The discovery of the field effect in graphene initiated the development of graphene field effect transistor (FET) sensors, wherein high mobility surface conduction is readily modulated by surface adsorption. For all graphene transistor sensors, low-frequency 1/f noise determines sensor resolution, and the absolute measure of 1/f noise is thus a crucial performance metric for sensor applications. Here we report a simple method for reducing 1/f noise by scaling the active area of graphene FET sensors. We measured 1/f noise in graphene FETs with size 5 μm × 5 μm to 5.12 mm × 5.12 mm, observing more than five orders of magnitude reduction in 1/f noise. We report the lowest normalized graphene 1/f noise parameter observed to date, 5 × 10-13, and we demonstrate a sulfate ion sensor with a record resolution of 1.2 × 10-3 log molar concentration units. Our work highlights the importance of area scaling in graphene FET sensor design, wherein increased channel area improves sensor resolution.