Residual strains have been evaluated in a variety of GaN layers grown on sapphire or 6H-SiC from wafer curvature at 293 K, which avoids needing to know the unstrained lattice parameters or energy gap of GaN in advance. Estimated strains at 1.7 K are correlated with the energy of theAfree exciton to determine its strain dependence. We find that strain-free GaN has anAexciton energy of3.468±0.002 eVat 1.7 K, and 293 K lattice parametersa=3.1912 Åandc=5.1836 Å.These values imply that GaN on SiC is frequently under net biaxial compressive stress due to residual lattice mismatch stress, and that several hundred &mgr;m thick GaN layers on sapphire and homoepitaxial layers grown on bulk platelets grown at high pressure are both under about1×10−3in-plane compressive strain. These conclusions conflict with most previous assumptions. ©1997 American Institute of Physics.