Using synchrotron high-pressure X-ray diffraction at cryogenic temperatures, we have established the phase diagram for calcium up to 110 GPa and 5-300 K. We discovered the long-sought for theoretically predicted β-tin structured calcium with I4(1)/amd symmetry at 35 GPa in a s mall low-temperature range below 10 K, thus resolving the enigma of absence of this lowest enthalpy phase. The stability and relations among various distorted simple-cubic phases in the Ca-III region have also been examined and clarified over a wide range of high pressures and low temperatures.