This paper proposes two fast calculation methods of ATC. These two methods evaluate ATC with thermal constraints(Thermal ATC) and ATC with voltage stability constraints(Voltage ATC) respectively. The ATC with thermal constraints was based on the linear incremental power flow to account for the line flow thermal loading effects when the n-1 security constraints were included. The ATC with voltage stability constraints used two-bus equivalents of the system to find the maximum load at a load bus before reaching the voltage stability problem. The methods were tested on the IEEE 30bus systems and the results obtained were compared with those found by some other methods.