Capacitance and transconductance are critical parameters determining the limiting operating frequency of a vacuum field effect transistor. We calculate the capacitance and the electric field of a vacuum field effect device using the charge density method. The cathode is modeled as a cone of half angle alpha with a rounded tip (a section of a sphere) of radius R, and the gate is represented by a thin circular disk of radius R2 with a concentric circular hole of radius R1, and placed a distance d above the tip. It is found that (1) The capacitance C is 0.2 fF for R=0.05 mum, R1 = 1 mum, R2=3 mum, d=0, and alpha=15-degrees. (2) For fixed R1, C increases linearly with DELTAR=R2 - R1. (3) For fixed DELTAR and d, C increases with increasing R1. (4) For fixed R1, and R2, C decreases with increasing d. (5) A significant field drop occurs close to the tip, as is expected. This strongly localized gradient focuses a majority of the electrons initially in the direction perpendicular to the plane of the gate.