Horsepower CalculatorTorque × RPM ÷ 5252
Horsepower equals torque (lb·ft) times rpm divided by 5,252: hp = τ × rpm ÷ 5252. In SI, power = torque × angular speed. Work out engine horsepower from a dyno torque reading, convert between kW, hp and metric PS, or estimate horsepower from quarter-mile trap speed or elapsed time. A dyno-style chart shows where your point sits.
Formula verified against OpenStax — University Physics, Volume 1 · NIST Special Publication 811 — Guide for the Use of the SI
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Engine data
Torque can be entered in lb·ft or N·m; the 5,252 rule is handled for you.
Step-by-step working
What is horsepower?
Horsepower is a unit of power, the rate of doing work, equal to 745.7 watts. James Watt introduced it in the 1780s to compare his steam engines with the draught horses they replaced.
Today it’s mainly used for engines and motors. Horsepower tells you how quickly an engine can do work, combining the torque it makes with how fast it spins.
Quick answers
How do I calculate horsepower from torque and rpm?
hp = torque (lb·ft) × rpm ÷ 5,252. An engine making 250 lb·ft at 6,000 rpm produces 285.6 hp at that speed.
How do I convert kW to hp?
Multiply kW by 1.341 for mechanical hp, or by 1.360 for metric PS. A 150 kW engine is 201 hp or 204 PS.
How do I estimate horsepower from a quarter-mile time?
Use the trap speed: hp ≈ weight (lb) × (mph ÷ 234)³. A 3,500 lb car trapping 105 mph makes roughly 316 hp. The ET method, weight ÷ (ET ÷ 5.825)³, gives a second opinion.
Why do torque and horsepower cross at 5,252 rpm?
Because hp = τ × rpm ÷ 5,252, the two numbers are equal at exactly that speed. Try different values in the torque calculator to see it hold.
Horsepower formulas
5252 ≈ 33,000 ÷ 2π, the constant that links lb·ft, rpm and mechanical horsepower.
| Symbol | Meaning | SI unit |
|---|---|---|
| hp | Mechanical horsepower | 1 hp = 745.7 W |
| τ | Torque | lb·ft or N·m |
| rpm | Engine speed | rev/min |
| ω | Angular velocity | rad/s |
| PS | Metric horsepower | 735.5 W |
How to calculate horsepower from torque
- Read the torque at a given rpm from the dyno sheet, in lb·ft.
- Multiply torque by rpm.
- Divide by 5,252 to get horsepower.
- For kW, multiply hp by 0.7457, or use τ(N·m) × rpm ÷ 9,549.
Worked example: 300 lb·ft at 5,000 rpm
An engine makes 300 lb·ft (406.7 N·m) of torque at 5,000 rpm. What is its power at that speed?
= 213.0 kW = 289.6 PS
A 3,500 lb car crossing the quarter-mile at 105 mph is making roughly 3,500 × (105 ÷ 234)³ ≈ 316 hp at the crank.
Horsepower unit conversions
The different “horsepowers” you’ll see on spec sheets.
| Unit | Watts | Used in |
|---|---|---|
| Mechanical hp (imperial) | 745.70 W | US and UK cars and engines |
| Metric hp (PS, CV, ch, pk) | 735.50 W | European spec sheets |
| Electrical hp | 746 W | Electric motor ratings |
| Boiler hp | 9,809.5 W | Steam boilers |
| 1 kW | 1,000 W | = 1.341 hp = 1.360 PS |
Common mistakes to avoid
- Using N·m with the 5,252 rule. It only works with lb·ft; with N·m, divide by 9,549 for kW.
- Comparing PS and hp directly. 300 PS ≈ 296 hp.
- Treating wheel horsepower as crank horsepower. Drivetrain losses typically take 10–20%.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Horsepower Calculator: frequently asked questions
hp = torque (lb·ft) × rpm ÷ 5,252. In SI, P (W) = torque (N·m) × angular speed (rad/s).
One mechanical horsepower is 745.7 W. One metric horsepower (PS) is 735.5 W.
James Watt defined 1 hp as 33,000 ft·lbf per minute. Converting rpm to radians per minute introduces 2π, and 33,000 ÷ 2π ≈ 5,252.
They describe the same thing. Torque is the twisting force; horsepower is how quickly that torque does work. Acceleration at any moment depends on the power available at that rpm and gear.
Brake (crank) horsepower is measured at the engine; wheel horsepower is measured at the wheels after drivetrain losses, usually 10–20% lower.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 7.4 and 10.8, Power and rotational work
- NIST Special Publication 811 — Guide for the Use of the SI — horsepower (550 ft·lbf/s) = 745.6999 W
- Wikipedia — Horsepower — unit history and variants
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.