Physical parameters of contact binaries are studied through 3-D correlations among them. Using the standard methods, the determination of mass, radius and luminosity requires both photometric and spectroscopic observations. Secondary quantities (e.g. orbital inclination, filling factor, radial velocities, the shape and the depth of the light curve during the eclipses, and the third light) are necessary for an accurate analysis, since their uncertainties strongly influence the determination of the physical parameters. In this study it is shown that orbital period and mass ratio are sufficient to determine the mass, radius and luminosity of contact binaries, taking advantage of the strong correlation between the geometric and physical parameters in the 3-D domain. These correlations are used to derive empirical laws, connecting orbital period and mass ratio of contact binaries with the masses, radii and luminosities of the two components within a 5% error. These laws can also be used as a quality check for the parameters in every given solution of a contact binary, as all their values should always lie on the same 3-D surface. The extracted empirical laws are a prefect tool for a quick estimate of physical parameters for the numerous contact binaries found in global sky surveys.