How 1 horsepower is calculated

One mechanical horsepower is defined as 550 foot-pounds per second, which equals about 745.7 watts; in metric usage, one metric horsepower is 75 kilogram-force meters per second, or about 735.5 watts. In rotating machinery, horsepower is typically calculated from torque and speed using hp = (torque in lb-ft × rpm) ÷ 5252, or in SI units by converting from kilowatts: hp(mech) ≈ kW × 1.341.

What “horsepower” means—and why there are different versions

Horsepower is a unit of power popularized by James Watt to compare steam engines to draft horses. Over time, several standardized versions emerged for different industries and regions, notably mechanical (imperial), metric, electrical, boiler, and hydraulic horsepower. The differences come from the base units and practical use-cases each standard was designed to describe.

Official definitions and exact values

The following list outlines the most common horsepower definitions, their base physical definitions, and exact conversions to watts so you can calculate consistently across systems.

• Mechanical (imperial) horsepower, hp: Defined as 550 ft·lbf/s (or 33,000 ft·lbf/min); exactly 745.699871582 W. Often approximated as 746 W in electrical contexts.
• Metric horsepower, PS/CV/hp(M): Defined as 75 kgf·m/s; exactly 735.49875 W. Used historically in Europe and some automotive specifications.
• Electrical horsepower: By convention exactly 746 W. Common in electrical motor ratings in North America.
• Boiler horsepower (steam): Defined as the energy to evaporate 34.5 lb of water per hour at 212°F to dry steam at the same temperature; 33,475 BTU/h ≈ 9.8095 kW.
• Hydraulic horsepower: Power imparted to a fluid; in US units HHP = (PSI × GPM) ÷ 1714. In SI, kW ≈ (bar × L/min) ÷ 600.

These definitions coexist; when comparing engines or systems, confirm which horsepower standard is in use to avoid errors of a few percent to an order of magnitude (as with boiler horsepower).

Calculating horsepower from torque and speed

Power in rotation is the product of torque and angular velocity. Using consistent units lets you convert to horsepower directly via well-known constants.

US customary formula (mechanical horsepower)

Use hp = (torque in lb-ft × rpm) ÷ 5252. The constant 5252 comes from 33,000 ft·lbf/min divided by 2π (to relate rpm to radians per second). Example: at 300 lb-ft and 2,000 rpm, hp ≈ (300 × 2000) ÷ 5252 ≈ 114.3 hp.

SI formula (start with watts or kilowatts)

Power in watts: P(W) = torque(N·m) × 2π × rpm ÷ 60. For convenience, kW ≈ torque(N·m) × rpm ÷ 9550. Then convert to horsepower: hp(mech) = kW × 1.341022, or hp(metric) = kW × 1.359622. Example: 400 N·m at 3,000 rpm gives kW ≈ (400 × 3000) ÷ 9550 ≈ 125.6 kW, which is ≈ 168.5 hp(mech) or ≈ 170.8 hp(metric).

Converting between kilowatts and horsepower

If you know power in kW (for example from a dynamometer), these factors translate to the various horsepower standards without needing torque or rpm.

• hp(mechanical) = kW × 1.341022 (exact factor 1 ÷ 0.745699871582)
• hp(metric, PS/CV) = kW × 1.359622 (exact factor 1 ÷ 0.73549875)
• kW from hp(mechanical) = hp × 0.745699871582
• kW from hp(metric) = hp × 0.73549875

Always check whether a spec uses mechanical or metric horsepower; automotive brochures sometimes round or mix conventions, leading to small discrepancies.

Context: ratings and real-world measurement

Engine horsepower ratings also depend on test protocols (for example, SAE net vs. gross, DIN, JIS), which specify accessories, correction factors, and environmental conditions. These protocols don’t change what 1 hp is, but they do affect the measured value you start from before applying the unit conversions above.

Summary

One mechanical horsepower is 550 ft·lbf/s, about 745.7 W; one metric horsepower is 75 kgf·m/s, about 735.5 W. For rotating systems, calculate hp from torque and speed using hp = (lb-ft × rpm) ÷ 5252 or, in SI, compute kW = N·m × rpm ÷ 9550 and convert to hp. Confirm which horsepower standard is used to ensure apples-to-apples comparisons.

Is 300 hp equal to 300 horses?

If you have a 300 HP engine, you can almost imagine 300 horses pulling your car forward. That’s definitely a lot of horses for one small car! An engineer named James Watt invented horsepower to sell his brand new steam engines back during the times when everything was horse-drawn.

How is 1 hp measured?

Watt defined one horsepower as the equivalent of the energy expended by a single horse raising 33,000 pounds of water one foot in the air from the bottom of a 1,000 foot deep well in 60 seconds.

How many humans does it take to equal 1 horsepower?

One horsepower is a unit of power that equals the work done in lifting 550 pounds one foot in one second. One manpower = a unit of power based on the rate at which a man can work; approximately 75 watts, or about one tenth of a horsepower. In other words, it takes ten strong men to do the work of one horse.

How is 1hp calculated?

To calculate one horsepower (1 hp), the most common approach is to define it in terms of watts: 1 hp is equal to 746 watts. For mechanical applications, horsepower is often calculated using the formula Horsepower = (Torque x RPM) / 5,252. 
1. Conversion to Watts

• Formula: 1 hp = 746 watts 
• Usage: This is the most straightforward way to quantify horsepower as a unit of power. 
• Example: If you have a motor with an output of 5 hp, you can convert it to watts by multiplying 5 hp * 746 watts/hp = 3,730 watts. 

2. Mechanical Horsepower Calculation (Torque and RPM)

• Formula: Horsepower = (Torque × RPM) / 5,252 
• Where:
  • Torque: The rotational force, usually in pound-feet (lb-ft). 
  • RPM: Rotational speed in revolutions per minute. 
  • 5,252: A constant derived from the unit conversion of foot-pounds per minute to horsepower. 
• Usage: This formula is used to calculate the horsepower of an engine or motor by measuring its rotational speed and the torque it produces. 
• Example: If an engine produces 100 lb-ft of torque at 3,000 RPM, its horsepower would be (100 x 3,000) / 5,252 = 57.12 hp. 

3. Basic Definition of Power

• Formula: Power = Force × Distance / Time 
• Usage: This is the fundamental definition of power, and it can be used to derive the standard horsepower definition. 
• 1 Horsepower Definition: 1 hp is equivalent to 550 foot-pounds of work done per second.