Horsepower Formulas Reference

This is a complete, printable reference of the formulas used across calchorsepower.com. Every equation here powers one of our calculators, so once you understand the math you can either compute it by hand or jump straight to the matching tool.

Core Horsepower Formulas

The constant 5252 is the heart of engine math: it equals 33,000 ft-lb/min ÷ 2π. Because horsepower and torque share it, their dyno curves always cross at 5252 RPM — see the 5252 rule explained.

Unit Conversion Formulas

Racing & Performance Formulas

Industrial Formulas

• Three-phase motor HP: HP = (V × A × √3 × PF × Eff) ÷ 746 — see Electric Motor HP.
• Hydraulic (water) HP: HHP = (GPM × Head ft) ÷ 3960 — see Pump HP.
• Engine displacement: V = π × (Bore ÷ 2)² × Stroke × Cylinders — see Engine Displacement.

Metric Formulas

Every imperial formula above has a metric twin with a different constant. Getting these mixed up is the most common source of wrong answers.

HVAC & Refrigeration Formulas

Engine Building Formulas

Every Constant, and Where It Comes From

The constants look arbitrary until you see the unit arithmetic behind them. None are empirical fudge factors — each is a pure conversion between measuring systems.

Picking the Right Formula

If you are unsure which applies, the how to calculate horsepower guide walks through all seven methods with their accuracy ranges.

What James Watt Actually Measured

The 33,000 figure has a specific origin, and it isn't a physical constant so much as a marketing decision that happened to stick for 250 years.

Watt needed a way to sell steam engines to mill owners who were already using horses, which meant expressing his engines in units the buyer already understood. Observing horses turning a mill wheel, he measured a horse walking a circle of roughly 24 feet in diameter, completing about 144 turns an hour (2.4 per minute) while pulling against a load of around 180 pounds. That works out to roughly 32,600 foot-pounds per minute, which he rounded to 33,000.

The unit outlived the reasoning entirely. It now describes aircraft engines, electric motors and industrial pumps in situations where no horse was ever involved, which is why the number looks so arbitrary today. Everything downstream — the 550 ft-lb/sec figure, the 745.7 watt equivalence, even the 5252 constant on dyno charts — traces back to that observation of a horse walking in a circle.

Where Foot-Pounds Per Minute Is Genuinely the Right Unit

For most modern purposes horsepower or kilowatts are more convenient. Foot-pounds per minute earns its place in one specific situation: any job defined as lifting a known weight at a known speed, where the arithmetic works out directly with no constant to remember.

Take a hoist required to lift 2,000 pounds at 30 feet per minute. The work rate is simply the weight multiplied by the speed:

That 1.82 HP is what reaches the hook, not what the motor must produce. A gearbox, cable drum and sheaves together typically run 65 to 80% efficient. So you need about 2.6 HP at the motor to deliver it. In practice you'd specify the next standard size up: a 3 HP unit. Sizing the motor at 1.82 HP would leave it permanently overloaded.

Compare the third and fourth rows. Doubling the load while halving the speed needs exactly the same power, which is the clearest possible demonstration that power is a rate rather than a quantity. The gearing changes, the torque at the drum doubles, but the motor size doesn't move. Convert any of these into metric with the HP to kW calculator.

The Full Work-Rate Unit Ladder

One horsepower can be written several ways depending on which length and time units the specification uses. They're all the same quantity:

Converting between any two is a matter of multiplying or dividing by 12 for the length unit and 60 for the time unit. The most frequent slip is dropping the factor of 60 between per-second and per-minute figures, which puts the answer out by a factor of sixty rather than a plausible-looking margin — usually obvious enough to catch. The factor of 12 error is more dangerous, because a result twelve times too large can still look believable on a small motor. For the metric route, use the watts to HP calculator.

Inch-Pounds Per Second Is Not Inch-Pounds

This is the single most common error with these units, and it produces answers that are wrong by whatever the RPM happens to be. Inch-pounds measure torque — a twisting effort that exists whether or not anything moves. Inch-pounds per second measure power — a rate of doing work, which requires motion by definition.

The practical test is simple: if a figure changes when the shaft speeds up, it is power. If it doesn't, it is torque. A bolt torqued to 90 in-lb stays at 90 in-lb whether the engine is running or parked. If you've a torque figure and need horsepower from it, the HP to inch-pounds torque calculator is the tool you want, because it asks for the RPM this one doesn't need.

The story behind the 33,000 figure, and what a real horse can produce, is in how much horsepower does a horse have?