Power Converter
Convert watts, kilowatts, BTU per hour and all four horsepowers — mechanical, metric, electrical and boiler — with the 1.39 per cent gap between hp and PS made explicit rather than glossed over.
Power Converter
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What this result does not account for
- Horsepower ratings on real machinery depend on the test standard used — SAE gross, SAE net, DIN and ECE all measure differently.
- Motor nameplate horsepower is mechanical output, not electrical input; efficiency and power factor are not modelled.
- Boiler horsepower measures evaporative capacity and is not comparable with engine horsepower despite sharing the name.
- The BTU and calorie both have several competing definitions; this engine uses International Table and thermochemical respectively.
In short: Power conversion routes through the watt, one joule per second. The trap is horsepower: there are four incompatible definitions. Mechanical hp is 550 ft·lbf/s = 745.69987 W; metric hp (PS) is 75 kgf·m/s = 735.49875 W; electrical hp is exactly 746 W; and boiler hp is 9,809.5 W, thirteen times larger and measuring a different quantity entirely. Mechanical and metric differ by 1.387%.
Formula
Each factor is the number of watts in one of that unit. The watt is one joule per second. Because the foot, the pound and standard gravity are all exactly defined, both mechanical and metric horsepower are exact values rather than measured approximations — they are simply exact values that disagree with each other.
Worked Example
- Identify which horsepower. Mechanical is 745.69987 W; metric (PS) is 735.49875 W. Getting this wrong is a 1.39% error.
- Convert to watts. 1 hp × 745.69987 = 745.69987 W.
- Identify the target factor. One kilowatt is 1,000 W.
- Divide. 745.69987 ÷ 1,000 = 0.74569987 kW.
- Sense-check. 200 hp is 149.14 kW, while 200 PS is only 147.10 kW.
Why James Watt chose 550. Watt needed a unit that would let mine owners compare his steam engines against the pit ponies they replaced, and settled on 33,000 foot-pounds per minute — 550 per second. Converting that definition into SI gives 745.69987158227 W exactly, because the foot, the pound and standard gravity all have exact metric definitions. The metric world independently defined its own horse as lifting 75 kg one metre per second, and the two have disagreed by 1.4% ever since.
Strengths & Limits Of This Model
Where this engine is strong
- Carries all four horsepowers and reports them simultaneously.
- States the 1.387 per cent mechanical-versus-metric gap explicitly.
- Flags boiler horsepower as a different physical quantity.
- Names which BTU and which calorie definition is in use.
Where it stops
- Cannot tell you which horsepower a given specification sheet intended.
- Does not model engine test standards, which vary the rated figure independently of the unit.
Practical Use Cases
Reading vehicle specifications across markets
European registration documents quote kilowatts, German press releases quote PS, and American ones quote mechanical hp. A car advertised at 150 PS is 147.9 mechanical hp and 110.3 kW — the same engine, three numbers.
Sizing electric motors
US motor nameplates use electrical horsepower, defined as exactly 746 W. Note that this rates mechanical OUTPUT: the electrical input drawn from the supply is higher, by the motor's efficiency and power factor.
HVAC and refrigeration
Cooling capacity is quoted in BTU per hour or in tons of refrigeration, where one ton is 12,000 BTU/h or 3,516.85 W — originally the rate of cooling from melting a short ton of ice in a day.
Steam plant and boilers
Boiler horsepower rates evaporative capacity at 9,809.5 W and must never be confused with engine horsepower — see the Energy Converter for the energy rather than the rate.
Methodology & Editorial Standards
All conversions route through the watt, defined as one joule per second. Mechanical horsepower is exactly 550 foot-pounds-force per second; since the foot is exactly 0.3048 m, the pound exactly 0.45359237 kg and standard gravity exactly 9.80665 m/s², that resolves to exactly 745.6998715822702 W. Metric horsepower is exactly 75 kilogram-force metres per second, or 735.49875 W. Electrical horsepower is defined as exactly 746 W by convention in US motor standards. Boiler horsepower, 9,809.5 W, measures the heat rate to evaporate 34.5 pounds of water per hour at 212 °F and is a different physical quantity from the others. The BTU used is the International Table BTU of 1055.05585262 J, and the calorie is the thermochemical calorie of exactly 4.184 J; both have several competing definitions and the choice is stated rather than assumed. The engine reports every horsepower reading simultaneously so a specification can be checked against all four. All conversion factors are exact by definition under the International System of Units, or exact by international agreement where the unit is defined by treaty. Values are held at full IEEE-754 double precision internally and rounded only for display, so chained conversions do not accumulate drift.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Power Converter — 10 Expert FAQs
10 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How many watts is one horsepower?
It depends which horsepower. Mechanical or imperial horsepower, the usual meaning in Britain and America for engines, is exactly 745.6998715822702 W. Metric horsepower, written PS, CV, pk or ch, is exactly 735.49875 W. Electrical horsepower is defined as exactly 746 W. Boiler horsepower is 9,809.5 W and measures something else entirely.
What is the difference between hp and PS?
Mechanical horsepower is defined as 550 foot-pounds-force per second; metric horsepower as 75 kilogram-force metres per second. The metric version is about 1.387 per cent smaller. That is why the same car is quoted as 150 PS in Germany and roughly 148 hp in Britain — the engine has not changed, only the unit.
Is one horsepower 746 watts?
That is the electrical horsepower, defined as exactly 746 W for rating US electric motors. Mechanical horsepower is 745.69987 W, so 746 is a convenient rounding that happens also to be a definition in its own right in electrical contexts. The difference is about four parts in ten thousand and rarely matters outside precision work.
What is boiler horsepower?
A measure of a steam boiler's evaporative capacity, standardised by ASME in 1884 as the heat required to evaporate 34.5 pounds of water per hour at 212 °F. It equals 9,809.5 W, more than thirteen times mechanical horsepower. It is not interchangeable with engine horsepower and appears only on steam-raising plant.
Why does my 1 hp motor draw more than 746 watts?
Because horsepower rates mechanical output while the wall socket supplies electrical input, and no motor is perfectly efficient. A nominal 1 hp motor typically draws somewhere between 900 and 1,200 W depending on its efficiency and power factor. The difference is dissipated as heat.
What is a ton of refrigeration?
12,000 BTU per hour, or 3,516.85 W. It derives from the rate of cooling produced by melting one short ton of ice over twenty-four hours, dating from when mechanical refrigeration was sold against ice delivery. It remains the standard capacity unit for commercial air conditioning in North America.
How do I convert kilowatts to horsepower?
Divide by 0.745699872 for mechanical horsepower, or by 0.73549875 for metric. So 150 kW is 201.15 mechanical hp or 203.94 PS. European vehicle documents quote kW precisely to sidestep the horsepower ambiguity, which is why the conversion comes up so often when reading a registration document.
Which BTU definition does this use?
The International Table BTU of exactly 1055.05585262 J. Several competing BTU definitions exist — thermochemical, 39 °F, 59 °F, mean — differing by up to about a quarter of a per cent. The IT BTU is the one used in HVAC and most engineering practice.
What is the difference between power and energy?
Power is the rate of energy transfer; energy is the quantity transferred. A watt is one joule per second, so power multiplied by time gives energy. A 2 kW heater running for three hours consumes 6 kWh of energy. Confusing the two is the reason electricity bills are quoted in kilowatt-hours, a unit of energy, not kilowatts.
Are these horsepower figures exact?
Yes, all of them, which is the counterintuitive part. Because the foot, the pound and standard gravity are all exactly defined, mechanical horsepower is exactly 745.6998715822702 W and metric horsepower exactly 735.49875 W. They are two exact numbers that disagree, rather than two approximations of one true value.