Ohm’s Law & Power

V = I × R and P = V × I. Any two of voltage, current, resistance and power fix the other two: for example P and R give I = √(P ÷ R) and V = I × R. This holds exactly for DC and for a purely resistive AC load (heaters, incandescent lamps), where the RMS values behave like DC values.

For an AC load the apparent power S (VA) is V × I for single-phase and √3 × V × I for a balanced three-phase load with line-to-line voltage and line current. Real power P (W) is S × power factor; reactive power Q (var) is √(S² − P²); the phase angle is arccos(PF). Given the voltage, the power factor and any one of current, real power or apparent power, the rest follows — so “amps to watts”, “watts to amps” and “kVA to amps” are the same calculation with a different known, which is why they share this page. The power factor is the load's, from its nameplate or a measurement; it is not assumed.

Power is shown in watts, kilowatts, mechanical horsepower (550 ft·lbf/s = 745.6999 W), metric horsepower (735.4988 W) and Btu/h (1 Btu_IT/h = 0.2930711 W), using the exact factors in NIST Special Publication 811, Appendix B.8. These are unit conversions of the same power. A motor's rated horsepower is shaft output; its electrical input is larger by its efficiency, and its current is on the nameplate — neither is derived here.

Conductor size, protection and the current a circuit may carry are set by the code that applies to you; this page gives the load's figures, not the installation's. Unbalanced three-phase loads need each phase worked separately. Inputs stay in your browser; the same four anonymous usage counts as the rest of the site apply.