  We have measured the relative strength $\epsilon_dd$ of the magnetic
dipole-dipole interaction compared to the contact interaction in a chromium
Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of
a dipolar chromium BEC with different orientations of the atomic magnetic
dipole moments. By comparing them with numerical solutions of the hydrodynamic
equations for dipolar condensates, we are able to determine $\epsilon_dd =
0.159\pm0.034$ with high accuracy. Since the absolute strength of the
dipole-dipole interaction is known exactly, the relative strength of the
dipoledipole interaction can be used to determine the s-wave scattering length
$a = 5.08\pm1.06\cdot10^-9 m = 96\pm20 a0$ of 52Cr. This is fully consistent
with our previous measurements on the basis of Feshbach resonances.
