Conventional Fowler-Nordheim theory assumes that the emitter is planar, while most tips used in practice have curved emitting surfaces. Using a revised potential distribution, standard image theory and a dimensionless parameter x, we express the experimental current as a multiple sigma of the current calculated using standard free-electron supply. A plot of sigma(x) for one carbon emitter shows a maximum at a value of x corresponding to the known emitter radius. The calculated field strength at the emitter surface varies little with x. The values found for sigma are sensitive to the accuracy of calculation and, to test the theory further, it is desirable both to improve the modelling of image effects and to obtain measurements of current-voltage characteristics and emitting radii together for more types of emitter. (C) 2003 American Vacuum Society.