We present a complete analytical treatment of elliptical field emitting structures in a diode geometry which correctly includes image charge effects off axis and the variation of field along the tip. The methodology may be extended to other geometries. The angular distribution of electron emission along the tip, the total emitted current, and the area factor may all be calculated as a function of emitter to anode distance, tip radius, tip height, and the anode‐tip voltage difference. We show not only where errors arise if the planar Fowler–Nordheim (FN) equation is used to govern electron emission, but also how the FN equation may be modified to correctly address the complications due to atomically sharp tips. Finally, we present an analytic form of the area factor and compare it to the exact calculation and the various approximations. ©1995 American Institute of Physics.