Power Converter

About the Power Converter

Convert power between watts (mW, W, kW, MW, GW), the four horsepowers — mechanical (hp, bhp), metric (PS, CV), electric (hp(E)) and boiler — Btu per hour, tons of refrigeration (TR, the “ton” of an air conditioner), kcal per hour, foot-pounds per second, kgf·m/s and erg/s. Type in either box and the other updates; the table underneath shows the value in every unit, and the arithmetic uses exact fractions: 1 hp is exactly 745.69987158227022 W and 1 PS exactly 735.49875 W.

Under the result you see the energy that power adds up to in an hour, and Energy used over time works it out for any running time. The page also keeps apart three things that share these units: what a motor delivers at its shaft, what it draws from the supply, and the cooling capacity of an air conditioner.

Common uses

• Car, motorcycle and boat engines in hp, bhp, PS, CV and kW.
• Pumps, motors and generators in hp, kW and electric horsepower.
• Air conditioners, heat pumps, heaters and boilers in tons, Btu/h, kcal/h and kW.
• Power plants and grids in MW and GW; small electronics in mW.
• Physics homework with ft·lbf/s, kgf·m/s and erg/s.

Output, input and cooling capacity

The same units describe three different things, so check which one a rating is before you compare it:

• Shaft output. The hp or kW on a motor, pump or engine is the mechanical power it delivers. It draws more than that from the supply, because no motor is perfectly efficient: input = output ÷ efficiency, so a 1 kW motor that is 85 % efficient draws about 1.18 kW. Many motor nameplates give the efficiency; HP to kW works out the input for you.
• Electrical input. The watts on a heater, kettle or light are what it draws from the socket. A resistance heater turns all of it into heat, so 1,500 W of electricity gives about 5,118 Btu/h of heat.
• Cooling or heating capacity. The tons, Btu/h, kcal/h or kW of an air conditioner or heat pump are the heat it moves. It draws only a fraction of that as electricity — the capacity divided by its efficiency (EER or COP) — so a 1.5-ton (5.28 kW) air conditioner with an EER of 3.5 W/W draws about 1.5 kW. Use the AC Ton Converter to estimate it from the label.

Volts, amps and kVA are not power units by themselves: for those use the Watts to Amps Calculator and the Three-Phase Power Calculator.

Which horsepower?

• Mechanical (imperial) horsepower, hp = 550 ft·lbf/s = 745.69987158227022 W exactly. bhp (brake horsepower) is the same unit, measured at the crankshaft.
• Metric horsepower, PS (also CV, ch or pk) = 75 kgf·m/s = 735.49875 W exactly, about 1.4 % less than a mechanical horsepower.
• Electric horsepower, hp(E) = exactly 746 W, used for electric motors.
• Boiler horsepower is a rate of raising steam, about 9,809.5 W — roughly 13 times a mechanical horsepower. NIST gives it to six digits, so results with it are marked ≈.

Where the factors come from

• NIST SP 811, Appendix B: electric horsepower = 746 W and erg/s = 10⁻⁷ W (exact); mechanical, metric and boiler horsepower, Btu/h and the ton of refrigeration (12,000 Btu/h).
• The International Table Btu is exactly 1,055.05585262 J and the International Table kilocalorie exactly 4,186.8 J (NIST SP 811 footnotes), so 1 Btu/h ≈ 0.293071 W, 1 TR ≈ 3,516.853 W and 1 kcal/h = 1.163 W.
• The mechanical and metric horsepowers follow from the exact pound (0.45359237 kg), foot (0.3048 m) and standard gravity (9.80665 m/s², 3rd CGPM).

Limitations

• Converting a unit does not change what a rating means: an engine’s hp is its output, an air conditioner’s tons are cooling capacity, and neither is the electricity or fuel it uses.
• kVA, kvar, volts and amps need the voltage and power factor, so they are not converted here.
• Boiler horsepower uses the 6-digit NIST factor; every other unit is exact.
• Results are exact fractions shown to 10 significant digits (marked ≈ when rounded).

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