The characteristic equation of hot-cathode ionization gauge is derived from the theory of Townsend discharge, with the form i+/ie=1-e(-(k1p-k2p2)) where i+ is the ion current, ie the electron current, p the gauge pressure, and both k1 and k2 are constants. Only at i+?ie, the equation shown above becomes i+/ie=Гp where Г is the sensitivity of gauge and approximately equals k1. The critical pressure, at which linearity between i+ and p breaks down, is Pc=0.22/Г while the permissible error of gauge calibrated is 1%. Plenty of experimental results shown by Nottingham, Schultz, Goto, Hinz-peter etc. can be easily explained. Data taken from a specially designed "drum" gauge give good coincidence with theoretical results. The "drum" gauge itself can be used for a wide range to measure pressures from 10-7 to 0.6 Torr.