We report Larmor precession in bulk InSb observed in the time domain from 77 to 300 K. The optically oriented polarization precesses coherently even at 300 K. The inferred Zeeman spin splitting is strongly nonparabolic, and the electron g factor (g^*) is in good agreement with k·p theory (provided we take only the dilational contribution to the change in energy gap with temperature). We also show here that correct application of the 14-band k·p model agrees with apparently anomalous trends previously reported for GaAs and confirm that the most widely quoted formula for g^* in GaAs is incomplete.