	J	M L2 T-2
heat	Q	Transfer of energy due to temperature difference.	scalar	J	M L2 T-2
heat capacity (isobaric)	Cp	The amount of heat to be supplied to an object to produce a unit change in its temperature in an isobaric process.	scalar	J K-1	Θ-1 M L2 T-2
heat capacity(isochoric)	Cv	The amount of heat to be supplied to an object to produce a unit change in its temperature in an isochoric process.	scalar	J K-1	Θ-1 M L2 T-2
heat current / heat flow / heat transfer	H	Heat transferred per unit time.	scalar	W	M L2 T-3
heat flux	φq	A flow of energy per unit area per unit time.	vector	W m-2	M T-3
Helmholtz free energy	F or A	A thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal).	scalar	J	M L2 T-2
Helmholtz free entropy / Massieu potential	Φ	Negative value of Helmholtz free energy divided by temperature.
internal energy	U	Energy inside a system.	scalar	J	M L2 T-2
internal pressure	πT	A measure of how the internal energy of a system changes when it expands or contracts at constant temperature.	scalar	Pa	M L-1 T-2
latent heat	Ql	Energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process.	scalar	J	M L2 T-2
latent internal energy	Ul	The internal energy a system requires to undergo a phase transition.	scalar	J	M L2 T-2
lattice energy	ΔElattice	The energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state.	scalar	J	M L2 T-2
lattice enthalpy	ΔHlattice	The enthalpy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state.	scalar	J	M L2 T-2
linear thermal expansion	Δd	Change in length due to a change in temperature.	scalar	m	L
loop entropy		The entropy lost upon bringing together two residues of a polymer within a prescribed distance.	scalar	J K-1	Θ-1 M L2 T-2
melting point	Tm	Temperature at which a substance changes from solid into liquid.	scalar	K	Θ
molar energy	em	Energy pr unit amount.	scalar	J mol-1	N M L2 T-2
molar enthalpy	Hm	Enthalpy per unit amount.	scalar	J mol-1	N M L2 T-2
molar Gibbs free energy	gm	Gibbs free energy per unit amount.	scalar	J mol-1	N M L2 T-2
molar heat capacity (isobaric)	cp,m	The amount of heat to be supplied to a unit amount of an object to produce a unit change in its temperature in an isobaric process.	scalar	J mol-1 K-1	N-1 Θ-1 M L2 T-2
molar heat capacity (isochoric)	cv,m	The amount of heat to be supplied to a unit amount of an object to produce a unit change in its temperature in an isochoric process. Equals to isobaric heat capacity minus the molar gas constant.	scalar	J mol-1 K-1	N-1 Θ-1 M L2 T-2
molar internal energy		Internal energy per unit amount.	scalar	J mol-1	N M L2 T-2
molar latent heat		Latent heat per unit amount.	scalar	J mol-1	N M L2 T-2
molar latent internal energy		Latent internal energy per unit amount.	scalar	J mol-1	N M L2 T-2
molar volume	Vm	Volume occupied by a unit amount. Used for calculating the thermal expansion of gases.	scalar	m3 mol-1	N-1 L3
phase transition pressure		Pressure where the phase change occurs.	scalar	Pa	M L-1 T-2
phase transition temperature		Temperature where the phase change occurs.	scalar	K	Θ
pressure energy	Ɛp	Product of pressure and volume.	scalar	J	M L2 T-2
Redlich–Kwong coefficient a	a	A parameter used in Redlich–Kwong equation.	scalar	Pa K½ m6 mol-2	N-2 Θ½ M L5 T-2
Redlich–Kwong coefficient b	b	A parameter used in Redlich–Kwong equation.	scalar	m3 mol-1	N-1 L3
specific energy	e	Energy per unit mass of a fuel.	scalar	J kg-1	L2 T-2
specific enthalpy	h	Enthalpy per unit mass.	scalar	J kg-1	L2 T-2
specific entropy	s	Entropy per unit mass.	scalar	J kg-1 K-1	Θ-1 L2 T-2
specific gas constant	Rspecific	The molar gas constant divided by the molar mass of a gas; the difference between both specific heat capacities.	scalar	J kg-1 K-1	Θ-1 L2 T-2
specific Gibbs free energy	g	Gibbs free energy per unit mass.	scalar	J kg-1	L2 T-2
specific heat capacity (isobaric)	cp	The amount of heat to be supplied to a unit mass of an object to produce a unit change in its temperature in an isobaric process.	scalar	J kg-1 K-1	Θ-1 L2 T-2
specific heat capacity (isochoric)	cv	The amount of heat to be supplied to a unit mass of an object to produce a unit change in its temperature in an isochoric process.	scalar	J kg-1 K-1	Θ-1 L2 T-2
specific internal energy		Internal energy per unit mass.	scalar	J kg-1	L2 T-2
specific latent heat	L	Latent heat per unit mass.	scalar	J kg-1	L2 T-2
specific latent internal energy		Latent internal energy per unit mass.	scalar	J kg-1	L2 T-2
specific power	PWR	Power delivered by unit mass.	scalar	W kg-1	L2 T-3
sublimation temperature	Ts	Temperature at which a substance changes from solid into vapor.	scalar	K	Θ
temperature	T	One of the base physical quanttities.	scalar	K	Θ
thermal admittance / heat transfer coefficient / U-value	h	The proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat.	scalar	W m-2 K-1	Θ-1 M T-3
thermal conductance	C	The ability of materials or systems to conduct heat and the opposition they offer to the heat current.	scalar	W K-1	Θ-1 M L2 T-3
thermal conductivity	κ	A measure of material's ability to conduct heat.	scalar	W m-1 K-1	Θ-1 M L T-3
thermal diffusivity	α	A measure of heat transfer inside a material.	scalar	m2 s-1	L2 T-1
thermal energy	Et	Energy that is measured by temperature.	scalar	J	M L2 T-2
thermal insulance / R-value	Rval	A measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists the conductive flow of heat.	scalar	m2 K W-1	Θ M-1 T3
thermal resistance	R	The ability of materials or systems to conduct heat and the opposition they offer to the heat current.	scalar	K W-1	Θ M-1 L-2 T3
thermal resistivity	ρ	The inverse of thermal conductivity; a material's resistance to conduct heat.	scalar	K m W-1	Θ M-1 L-1 T3
thermodynamic potential		Can refer to either internal energy, Helmholtz free energy, enthalpy, Gibbs free energy, or grand potential.	scalar	J	M L2 T-2
thermodynamic work	Wt	Work done by a thermodynamic system.	scalar	J	M L2 T-2
triple point pressure		Pressure where the triple point is situated.	scalar	Pa	M L-1 T-2
triple point temperature		Temperature where the triple point is situated.	scalar	K	Θ
Van der Waals parameter a	a	A parameter used in Van der Waals equation.	scalar	Pa m6 mol-2	N-2 M L5 T-2
Van der Waals parameter b	b	A parameter used in Van der Waals equation.	scalar	m3 mol-1	N-1 L3
vapor pressure		The pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.	scalar	Pa	M L-1 T-2
volumetric thermal expansion	ΔV	Change in volume due to a change in temperature.	scalar	m3	L3
volumetric thermal expansion coefficient	αV	Volumetric thermal expansion per unit temperature.	scalar	K-1	Θ-1
work	W	Energy transferred to an object or from it.	scalar	J	M L2 T-2

Electromagnetism

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
admittance	Y	A measure of how easily a circuit or device will allow a current to flow.	scalar	A	I
amplitude (of electric current)		A measure of its change in a single period in AC current.	scalar	A	I
amplitude (of magnetic flux)		A measure of its change in a single period produced by or producing AC current.	vector	Wb	I-1 M L2 T−2
amplitude (of magnetomotive force)		A measure of its change in a single period produced by or producing AC current.	vector	A	I
amplitude (of voltage)		A measure of its change in a single period in AC current.	scalar	V	I-1 M L2 T−3
capacitive reactance	XC	Reactance due to the capacitance.	scalar	Ω	I-2 M L2 T-3
electric current (intensity)	I	One of the base quantities.	scalar	A	I
electric field work	We	Work done by the electric field.	scalar	J	M L2 T-2
electric force	Fe	Force due to the electric field.	vector	N	M L T-2
electric potential energy	Ee	Energy gained due to electric field work.	scalar	J	M L2 T-2
electrical admittance	Y	A measure of how easily a circuit or device will allow a current to flow.	scalar	S	I2 M-1 L-2 T3
electrical conductance	G	The inverse of electrical resistance.	scalar	S	I2 M-1 L-2 T3
electrical conductivity	σ	The inverse of electrical resistivity.	scalar	S m-1	I2 M-1 L-3 T3
electrical impedance	Z	The inverse of electrical admittance.	scalar	Ω	I-2 M L2 T-3
electrical reactance	X	The opposition presented to alternating current by inductance and capacitance.	scalar	Ω	I-2 M L2 T-3
electrical resistance	R	A measure of an object's opposition to the flow of electric current.	scalar	Ω	I-2 M L2 T-3
electrical resistivity	ρ	A measure of a matterial's opposition to the flow of electric current.	scalar	Ω m	I-2 M L3 T-3
electrical susceptance	B	The inverse of electrical reactance.	scalar	S	I2 M-1 L-2 T3
inductive reactance	XL	Reactance due to inductance.	scalar	Ω	I-2 M L2 T-3
Lorentz force / electromagnetic force	Fl	Force due to the electromagnetic field.	vector	N	M L T-2
magnetic field work	Wm	Work done by the magnetic field.	scalar	J	M L2 T-2
magnetic force	Fm	Force due to the magnetic field.	vector	N	M L T-2
magnetic potential energy	Em	Energy gained due to the magnetic field work.	scalar	J	M L2 T-2
peak amplitude (of electric current)	Ipeak	The maximum absolute value of current in AC current.	scalar	A	I
peak amplitude (of magnetic flux)	φpeak	The maximum absolute value of magnetic flux produced by or producing AC current.	vector	Wb	I-1 M L2 T−2
peak amplitude (of magnetomotive force)	${\mathcal {F}}$peak	The maximum absolute value of magnetomotive force produced by or producing AC current.	vector	A	I
peak amplitude (of voltage)	Vpeak	The maximum absolute value of voltage in AC current.	scalar	V	I-1 M L2 T−3
peak-to-peak amplitude (of electric current)		Twice the maximum absolute value of current in AC current.	scalar	A	I
peak-to-peak amplitude (of magnetic flux)		Twice the maximum absolute value of magnetic flux produced by or producing AC current.	vector	Wb	I-1 M L2 T−2
peak-to-peak amplitude (of magnetomotive force)		Twice the maximum absolute value of magnetomotive force produced by or producing AC current.	vector	A	I
peak-to-peak amplitude (of voltage)		Twice the maximum absolute value of voltage in AC current.	scalar	V	I-1 M L2 T−3
root mean square amplitude (of electric current)		Twice the maximum absolute value of current in AC current.	scalar	A	I
root mean square amplitude (of magnetic flux)		Twice the maximum absolute value of magnetic flux produced by or producing AC current.	vector	Wb	I-1 M L2 T−2
root mean square amplitude (of magnetomotive force)		Twice the maximum absolute value of magnetomotive force produced by or producing AC current.	vector	A	I
root mean square amplitude (of voltage)		Twice the maximum absolute value of voltage in AC current.	scalar	V	I-1 M L2 T−3
voltage	V	Difference in electric potential between two points in space.	scalar	V	I-1 M L2 T−3

Astrophysics and cosmology

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
anomalistic period		The time that elapses between two passages of an object at its periapsis.	scalar	s	T
Coriolis frequency	f	Frequency of inertial oscillation resulting from Coriolis effect.	scalar	Hz	T-1
gravitational field strength	g	Weight experienced by one unit of mass. Magnitude of gravity.	scalar	N kg-1	L T-2
gravitational field work	Wg	Work done by the gravitational field.	scalar	J	M L2 T-2
gravitational force	Fg	Force due to the gravitational attraction.	vector	N	M L T-2
gravitational potential	Vg	Gravitational potential energy per unit mass of an object.	scalar	J kg-1	L2 T-2
gravitational potential energy	Eg	Energy gained due to the gravitational field work.	scalar	J	M L2 T-2
gravity	g	Acceleration due to weight.	vector	m s-2	L T-2
nodal period / draconic period	Tn	The time that elapses between two passages of the object through its ascending node, the point of its orbit where it crosses the ecliptic from the southern to the northern hemisphere.	scalar	s	T
orbital period / revolution period	T	The amount of time a given astronomical object takes to complete one orbit around another object.	scalar	s	T
sidereal period	Tsid	A 360° revolution of one body around its primary relative to the fixed stars projected in the sky	scalar	s	T
sidereal rotation period		The time that the object takes to complete a full rotation around its axis relative to the background stars.	pseudoscalar	s	T
synodic period	Tsyn	The amount of time that it takes for an object to reappear at the same point in relation to two or more other objects.	scalar	s	T
synodic rotation period		The period for a celestial object to rotate once in relation to the star it is orbiting.	pseudoscalar	s	T
tropical period		The interval between two alignments of its rotational axis with the Sun, also viewed as two passages of the object at a right ascension of 0 hr.	scalar	s	T
rotation period	T	The time that the object takes to complete a full rotation about its axis.	scalar	s	T
specific weight	γ (scalar) γ (vector)	Density times gravitational field strength (scalar) or weight per unit volume (vector).	scalar or vector	N m-3	M L-2 T-2
weight	W (vector) W (scalar)	Force due to the gravitational attraction (vector) or its magnitude (scalar). Usually used for objects with negligible effect on gravitational field. See also gravitational force.	vector or scalar	N	M L T-2

Atomic, nuclear and particle physics

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
absorbed dose	D	The energy deposited in matter by ionizing radiation per unit mass.	scalar	Gy	L2 T-2
absorbed dose rate	Ḋ	Rate of absorbing ionizing radiation per unit mass.	scalar	Gy s-1	L2 T-3
activity	A	The number of radioactive transformations per second that occur in a particular radionuclide.	scalar	Bq	T-1
chemical energy	Ec	Energy stored in chemical bonds.	scalar	J	M L2 T-2
chromodynamic energy		Energy binding quarks in a hadron.	scalar	J	M L2 T-2
decay constant	λ	Reciprocal of mean lifetime.	scalar	s-1	T-1
energy	E	The quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.	scalar	J	M L2 T-2
half-life	t½	Time taken for half of the radioactive particles to decay.	scalar	s	T
kerma	K	Kinetic energy released per unit mass.	scalar	Gy	L2 T-2
mean lifetime	τ	Average lifetime of a radioactive particle.	scalar	s	T
nuclear binding energy	En	Energy required to separate particles in a nucleus.	scalar	J	M L2 T-2
nuclear force	Fn	Force due to strong interaction.	usually scalar	N	M L T-2
rest energy		Energy due to the object's rest mass.	scalar	J	M L2 T-2
specific activity	a	Activity of a radioactive substance per unit mass.	scalar	Bq kg-1	M-1 T-1

Chemistry

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
activation energy	Ea	Energy needed for a reaction to occur.	scalar	J	M L2 T-2
chemical energy	Ec	Energy stored in chemical bonds.	scalar	J	M L2 T-2
energy	E	The quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.	scalar	J	M L2 T-2
enthalpy	H	Sum of its internal energy and the product of its pressure and volume.	scalar	J	M L2 T-2
enthalpy of reaction	ΔHreaction	Change of enthalpy during a reaction.	scalar	J	M L2 T-2
incipient lethal level	LC50	Lethal concentration of a substance, independent of time.	scalar	kg m-3	M L-3
internal energy	U	Energy inside a system.	scalar	J	M L2 T-2
ionization energy (per electron)	IE	Energy needed to remove an electron from an atom, ion or molecule.	scalar	J	M L2 T-2
lowest lethal concentration	LCLo	The lowest concentration of a chemical, given over a period of time, that results in the fatality of an individual animal. LCLo is typically for an acute (<24 hour) exposure.	scalar	kg m-3	M L-3
median lethal concentration	LCt50	A measure of how toxic a substance is when inhaled or spilled on body tissue.	scalar	kg s m-3	M L-3 T
standard enthalpy of reaction	$\Delta H_{\text{reaction}}^{\ominus }$	The difference between total product and total reactant molar enthalpies, calculated for substances in their standard states.	scalar	J	M L2 T-2
vapor concentration (by mass)	C*	Concentration of vapor of a substance in the air.	scalar	kg m-3	M L-3
vapor pressure		The pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.	scalar	Pa	M L-1 T-2
work	W	Energy transferred to an object or from it.	scalar	J	M L2 T-2

Biology, medicine & sports

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
ambient dose equivalent	H*(d)		scalar	Sv	L2 T-2
acceleration density		Acceleration load per unit time.	scalar	m s-3	L T-3
acceleration density index		Acceleration load per distance moved.	scalar	s-3	T-3
acceleration load		Magnitude of acceleration during activity.	scalar	m s-2	L T-2
directional dose equivalent	H' (d, Ω)		scalar	Sv	L2 T-2
effective dose	E	The tissue-weighted sum of the equivalent doses in all specified tissues and organs of the human body and represents the stochastic health risk to the whole body, which is the probability of cancer induction and genetic effects, of low levels of ionizing radiation.	scalar	Sv	L2 T-2
energy	E	The quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.	scalar	J	M L2 T-2
energy density	we	Energy per unit volume (of food).	scalar	J m-3	M L-1 T-2
equivalent dose	H	It is derived from the physical quantity absorbed dose, but also takes into account the biological effectiveness of the radiation, which is dependent on the radiation type and energy.	scalar	Sv	L2 T-2
heating value / calorific value (per amount)		Energy released per mole.	scalar	J mol-1	M L2 T-2 N-1
heating value / calorific value (per mass)		Energy released per unit mass.	scalar	J kg-1	M2 T2
heating value / calorific value (per volume)		Energy released per unit volume.	scalar	J m-3	M L-1 T-2
infective dosage	ICt50	The number of infective doses per minute for a cubic meter.	scalar	s m-3	L-3 T
organ absorbed dose	DT	The energy deposited in matter by ionizing radiation per unit mass of an organ.	scalar	Gy	L2 T-2
organ equivalent dose	HT	Equivalent dose received by an organ.	scalar	Sv	L2 T-2
personal dose equivalent	Hp		scalar	Sv	L2 T-2
specific energy	e	Energy per unit mass of food.	scalar	J kg-1	L2 T-2
specific power	PWR	Power delivered by unit mass.	scalar	W kg-1	L2 T-3

Energy production and consumption

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
chemical energy	Ec	Energy stored in a fuel, released when burned.	scalar	J	M L2 T-2
emissions per energy produced		Mass of emissions per unit of energy produced from fuel.	scalar	kg J-1	L-2 T2
energy	E	The quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.	scalar	J	M L2 T-2
energy density	we	Energy per unit volume (of a fuel).	scalar	J m-3	M L-1 T-2
energy efficiency (per fuel volume)		Reciprocal of fuel efficiency.	scalar	m m-3	L-2
fuel consumption (per fuel mass)		Mass of fuel consumed per time unit.	scalar	kg s-1	M T-1
fuel consumption (per fuel volume)		Volume of fuel consumed per time unit.	scalar	m3 s-1	L3 T-1
fuel efficiency / fuel economy (per fuel mass)		Measure of the fuel used to traverse a set distance.	scalar	kg m-1	M L-1
fuel efficiency / fuel economy (per fuel volume)		Measure of the fuel used to traverse a set distance. (usually in L/100 km)	scalar	m3 m-1	L2
heating value / calorific value (per amount)		Energy released per mole.	scalar	J mol-1	M L2 T-2 N-1
heating value / calorific value (per mass)		Energy released per unit mass.	scalar	J kg-1	M2 T2
heating value / calorific value (per volume)		Energy released per unit volume.	scalar	J m-3	M L-1 T-2
power density	Pd	Power per unit volume.	scalar	W m-3	M L-1 T-3
ramping rate		Rate of power production during powering up and down of power stations.	scalar	W s-1	M L2 T-4
specific energy	e	Energy per unit mass of a fuel.	scalar	J kg-1	L2 T-2
specific enthalpy	h	Enthalpy per unit mass	scalar	J kg-1	L2 T-2
specific power	PWR	Power delivered by unit mass.	scalar	W kg-1	L2 T-3
surface energy density		Energy per unit area.	scalar	J m-2	M T-2
surface power density	Pd	Power per unit area.	scalar	W m-2	M T-3

Geography

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
Coriolis frequency	f	Frequency of inertial oscillation resulting from Coriolis effect.	scalar	Hz	T-1
Gauckler–Manning coefficient	n	A coefficient in Manning formula.	scalar	s m-⅓	L-⅓ T
volumetric flow acceleration	V̈	Acceleration of volumetric flow rate.	scalar	m3 s-2	L3 T-2
volumetric flow rate / discharge	Q	Rate of flow in regard to volume.	scalar	m3 s-1	L3 T-1

Transportation

Quantity	Symbol	Description	Vector/scalar	SI unit	Dimension
emissions per payload-distance		Mass of emissions per movement of freight.	scalar	kg kg-1 m-1	L-1
energy efficiency (per fuel volume)		Reciprocal of fuel efficiency.	scalar	m m-3	L-2
energy per freight moved		Energy consumed for freight movement for a unit distance.	scalar	J kg-1 m-1	L T-2
fuel efficiency / fuel economy (per unit mass)		Measure of the fuel used to traverse a set distance.	scalar	kg m-1	M L-1
fuel efficiency / fuel economy (per fuel volume)		Measure of the fuel used to traverse a set distance. (usually in L/100 km)	scalar	m3 m-1	L2
payload-distance		Mass of freight moved by a set distance.	scalar	kg m	M L