Key facts
- Mechanical (imperial) horsepower is exactly 550 foot-pounds per second, which is 745.6998715822702 watts.
- Metric horsepower (PS, CV, pk or ch) is 75 kgf·m/s, or 735.49875 watts, so it is about 1.4% smaller.
- Electrical horsepower is defined as exactly 746 watts, and differs from mechanical horsepower by 0.05 hp at 100 kW.
- One kilowatt equals 1.34102 mechanical horsepower or 1.35962 metric horsepower.
- Power is a rate: 1 W = 1 J/s. A kilowatt-hour is an amount of energy, so the two are not interchangeable.
Three horsepowers in circulation
Three different horsepower figures are in regular use, and the differences are large enough to change a spec sheet. Mechanical horsepower, the imperial or mechanical figure, is exactly 550 foot-pounds per second, which is 745.6998715822702 watts. Metric horsepower is smaller at 735.49875 watts, and electrical horsepower is defined as exactly 746 watts.
Each of these is stored as a fixed number of watts, so every conversion is one multiplication and one division, with no figure hidden in the calculator. The UnitUtils power converter works this way throughout, with every unit expressed as a multiple of the watt, as set out in the methodology.
Mechanical horsepower
One foot-pound of force is 0.3048 m × 4.4482216152605 N = 1.355817948 N·m, so 550 foot-pounds per second is 550 × 1.355817948 = 745.6998715822702 W. The unit is written hp and comes from James Watt's estimate, in the 1780s, of the work a draught horse could sustain, used to compare steam engines with the horses they replaced.
The abbreviation bhp in car advertising means this same unit. It stands for brake horsepower, which describes how the figure was measured, at the crankshaft on a dynamometer, rather than a separate quantity of power. The UnitUtils power converter treats bhp as another name for mechanical horsepower, so typing it gives the 745.6998715822702 W figure.
Metric horsepower
Metric horsepower is a kilogram-force raised one metre per second: 75 kgf·m/s, which with standard gravity of 9.80665 m/s² gives exactly 735.49875 W. Its names include PS (German Pferdestärke), ch (French cheval-vapeur), CV (Italian cavalli vapore and Spanish caballos de vapor) and pk (Dutch paardenkracht).
Because each PS is fewer watts than an hp, the same engine reads about 1.4% higher in PS than in hp. A car sold as 150 hp is the same machine as one sold as 152.08 PS.
Electrical horsepower
Electrical horsepower is exactly 746 W, a rounded value close to mechanical horsepower but not identical to it. The difference is small: a 100 kW motor is 134.05 electrical horsepower and 134.10 mechanical horsepower, a gap of 0.05 hp. On a specification sheet, quoting the wrong one is an error, even where the percentage is negligible.
Converting kilowatts to horsepower and PS
Divide the watt figure by the watts in one unit. In full: hp = kW × 1,000 ÷ 745.6998715822702, and PS = kW × 1,000 ÷ 735.49875.
Equivalently, 1 kW = 1.34102 hp and 1 kW = 1.35962 PS, so multiplying the kilowatt figure by those numbers gives the same results to two decimal places for any car engine.
| kW | hp (mechanical) | PS |
|---|---|---|
| 50 | 67.05 | 67.98 |
| 75 | 100.58 | 101.97 |
| 100 | 134.10 | 135.96 |
| 125 | 167.63 | 169.95 |
| 150 | 201.15 | 203.94 |
| 200 | 268.20 | 271.92 |
Going the other way
The reverse conversion multiplies instead of dividing: kW = hp × 0.74570, and kW = PS × 0.73550. Take 150 mechanical horsepower as a worked example. 150 × 745.6998715822702 ÷ 1,000 gives 111.85 kW, and that same engine is 152.08 PS, since 111.85 kW × 1.35962 lands within a rounding step of the exact value.
| hp (mechanical) | kW | PS |
|---|---|---|
| 50 | 37.28 | 50.69 |
| 100 | 74.57 | 101.39 |
| 150 | 111.85 | 152.08 |
| 200 | 149.14 | 202.77 |
| 250 | 186.42 | 253.47 |
Choosing the right horsepower in the converter
The UnitUtils power converter lists mechanical horsepower (hp) and metric horsepower (PS) as separate units, so pick the one your figure uses. For a European car brochure or registration document that is usually PS; for a UK or US figure in hp or bhp it is mechanical horsepower.
The difference matters at engine sizes: 180 kW is 244.73 PS but 241.38 hp. The two numbers describe one engine, not two.
Why a car lists two power numbers
In the European Union, vehicle documents state engine power in kilowatts, and manufacturers often print PS alongside it. In the United Kingdom and the United States, power is usually quoted in horsepower or bhp.
That is why the same car can appear as 150 hp, 152 PS and 111.85 kW in three different places. Read the unit before the number. A figure with no unit, or with hp where PS was expected, is not a contradiction to solve but a number you cannot yet compare.
Power is a rate, energy is an amount
A watt is a rate of energy flow: 1 W = 1 joule per second. A kilowatt is therefore not an amount of anything, and it cannot be added to an electricity bill. A kilowatt-hour is the amount: 3,600,000 J, or 3.6 MJ.
A 2 kW heater left on for 3 hours uses 6 kWh, because 2 kW × 3 h = 6 kWh. The kilowatt describes how fast the heater works, the kilowatt-hour describes how much energy it moved. The same distinction reappears on an electricity bill, so the energy converter and the power converter are separate tools.
The kilo prefix means 1,000 in both cases, which is worth keeping in mind whenever a rate and an amount are written with the same word. The metric prefixes guide covers the other prefixes.
How many digits are worth printing
Six significant figures is enough for almost any figure you will quote, which is why 100 kW reads as 134.102 hp rather than 134.10 hp in the default output of the power converter. Rounding to two decimal places, as the tables above do, suits a specification sheet; whole horsepower suits conversation.
Beyond that, extra digits describe arithmetic rather than the engine. The gap between 745.6998715822702 W and 735.49875 W is exact and worth stating, so no precision is lost in the conversion itself. The precision notes cover how the displayed figures are chosen.