Power Conversion Calculator — W, kW, hp and Btu/h

Background.

How many horsepower is 150 kW? That depends on which horsepower you mean. In mechanical horsepower, the unit of American engine and motor ratings, it is 201.1533 hp. In metric horsepower, the PS of German and Japanese specifications and the ch or CV of French and Italian ones, it is 203.9432 PS. Both answers are right: they are different units that share a name and differ by about 1.4%.

Power conversion is full of pairs like that. There are two kilocalories in common use, the thermochemical one of 4,184 J and the International Table one of 4,186.8 J. Air-conditioning output is quoted in Btu per hour, motors in horsepower, generators in kilowatts and power stations in megawatts. Each is a rate, energy per unit of time, and each traces back to the watt, the SI unit equal to one joule per second. The converter takes a figure in any of eight units, turns it into watts, and reports it in all eight together, so the answer you asked for sits beside the watt value it came from.

Every factor is fixed by definition rather than measured. Mechanical horsepower is 550 foot-pound-force per second, which the exact international foot and pound and standard gravity make 745.69987158227022 W. Metric horsepower is 75 kilogram-force metres per second, exactly 735.49875 W. A Btu per hour and a kilocalorie per hour are their energy units spread over the 3,600 seconds of an hour.

A conversion changes the unit, never the physics. Expressing a motor's horsepower in kilowatts does not tell you what it draws from the supply, because some energy is lost as heat, and expressing an air conditioner's Btu/h in watts gives its cooling output, not its electricity use. Nor is a kilowatt a kilowatt-hour: one is a rate, the other the energy that rate delivers over time.

What is power conversion calculator?

Power measures how fast energy moves: a 2 kW heater turns electrical energy into heat twice as fast as a 1 kW heater. Its SI unit, the watt, is one joule per second, and the kilowatt and megawatt are a thousand and a million watts.

The other units each pair an energy unit with a time. Mechanical horsepower (hp) is 550 foot-pound-force per second, the customary engine and motor rating in the United States and Britain. Metric horsepower (PS) is 75 kilogram-force metres per second, used for vehicles in much of continental Europe and in Japan. The Btu per hour uses the International Table British thermal unit of 1,055.05585262 J and dominates US heating and air-conditioning ratings. The kilocalorie per hour here is the thermochemical kilocalorie of exactly 4,184 J per hour. The foot-pound-force per second is the customary unit of mechanical power from which horsepower is built. Labels such as brake horsepower (bhp) and wheel horsepower describe where an engine's output was measured, at the crankshaft or at the driven wheels, rather than a different size of unit; both are counted in mechanical horsepower.

None of these is energy. Energy is power multiplied by time: a kilowatt-hour is 1 kW sustained for an hour, or 3.6 MJ. A power figure therefore says how fast something works, and only a duration turns it into how much work was done.

How to use this calculator.

1. 01Enter the figure in Power. Negative values are accepted when you are tracking direction, for example power exported to the grid as negative and power drawn from it as positive; the sign carries through unchanged. Values up to a trillion in either direction are allowed.
2. 02Choose the unit the figure is in under 'From unit'. Check which horsepower your source means: a European car document in PS or ch, a US engine or motor rating in hp. For kcal/h, note that the option is the thermochemical kilocalorie.
3. 03Choose the unit you want under 'To unit'. The answer appears as the converted power, and the same power is listed below in all eight units.
4. 04Use the watts line as the anchor, since every other figure is that number divided by the size of the unit. A result that looks wrong by a factor of about 1,000 usually means a kilowatt figure was entered as watts, or the reverse.
5. 05Apply efficiency, coefficient of performance or duty cycle yourself afterwards; the conversion assumes the same power on both sides.

The formula.

target = value × (watts per source unit) ÷ (watts per target unit). Every conversion goes through watts in one step, so converting PS to Btu/h uses the same two factors as any other pair, and all eight outputs are divisions of a single watt value.

The factors are definitions. Since 1959 the international foot has been exactly 0.3048 m and the pound exactly 0.45359237 kg, and standard gravity, which turns a pound of mass into a pound of force, is exactly 9.80665 m/s². One foot-pound-force is therefore 0.3048 × 0.45359237 × 9.80665 = 1.3558179483314004 J exactly, and 1 hp = 550 ft·lbf/s = 745.69987158227022 W. Metric horsepower uses the kilogram-force instead: 75 × 9.80665 = 735.49875 W exactly. The gap between the two horsepowers is easiest to see in the same terms: 550 ft·lbf/s is 550 × 0.3048 × 0.45359237 = 76.0402 kilogram-force metres per second, against 75 for the metric unit, so one mechanical horsepower is 1.0139 PS, about 1.39% more.

The heat-rate units divide an energy unit by 3,600 seconds. 1 Btu/h = 1,055.05585262 J ÷ 3,600 s ≈ 0.2930711 W, so one watt is 3.4121 Btu/h and one horsepower is 2,544.4336 Btu/h. 1 kcal/h = 4,184 J ÷ 3,600 s ≈ 1.1622 W, so one kilowatt is 860.4207 kcal/h. Kilo and mega are the SI prefixes for 10³ and 10⁶. Every factor is positive, so a negative input stays negative on every line and only its size changes.

Because every factor is exact, a small disagreement with another converter almost always traces to a different definition on the other side: horsepower taken as a round 746 W, the International Table kilocalorie in place of the thermochemical one, or one of the other Btu definitions.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST SP 811 Appendix B.9 supplies power factors for horsepower, Btu/h, kcal/h and foot-pound-force per second.
2. [2]BIPM SI Brochure defines watt as joule per second and the SI prefix system.
3. [3]NIST SP 330 independently lists watt in the SI derived-unit table.
4. [4]NIST SP 811 Appendix B.8 supplies the energy factors used to independently derive heat-rate units.
5. [5]NIST Handbook 44 Appendix C supplies a customary/SI legal-metrology cross-check.