Four horsepowers, and why they are all different
Power is the rate of doing work, measured in the SI system as watts — one joule per second. Horsepower is a pre-SI unit that survived because James Watt needed a way to sell steam engines to people who owned horses, and it survived in four incompatible versions because different industries fixed it in different unit systems.
Mechanical horsepower is Watt's own: 33,000 foot-pounds per minute, which is 550 ft·lbf/s. Because a foot-pound is 1.3558179483 J, that comes to 745.6999 W. This is what US and UK engine ratings mean, and it is what the abbreviation ‘bhp’ means in automotive writing — brake horsepower, meaning shaft power measured on a brake dynamometer.
Metric horsepower was defined on the continent as 75 kilogram-force metres per second. One kilogram-force is 9.80665 N by definition, so metric horsepower is exactly 735.49875 W. It appears as PS in Germany, CV in France, Italy and Spain, pk in the Netherlands and hk in Scandinavia. Because it is 1.39% smaller, the same engine always carries a larger number in PS than in hp: 745.6999 ÷ 735.49875 = 1.0138697, so 300 hp is 304.2 PS.
Electrical horsepower is exactly 746 W, a rounding adopted so that motor nameplates could carry clean numbers. It is within 0.04% of mechanical horsepower, which is why a ‘5 hp’ motor is universally treated as 3.73 kW.
Boiler horsepower is not a shaft power at all. It is a heat rate of 9,809.5 W, roughly 33,471 BTU/h, derived from the steam a boiler could raise to drive one horsepower through a nineteenth-century engine. Because it is more than thirteen times mechanical horsepower, mixing it with an engine rating is a factor-of-thirteen error, not a rounding error.
Where the numbers come from
Each factor is a definition chain, not a measurement, so you can derive every one of them from scratch.
Mechanical. One pound-force is the international avoirdupois pound, 0.45359237 kg, times standard gravity, 9.80665 m/s², giving 4.4482216152605 N. One foot is 0.3048 m. So one foot-pound is 1.3558179483 J, and 550 of them per second is 745.6998716 W.
Metric. One kilogram-force is 1 kg × 9.80665 m/s² = 9.80665 N. Seventy-five of those acting through one metre per second is 75 × 9.80665 = 735.49875 W, exactly, with no rounding anywhere.
Heat rate. One watt sustained for an hour is 3,600 J, and an International Table BTU is 1,055.05585262 J, so one watt is 3.412141633 BTU/h and one kilowatt is 3,412.14 BTU/h. That single factor lets you put an engine rating, a heater rating and an air-conditioner rating on one axis; the energy side of the same conversion is on our BTU to kWh calculator.
The relationship people most often want is the PS-to-hp ratio, and it is worth memorising rather than looking up: 1 PS = 0.98632 hp and 1 hp = 1.013870 PS. A 500 PS supercar is 493.2 hp; a 500 hp muscle car is 506.9 PS. The gap grows with the number, so at 1,000 PS the two figures differ by nearly 14 units.
Power at the crank also relates directly to torque and speed: power equals torque times angular velocity. In SI, kW = N·m × rpm ÷ 9,549. In imperial, hp = lbf·ft × rpm ÷ 5,252, and 5,252 is simply 33,000 ÷ 2π. The torque half of that relationship converts on our torque unit converter.
Worked example: a 300 hp engine in kW, PS and BTU/h
A US brochure quotes 300 hp. A European dealer quotes the same car as 304 PS and 224 kW. Check whether those agree.
- Into watts. 300 × 745.6998716 = 223,709.96 W.
- Out to kilowatts. 223,709.96 ÷ 1,000 = 223.71 kW. The dealer's 224 kW is the same figure rounded, so it agrees.
- Out to metric horsepower. 223,709.96 ÷ 735.49875 = 304.16 PS. The quoted 304 PS agrees. Equivalently, 300 × 1.0138697 = 304.16.
- As a heat rate. 223,709.96 ÷ 0.29307107 W per BTU/h = 763,331 BTU/h. That is what the engine would dissipate if all of it turned to heat, and it is a useful reminder that a 300 hp engine rejecting a similar amount to coolant and exhaust needs a serious radiator.
- Sanity check the other direction. 224 kW ÷ 0.7456999 = 300.39 hp, and 224 × 1.3596216 = 304.6 PS. Both land within the rounding of the published figures, so the three brochures describe one engine.
The trap here is assuming the difference between 300 and 304 is a measurement difference or a market-specific tune. It is neither. It is the same power written in two units that differ by 1.39%.
Power unit equivalences
| One unit of | Watts | kW | hp (mech) | PS | BTU/h |
|---|---|---|---|---|---|
| hp, mechanical | 745.6998716 | 0.7456999 | 1 | 1.0138697 | 2,544.43 |
| PS, metric hp | 735.49875 | 0.73549875 | 0.9863201 | 1 | 2,509.63 |
| hp, electrical | 746 (exact) | 0.746 | 1.0004025 | 1.0142780 | 2,545.46 |
| kilowatt | 1,000 | 1 | 1.3410221 | 1.3596216 | 3,412.14 |
| watt | 1 | 0.001 | 0.001341022 | 0.001359622 | 3.412142 |
| boiler horsepower | 9,809.5 | 9.8095 | 13.1548 | 13.3372 | 33,471.4 |
| BTU per hour | 0.29307107 | 0.00029307 | 0.000393015 | 0.000398465 | 1 |
The PS, electrical hp and kilowatt values are exact by definition. Mechanical horsepower and the BTU rate are irrational in decimal and shown to the digits given.
“bhp” means two completely different things
In automotive and marine writing, bhp is brake horsepower — shaft power measured at the flywheel on a brake dynamometer, in mechanical horsepower. In boiler and steam engineering, bhp is boiler horsepower, a heat rate of 9,809.5 W. The two differ by a factor of 13.15. If a document mentions steam, evaporation rate or square feet of heating surface, it means boiler horsepower. If it mentions a crankshaft, a dyno or a drivetrain loss, it means brake horsepower. This calculator lists them separately for that reason, and comparing an engine rating against a boiler rating is never meaningful.
Mistakes that make a power comparison wrong
- Treating PS and hp as the same. They differ by 1.39%. On a 400-unit rating that is 5.5 units — enough to make two identical cars look different in a comparison table.
- Using 0.75 kW per hp. The factor is 0.7456999. The shortcut is 0.6% high, which compounds badly when you convert a whole product range.
- Comparing crank power with wheel power. A chassis dyno measures at the wheels and reads lower than a flywheel figure by the drivetrain loss. No unit conversion accounts for that; you need to know which measurement each number is.
- Confusing peak with continuous. Engine ratings are peak values at a stated speed; electric motor nameplates are continuous ratings. Converting the units does not make the two comparable.
- Mixing input and output power on a motor. A motor nameplate hp is shaft output. Electrical input is that divided by efficiency, so a 10 hp motor at 92% efficiency draws 7.457 ÷ 0.92 = 8.11 kW electrically.
- Using boiler horsepower anywhere near an engine. It is a heat rate more than thirteen times larger, and the abbreviation collides with brake horsepower.
Which unit each industry actually uses
Cars and motorcycles. The European Union type-approval figure is kW, and manufacturers publish PS alongside because buyers recognise it. US and UK marketing uses mechanical hp, and SAE J1349 defines the correction factors and accessory conditions that make a US rating repeatable. When comparing two cars, convert both to kW first — it is the only figure that carries no definitional ambiguity. If you are working out what that power does at the strip, the quarter mile ET calculator uses power-to-weight directly, and the volumetric efficiency calculator explains where the airflow to make it comes from.
Electric motors. North American motors are labelled in hp using the 746 W definition; the rest of the world labels in kW. Standard frame sizes therefore differ: a 5 hp motor is 3.73 kW and sits between the standard 3.7 kW and 4 kW metric frames. Nameplate power is mechanical output, so sizing the supply needs the input power — see the motor full load amps calculator and the electrical power calculator for the electrical side.
Boilers and process heat. Boiler horsepower persists in North American packaged-boiler catalogues alongside BTU/h and pounds of steam per hour. One boiler horsepower is 9.8095 kW of heat, 33,471 BTU/h, or 34.5 lb/h of steam from and at 212 °F.
Aviation and marine. Piston aircraft engines are rated in mechanical hp; turboprops in shaft horsepower (shp) or equivalent shaft horsepower (eshp), which adds a credit for residual jet thrust. Marine diesels are usually kW with PS or hp in brackets. In every case the unit is the easy part; what the rating includes — accessories, gearbox, ambient conditions — is where genuine differences hide.
Fitness and physiology. A trained cyclist sustains around 300 W, which is 0.402 hp. A real horse, incidentally, can exceed one horsepower substantially for short periods; Watt's unit was chosen to be a comfortable continuous rate for a working animal, not a peak.
Why two ratings that agree on units can still disagree
A unit conversion is exact, but the number you start with often is not. Two spec sheets for what looks like the same engine can disagree by more than the entire PS/hp gap, and the cause is usually the measurement standard behind the figure rather than any conversion error.
Gross versus net is the biggest single source of confusion. A gross rating is measured on a stand-alone engine with no accessories — no alternator, no water pump, no exhaust back-pressure, no intake restriction. A net rating, the one SAE J1349 defines and the one used on modern vehicle spec sheets, includes all of that. The gap between the two figures on the same physical engine has nothing to do with hp, PS or kW; converting a gross figure to kilowatts and comparing it against a net figure in kilowatts still compares two different things measured two different ways.
Regional test standards add a second layer. DIN 70020 in Germany and JIS D1001 in Japan correct for different reference conditions of ambient temperature and pressure than SAE J1349 does, so the same physical engine tested under each standard can produce figures that are measurably different from one another before any unit is converted at all.
The practical rule: before treating a difference between two power figures as meaningful, confirm both are on the same measurement basis — gross or net, under the same test standard — not just the same unit. This calculator, like any unit converter, assumes the number you enter is already on the basis you want the answer in; it has no way to detect that two inputs were measured under different rules.