Recent experimental results on a carefully cleaned carbon nanotube show that the slope of its Fowler-Nordheim (FN) plot is not constant but increases slightly in magnitude as the anode-cathode voltage V-a is reduced. Theory for emission from a spherical surface shows that this curvature of slope increases with the curvature of the emitting surface. By detailed calculation using the change of FN slope, it is possible to deduce the radius of curvature of the emitting region, surface field, effective solid angle of emission, and an electron supply factor, all more accurately than is feasible using planar theory. (c) 2006 American Vacuum Society.