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We establish that two-dimensional dipolar quantum gases admit a universaldescription, i.e., their thermodynamic properties are independent of details ofthe interaction at short distances. The only relevant parameters are the dipolelength as well as the scattering length of the combined short-range plusdipolar interaction potential. We derive adiabatic relations that link thechange in the thermodynamic potentials with respect to the scattering lengthand the dipole length to a generalized Tan contact parameter and a new dipolarcontact, which involves an integral of a short-distance regularized pairdistribution function. These two quantities determine the scale anomaly in thedifference between pressure and energy density and also the internal energy inthe presence of a harmonic confinement. For a weak transverse confinement,configurations with attractive interactions appear, which lead to adensity-wave instability beyond a critical strength of the dipolar interaction.We show that this instability essentially coincides with the onset of a rotonminimum in the excitation spectrum and may be understood in terms of a quantumanalog of the Hansen-Verlet criterion for freezing of a classical fluid.

Universal relations for dipolar quantum gases