Quasi-static to dynamic compression behavior of Kota sandstone is investigated herein under low (0.00001–0.1/s) and medium (1/s) strain rates in order to characterize the rate-dependent stress–strain response of the sandstone found in the region of Kota in India. Both quasi-static and dynamic tests are performed in a universal testing machine. From the stress–strain response of Kota sandstone, the effect of strain rate on peak stress, failure strain and modulus of elasticity have been studied. It is observed that with the increase in strain rate, the peak stress of sandstone increases. The failure strain and the modulus of elasticity also increase with increase in strain rate. Conversely, peak stress decreases for the tests which are carried out at a rate slower than usual static test. The strength increase factor of Kota sandstone, namely the dynamic increase factor (DIF) has been calculated. Based on the results obtained from the tests conducted on the sandstone, an empirical equation has been developed for correlating the DIF with the applied strain rates. Further, effect of rock sample diameter and aspect ratio on strain rate dependent strength of rock has been studied. Correction equations have been developed for taking into account the effect of sample sizes as per the ASTM D7012-13 on the peak stress in Kota sandstone.