Commercial thermogravimetric analyzers (TGA) can precisely measure the evaporation of liquids from an open pot. Analysis of this data to determine vapour pressure has often been based on the Langmuir equation for evaporation in a vacuum. These methods are flawed, since they cannot account correctly for the effects of ambient air. We formulate an improved model for evaporation in a TGA, based on the Stefan tube. It incorporates these effects explicitly. We demonstrate its validity by determining accurate vapour pressures for pure liquids, without using a reference sample. Calculated values typically agree with literature data to within a few per cent, over a range of vapour pressures from 60 Pa to 30 kPa. A weakness of thermogravimetric determination of vapour pressure has been that its accuracy depends on the end correction. Our data analysis avoids this problem. Also, the air flow rate and the end effect are shown to act separately on evaporation. Accurate results depend on correctly accounting for both. Finally, a simple heat balance is used to account for the effect of evaporative cooling. (C) 2014 Elsevier B.V. All rights reserved.