Recent estimates of the properties of the Crab nebula are used to derive constraints on the moment of inertia, mass and radius of the pulsar. To this purpose, we employ an approximate formula combining these three parameters. Our "empirical formula" I = a(x)MR^2, where x = (M/M_sun)(km/R), is based on numerical results obtained for thirty theoretical equations of state of dense matter. The functions a(x) for neutron stars and strange stars are qualitatively different. For neutron stars a_NS(x) = x/(0.1+2x) for x 0.2 M_sun) and a_NS(x) = (2/9)(1+5x) for x > 0.1. For strange stars a_SS(x) = (2/5)(1+x) (not valid for strange stars with crust and M 1.4 M_sun and R_Crab = 10-14 km. Setting the most recent evaluation ("central value") M_neb = 4.6 M_sun rules out most of the existing equations of state, leaving only the stiffest ones: M_Crab > 2 M_sun, R_Crab = 14-15 km
