Horsepower (hp) is a unit of measurement of power, or the rate at which work is done. There are many different standards and types of horsepower. Two common definitions being used today are the mechanical horsepower (or imperial horsepower), which is about 745.7 watts, and the metric horsepower, which is approximately 735.5 watts.

The term was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses. It was later expanded to include the output power of other types of piston engines, as well as turbines, electric motors and other machinery.^[1][2] The definition of the unit varied among geographical regions. Most countries now use the SI unit watt for measurement of power. With the implementation of the EU Directive 80/181/EEC on January 1, 2010, the use of horsepower in the EU is permitted only as a supplementary unit.^[3]

The development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in The Miner's Friend:^[4]

The idea was later used by James Watt to help market his improved steam engine. He had previously agreed to take royalties of one third of the savings in coal from the older Newcomen steam engines.^[5] This royalty scheme did not work with customers who did not have existing steam engines but used horses instead.

Watt determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute).^[6] The wheel was 12 feet (3.7 m) in radius; therefore, the horse travelled 2.4 × 2π × 12 feet in one minute. Watt judged that the horse could pull with a force of 180 pounds-force (800 N). So:

Watt defined and calculated the horsepower as 32,572 ft⋅lbf/min, which was rounded to an even 33,000 ft⋅lbf/min.^[7]

Watt determined that a pony could lift an average 220 lbf (0.98 kN) 100 ft (30 m) per minute over a four-hour working shift.^[8] Watt then judged a horse was 50% more powerful than a pony and thus arrived at the 33,000 ft⋅lbf/min figure.^[9] Engineering in History recounts that John Smeaton initially estimated that a horse could produce 22,916 foot-pounds (31,070 N⋅m) per minute.^[10] John Desaguliers had previously suggested 44,000 foot-pounds (59,656 N⋅m) per minute, and Tredgold suggested 27,500 foot-pounds (37,285 N⋅m) per minute. "Watt found by experiment in 1782 that a 'brewery horse' could produce 32,400 foot-pounds [43,929 N⋅m] per minute."^[11] James Watt and Matthew Boulton standardized that figure at 33,000 foot-pounds (44,742 N⋅m) per minute the next year.^[11]

A common legend states that the unit was created when one of Watt's first customers, a brewer, specifically demanded an engine that would match a horse, and chose the strongest horse he had and driving it to the limit. Watt, while aware of the trick, accepted the challenge and built a machine that was actually even stronger than the figure achieved by the brewer, and it was the output of that machine which became the horsepower.^[12]

In 1993, R. D. Stevenson and R. J. Wassersug published correspondence in Nature summarizing measurements and calculations of peak and sustained work rates of a horse.^[13] Citing measurements made at the 1926 Iowa State Fair, they reported that the peak power over a few seconds has been measured to be as high as 14.9 hp (11.1 kW)^[14] and also observed that for sustained activity, a work rate of about 1 hp (0.75 kW) per horse is consistent with agricultural advice from both the 19th and 20th centuries and also consistent with a work rate of about 4 times the basal rate expended by other vertebrates for sustained activity.^[13]

When considering human-powered equipment, a healthy human can produce about 1.2 hp (0.89 kW) briefly (see orders of magnitude) and sustain about 0.1 hp (0.075 kW) indefinitely; trained athletes can manage up to about 2.5 hp (1.9 kW) briefly^[15] and 0.35 hp (0.26 kW) for a period of several hours.^[16] The Jamaican sprinter Usain Bolt produced a maximum of 3.5 hp (2.6 kW) 0.89 seconds into his 9.58 second 100-metre (109.4 yd) dash world record in 2009.^[17]

The constant 5252 is the rounded value of (33,000 ft⋅lbf/min)/(2π rad/rev).

The constant 63,025 is the approximation of

If torque and rotational speed are expressed in coherent SI units, the power is calculated as

The following definitions have been or are widely used:

In certain situations it is necessary to distinguish between the various definitions of horsepower and thus a suffix is added: hp(I) for mechanical (or imperial) horsepower, hp(M) for metric horsepower, hp(S) for boiler (or steam) horsepower and hp(E) for electrical horsepower.

Assuming the third CGPM (1901, CR 70) definition of standard gravity, gn = 9.80665 m/s2, is used to define the pound-force as well as the kilogram force, and the international avoirdupois pound (1959), one mechanical horsepower is:

Or given that 1 hp = 550 ft⋅lbf/s, 1 ft = 0.3048 m, 1 lbf ≈ 4.448 N, 1 J = 1 N⋅m, 1 W = 1 J/s: 1 hp ≈ 746 W

The various units used to indicate this definition (PS, cv, hk, pk, ks and ch) all translate to horse power in English. British manufacturers often intermix metric horsepower and mechanical horsepower depending on the origin of the engine in question. Sometimes the metric horsepower rating of an engine is conservative enough so that the same figure can be used for both 80/1269/EEC with metric hp and SAE J1349 with imperial hp.

DIN 66036 defines one metric horsepower as the power to raise a mass of 75 kilograms against the Earth's gravitational force over a distance of one metre in one second:^[18] 75 kg × 9.80665 m/s2 × 1 m / 1 s = 75 kgf⋅m/s = 1 PS. This is equivalent to 735.499 W, or 98.6% of an imperial mechanical horsepower.

In 1972, the PS was rendered obsolete by EEC directives, when it was replaced by the kilowatt as the official power-measuring unit.^[19] It is still in use for commercial and advertising purposes, in addition to the kilowatt rating, as many customers are still not familiar with the use of kilowatts for engines.

Other names for the metric horsepower are the Italian Cavallo vapore (cv), Dutch paardenkracht (pk), the French cheval (ch), the Spanish caballo de potencia and Portuguese cavalo-vapor (cv), the Russian лошадиная сила (л. с.), the Swedish hästkraft (hk), the Finnish hevosvoima (hv), the Estonian hobujõud (hj), the Norwegian and Danish hestekraft (hk), the Hungarian lóerő (LE), the Czech koňská síla and Slovak konská sila (k or ks), the Bosnian/Croatian/Serbian konjska snaga (KS), the Bulgarian конска сила, the Macedonian коњска сила (KC), the Polish koń mechaniczny (KM), Slovenian konjska moč (KM), the Ukrainian кінська сила (к. с.) and the Romanian cal-putere (CP), which all equal the German Pferdestärke (PS).

In the 19th century, the French had their own unit, which they used instead of the CV or horsepower. It was called the poncelet and was abbreviated p.

The horsepower used for electrical machines is defined as exactly 746 W.^[21] In the US, nameplates on electrical motors show their power output in hp, not their power input. Outside the United States watts or kilowatts are generally used for electric motor ratings and in such usage it is the output power that is stated.

Hydraulic horsepower can represent the power available within hydraulic machinery, power through the down-hole nozzle of a drilling rig,^[22] or can be used to estimate the mechanical power needed to generate a known hydraulic flow rate.

It may be calculated as^[22]

where pressure is in psi, and flow rate is in US gallons per minute.

Drilling rigs are powered mechanically by rotating the drill pipe from above. Hydraulic power is still needed though, as between 2 and 7 hp are required to push mud through the drill bit to clear waste rock. Additional hydraulic power may also be used to drive a down-hole mud motor to power directional drilling.^[22]

Boiler horsepower is a boiler's capacity to deliver steam to a steam engine and is not the same unit of power as the 550 ft-lb/s definition. One boiler horsepower is equal to the thermal energy rate required to evaporate 34.5 lb of fresh water at 212 °F in one hour. In the early days of steam use, the boiler horsepower was roughly comparable to the horsepower of engines fed by the boiler.^[23]

The term "boiler horsepower" was originally developed at the Philadelphia Centennial Exhibition in 1876, where the best steam engines of that period were tested. The average steam consumption of those engines (per output horsepower) was determined to be the evaporation of 30 pounds of water per hour, based on feed water at 100 °F, and saturated steam generated at 70 psi. This original definition is equivalent to a boiler heat output of 33,485 Btu/h. Years later in 1884, the ASME re-defined the boiler horsepower as the thermal output equal to the evaporation of 34.5 pounds per hour of water "from and at" 212 °F. This considerably simplified boiler testing, and provided more accurate comparisons of the boilers at that time. This revised definition is equivalent to a boiler heat output of 33,469 Btu/h. Present industrial practice is to define "boiler horsepower" as a boiler thermal output equal to 33,475 Btu/h, which is very close to the original and revised definitions.

Boiler horsepower is still used to measure boiler output in industrial boiler engineering in Australia, the US, and New Zealand. Boiler horsepower is abbreviated BHP, not to be confused with brake horsepower, below, which is also abbreviated BHP.

Drawbar horsepower (dbhp) is the power a railway locomotive has available to haul a train or an agricultural tractor to pull an implement. This is a measured figure rather than a calculated one. A special railway car called a dynamometer car coupled behind the locomotive keeps a continuous record of the drawbar pull exerted, and the speed. From these, the power generated can be calculated. To determine the maximum power available, a controllable load is required; it is normally a second locomotive with its brakes applied, in addition to a static load.

Example: How much power is needed to pull a drawbar load of 2,025 pounds-force at 5 miles per hour?

This formula may also be used to calculate the horsepower of a jet engine, using the speed of the jet and the thrust required to maintain that speed.

Example: How much power is generated with a thrust of 4,000 pounds at 400 miles per hour?

This measure was instituted by the Royal Automobile Club in Britain and was used to denote the power of early 20th-century British cars. (An identical measure, known as ALAM horsepower or NACC horsepower, was used for early U.S. automobiles.) Many cars took their names from this figure (hence the Austin Seven and Riley Nine), while others had names such as "40/50 hp", which indicated the RAC figure followed by the true measured power.

Taxable horsepower does not reflect developed horsepower; rather, it is a calculated figure based on the engine's bore size, number of cylinders, and a (now archaic) presumption of engine efficiency. As new engines were designed with ever-increasing efficiency, it was no longer a useful measure, but was kept in use by UK regulations which used the rating for tax purposes.

where

This is equal to the engine displacement in cubic inches divided by 0.625π, then divided again by the stroke in inches.

Since taxable horsepower was computed based on bore and number of cylinders, not based on actual displacement, it gave rise to engines with "undersquare" dimensions (bore smaller than stroke), which tended to impose an artificially low limit on rotational speed, hampering the potential power output and efficiency of the engine.

The situation persisted for several generations of four- and six-cylinder British engines: for example, Jaguar's 3.4-litre XK engine of the 1950s had six cylinders with a bore of 83 mm (3.27 in) and a stroke of 106 mm (4.17 in),^[25] where most American automakers had long since moved to oversquare (large bore, short stroke) V8 engines (see, for example, the early Chrysler Hemi).

The power of an engine may be measured or estimated at several points in the transmission of the power from its generation to its application. A number of names are used for the power developed at various stages in this process, but none is a clear indicator of either the measurement system or definition used.

In the case of an engine dynamometer, power is measured at the engine's flywheel.

In general:

All the above assumes that no power inflation factors have been applied to any of the readings.

Engine designers use expressions other than horsepower to denote objective targets or performance, such as brake mean effective pressure (BMEP). This is a coefficient of theoretical brake horsepower and cylinder pressures during combustion.

Nominal horsepower (nhp) is an early 19th-century rule of thumb used to estimate the power of steam engines.^[26] It assumed a steam pressure of 7 psi (48 kPa).^[27]

nhp = 7 × area of piston in square inches × equivalent piston speed in feet per minute/33,000

For paddle ships, the Admiralty rule was that the piston speed in feet per minute was taken as 129.7 × (stroke)1/3.38.^[26][27] For screw steamers, the intended piston speed was used.^[27]

The stroke (or length of stroke) was the distance moved by the piston measured in feet.

For the nominal horsepower to equal the actual power it would be necessary for the mean steam pressure in the cylinder during the stroke to be 7 psi (48 kPa) and for the piston speed to be that generated by the assumed relationship for paddle ships.^[26]

The French Navy used the same definition of nominal horse power as the Royal Navy.^[26]

Indicated horsepower (ihp) is the theoretical power of a reciprocating engine if it is completely frictionless in converting the expanding gas energy (piston pressure × displacement) in the cylinders. It is calculated from the pressures developed in the cylinders, measured by a device called an engine indicator – hence indicated horsepower. As the piston advances throughout its stroke, the pressure against the piston generally decreases, and the indicator device usually generates a graph of pressure vs stroke within the working cylinder. From this graph the amount of work performed during the piston stroke may be calculated.

Indicated horsepower was a better measure of engine power than nominal horsepower (nhp) because it took account of steam pressure. But unlike later measures such as shaft horsepower (shp) and brake horsepower (bhp), it did not take into account power losses due to the machinery internal frictional losses, such as a piston sliding within the cylinder, plus bearing friction, transmission and gear box friction, etc.

Brake horsepower (bhp) is the power measured at the crankshaft just outside the engine, before the losses of power caused by the gearbox efficiency and drive train efficiency.^[28]

In Europe, the DIN 70020 standard tests the engine fitted with all ancillaries and exhaust system as used in the car. The older American standard (SAE gross horsepower, referred to as bhp) used an engine without alternator, water pump, and other auxiliary components such as power steering pump, muffled exhaust system, etc., so the figures were higher than the European figures for the same engine. The newer American standard (referred to as SAE net horsepower) tests an engine with all the auxiliary components (see "Engine power test standards" below).

Brake refers to the device which was used to load an engine and hold it at a desired rotational speed. During testing, the output torque and rotational speed were measured to determine the brake horsepower. Horsepower was originally measured and calculated by use of the "indicator diagram" (a James Watt invention of the late 18th century), and later by means of a Prony brake connected to the engine's output shaft. More recently, an electrical brake dynamometer is used instead of a Prony brake, in order to measure the engines brake horsepower, the actual output of the engine itself, before losses to the drivetrain.

Shaft horsepower (shp) is the power delivered to a propeller shaft, a turbine shaft, or to an output shaft of an automotive transmission.^[29] Shaft horsepower is a common rating for turboshaft and turboprop engines, industrial turbines, and some marine applications.

Equivalent shaft horsepower (eshp) is sometimes used to rate turboprop engines. It includes the equivalent power derived from residual jet thrust from the turbine exhaust.^[30]

There exist a number of different standard determining how the power and torque of an automobile engine is measured and corrected. Correction factors are used to adjust power and torque measurements to standard atmospheric conditions, to provide a more accurate comparison between engines as they are affected by the pressure, humidity, and temperature of ambient air.^[31] Some standards are described below.

In the early twentieth century, a so-called "SAE horsepower" was sometimes quoted for U.S. automobiles. This long predates the Society of Automotive Engineers (SAE) horsepower measurement standards and was really just another term for the widely used ALAM or NACC horsepower figure, which was the same as the British RAC horsepower, used for tax purposes.

Prior to the 1972 model year, American automakers rated and advertised their engines in brake horsepower, bhp, which was a version of brake horsepower called SAE gross horsepower because it was measured according to Society of Automotive Engineers (SAE) standards (J245 and J1995) that call for a stock test engine without accessories (such as dynamo/alternator, radiator fan, water pump),^[32] and sometimes fitted with long tube test headers in lieu of the OEM exhaust manifolds. This contrasts with both SAE net power and DIN 70020 standards, which account for engine accessories (but not transmission losses). The atmospheric correction standards for barometric pressure, humidity and temperature for SAE gross power testing were relatively idealistic.

In the United States, the term bhp fell into disuse in 1971–1972, as automakers began to quote power in terms of SAE net horsepower in accord with SAE standard J1349. Like SAE gross and other brake horsepower protocols, SAE net hp is measured at the engine's crankshaft, and so does not account for transmission losses. However, similar to the DIN 70020 standard, SAE net power testing protocol calls for standard production-type belt-driven accessories, air cleaner, emission controls, exhaust system, and other power-consuming accessories. This produces ratings in closer alignment with the power produced by the engine as it is actually configured and sold.

In 2005, the SAE introduced "SAE Certified Power" with SAE J2723.^[33] This test is voluntary and is in itself not a separate engine test code but a certification of either J1349 or J1995 after which the manufacturer is allowed to advertise "Certified to SAE J1349" or "Certified to SAE J1995" depending on which test standard have been followed. To attain certification the test must follow the SAE standard in question, take place in an ISO 9000/9002 certified facility and be witnessed by an SAE approved third party.

A few manufacturers such as Honda and Toyota switched to the new ratings immediately.^[34] The rating for Toyota's Camry 3.0 L 1MZ-FE V6 fell from 210 to 190 hp (160 to 140 kW).^[34] The company's Lexus ES 330 and Camry SE V6 (3.3 L V6) were previously rated at 225 hp (168 kW) but the ES 330 dropped to 218 hp (163 kW) while the Camry declined to 210 hp (160 kW). The first engine certified under the new program was the 7.0 L LS7 used in the 2006 Chevrolet Corvette Z06. Certified power rose slightly from 500 to 505 hp (373 to 377 kW).

While Toyota and Honda are retesting their entire vehicle lineups, other automakers generally are retesting only those with updated powertrains.^[34] For example, the 2006 Ford Five Hundred is rated at 203 horsepower, the same as that of 2005 model. However, the 2006 rating does not reflect the new SAE testing procedure, as Ford is not going to incur the extra expense of retesting its existing engines.^[34] Over time, most automakers are expected to comply with the new guidelines.

SAE tightened its horsepower rules to eliminate the opportunity for engine manufacturers to manipulate factors affecting performance such as how much oil was in the crankcase, engine control system calibration, and whether an engine was tested with premium fuel. In some cases, such can add up to a change in horsepower ratings. A road test editor at Edmunds.com, John Di Pietro, said decreases in horsepower ratings for some 2006 models are not that dramatic. For vehicles like a midsize family sedan, it is likely that the reputation of the manufacturer will be more important.^[34]

DIN 70020 is a German DIN standard for measuring road vehicle horsepower. Similar to SAE net power rating, and unlike SAE gross power, DIN testing measures the engine as installed in the vehicle, with cooling system, charging system and stock exhaust system all connected. DIN 70020 is often seen abbreviated as "PS", derived from the German word for horsepower Pferdestärke. DIN hp is measured at the engine's output shaft, usually expressed in metric horsepower rather than mechanical horsepower.

A test standard by Italian CUNA (Commissione Tecnica per l'Unificazione nell'Automobile, Technical Commission for Automobile Unification), a federated entity of standards organisation UNI, was formerly used in Italy. CUNA prescribed that the engine be tested with all accessories necessary to its running fitted (such as the water pump), while all others—such as alternator/dynamo, radiator fan, and exhaust manifold—could be omitted.^[32] All calibration and accessories had to be as on production engines.^[32]

ECE R24 is a UN standard for the approval of compression ignition engine emissions, installation and measurement of engine power.^[35] It is similar to DIN 70020 standard, but with different requirements for connecting an engine's fan during testing causing it to absorb less power from the engine.^[36]

ECE R85 is a UN standard for the approval of internal combustion engines with regard to the measurement of the net power.^[37]

80/1269/EEC of 16 December 1980 is a European Union standard for road vehicle engine power.

The International Organization for Standardization (ISO) publishes several standards for measuring engine horsepower.

JIS D 1001 is a Japanese net, and gross, engine power test code for automobiles or trucks having a spark ignition, diesel engine, or fuel injection engine.^[44]