The theoretical relations between the orbital period and mean densities of component stars of contact binaries are deduced. It is found that the orbital period of a contact binary is inversely proportional to the square root of the mean densities of component stars with the slopes as functions of mass ratio and fill-out factor of system. A test of 148 well-studied contact binaries with physical parameters determined from comprehensive photometric and spectroscopic solutions shows that the upper limit of secondaries' mean densities depends strongly on the total masses, M 1 + M 2, of the contact systems. For a low-mass contact system with ( M + M 2) = 2 M circle dot, the maximum mean density of the secondary is strictly lower than that of a 5 Gyr star with a mass of (M + M 2)/2. Taking this as the basic constraint, the derived period-density relation was applied to simulate the orbital period distribution of low-mass contact binaries over the total-mass range of 1-2 M circle dot. It reproduces a period cut-off at 0.12-0.16 d, depending on the fill-out factor.