We experimentally demonstrate an original method to measure very accurately the density of a frozen Rydberg gas. It is based on the use of adiabatic transitions induced by the long-range dipole-dipole interaction in pairs of nearest neighbor Rydberg atoms by sweeping an electric field with time. The efficiency of this two-body process is experimentally tunable, depends strongly on the density of the gas and can be accurately calculated. The analysis of this efficiency leads to an accurate determination of the Rydberg gas density, and to a calibration of the Rydberg detection. Our method does not require any prior knowledge or estimation of the volume occupied by the Rydberg gas, or of the efficiency of the detection.
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