Ab initio values of the absolute shielding constants of phosphorus and hydrogen in PH3 were determined, and their accuracy is discussed. In particular, we analyzed the relativistic corrections to nuclear magnetic resonance (NMR) shielding constants, comparing the constants computed using the four-component Dirac-Hartree-Fock approach, the four-component density functional theory (DFT), and the Breit-Pauli perturbation theory (BPPT) with nonrelativistic Hartree-Fock or DFT reference functions. For the equilibrium geometry, we obtained sigma(P) = 624.309 ppm and sigma(H) = 29.761 ppm. Resonance frequencies of both nuclei were measured in gas-phase NMR experiments, and the results were extrapolated to zero density to provide the frequency ratio for an isolated PH3 molecule. This ratio, together with the computed shielding constants, was used to determine a new value of the nuclear magnetic dipole moment of P-31: mu(P) = 1.1309246(50) mu(N).