We prove a formula expressing the gradient of the phase function of a function f : R-d bar right arrow C as a normalized first frequency momentof the Wigner distribution for fixed time. The formula holds when f is the Fourier transform of a distribution of compact support, or when f belongs to a Sobolev space Hd/2+1+epsilon(R-d) where epsilon > 0. The restriction of the Wigner distribution to fixed time is well defined provided a certain condition on its wave front set is satisfied. Therefore we first need to study the wave front set of the Wigner distribution of a tempered distribution.