Here we present an analysis of the force-transmission error for a commercial gravimetric sorption analyzer that applies equally to single-sinker densimeters. Gravimetric sorption analyzers are commonly used for the investigation of gas adsorption on porous materials (e.g., zeolites) with a simultaneous density measurement of the sample gas. The key component of the instrument is a magnetic-suspension coupling; this coupling transmits, without contact, the weight of the “density sinker” and of the sample container with the porous sample (which are both inside a pressurized measuring cell) to a balance at ambient pressure. However, since neither the coupling housing nor the sample gas are magnetically neutral, a small, systematic force-transmission error (FTE) occurs. For the correction of this FTE, an empirical correction model was developed. We show that the FTE can be subdivided into two parts: an apparatus contribution, and a fluid contribution. In the current paper we describe the effect of the FTE on the accuracy of the density measurements; the effect of the FTE on the accuracy of sorption measurements on porous and non-porous materials will be presented in a companion paper. The magnitude of the FTE in case of density measurement is shown by comparing the results of density measurements of four pure gases with values calculated from reference equations of state. The apparatus contribution of the FTE is typically (0.23 kg m−3 + 50 × 10−6·ρfluid), and the fluid contribution can reach values up to 500 × 10−6·ρfluid for diamagnetic fluids; for oxygen-containing gas mixtures it can be much greater.