AM station powers are generally given as what the FCC calls ``nominal power'', which is something the Commission made up in 47 CFR 73.14, and does not necessarily correspond to antenna input power, transmitter output power, effective radiated power, or any other more commonly measured value. Where two powers are given for full-time stations, the first represents the daytime power, and the second the night; for daytime stations, the first represents daytime power, and the second is pre-sunrise (post-sunset) service authority (PSSA).
Note that power is not the only factor governing the quality of an AM station's signal. Other factors involved include the directionality of the signal, the ground conductivity (a station in a swamp carries farther than a station in the desert), and interference from other co-channel or adjacent-channel stations. For example, WJIB's five-Watt, non-directional night-time signal can be heard quite clearly in Provincetown when there is no interference (i.e., during the daytime), but as soon as night falls in Toronto, co-channel CBL blasts WJIB away for most people more than five miles away from the transmitter.
The maximum power licensed for mediumwave stations in the US and Canada is 50 kW. Mediumwave stations in Mexico are allowed up to 250 kW, and stations in other parts of the world can have up to 2000 kW, which is the practical limit for how large a transmitter can be constructed. The city-grade contour for AM stations is defined by an electrical field strength of 5.0 mV/m groundwave; the canonical ``night pattern'' is defined by the area which receives at least 0.5 mV/m skywave at least 50% of the time.
All stations in the new AM ``expanded band'' (from 1610 to 1700 kHz) are licensed for a standard 10 kW day, 1 kW night, non-directional.