In this paper, we report about a fast and straightforward method for estimating vapour pressures of pure liquids from mass loss rates measured with a magnetic suspension balance (MSB). For a measurement, the sample is placed in an open cylinder, attached to the MSB. Nitrogen flows vertically downwards along the sample cylinder to purge all vapour out of the measuring cell of the balance. To determine the total mass transfer of the liquid into the gas phase, the transport process is divided into an internal and an external part. The internal mass transfer takes place inside the sample cylinder and is only based on diffusion while the external mass transfer outside the cylinder consists of diffusion and convection. To describe the external mass transfer, a correlation for the Sherwood number based on numerical data is found. The numerical simulation is validated with experiments using four different alcohols. Furthermore, the influence of the purge gas flow rate and the filling level of the sample cylinder on the evaporation rate are discussed. Lastly, the found equation is tested to calculate vapour pressures of different substances in a range of 100 Pa to 20 kPa. Our results deviate by 10% from literature values. The relative combined expanded uncertainty (P = 95.5%) of the presented method has been calculated to be 12% in the full vapour pressure range considered.