# How much hp from torque and rpm?

Computes engine horsepower from torque and rpm with P = τ × ω, or the torque or rpm for a power, in horsepower, kilowatts, and metric horsepower.

- Page: https://www.acalculator.org/physics/horsepower-calculator
- JSON spec: https://www.acalculator.org/physics/horsepower-calculator.json
- Version: 8cecb033f294

## Default answer

Example with the default inputs (Torque 300, Engine speed (rpm) 5,000, Torque unit lb·ft): 300 lb·ft at 5,000 rpm is 285.599332 hp, or 212.971385 kW.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| tq | Torque | The twisting force at the crankshaft or shaft, in the torque unit below. |
| rpm | Engine speed (rpm) | How fast the shaft turns, in revolutions per minute. |
| p | Power | The power the shaft delivers at that torque and speed. |
| u | Torque unit | Pound-feet (lb·ft), as US engine specs give it, or newton-meters (N·m). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| torque | Torque | The twisting force at the crankshaft or shaft, in the torque unit below. |
| rpm | Engine speed (rpm) | How fast the shaft turns, in revolutions per minute. |
| power | Power | The power at that torque and speed. |
| hp | Horsepower (hp) | The power in mechanical horsepower (550 ft·lbf/s). |
| kw | Kilowatts (kW) | The power in kilowatts. |
| ps | Metric horsepower (PS) | The power in metric horsepower (75 kgf·m/s). |
| torqueLbft | Torque (lb·ft) | The torque in pound-feet. |
| torqueNm | Torque (N·m) | The torque in newton-meters. |

## Method

P = τ × ω, with ω = 2π × rpm ÷ 60; in US units hp = torque (lb·ft) × rpm ÷ 5,252.11

## Assumptions

- This is the power at the shaft where the torque is measured: at the crankshaft it is brake horsepower; at the wheels it is lower, after drivetrain losses.
- 1 hp = 550 ft·lbf/s = 745.69987 W; 1 PS (metric horsepower) = 75 kgf·m/s = 735.49875 W; 1 lb·ft = 1.3558179 N·m, from the exact definitions in NIST SP 811.
- 5,252.11 is 33,000 ÷ 2π: 33,000 ft·lbf per minute is 1 hp, and one turn is 2π radians.

## Worked examples

1. tq = 300, rpm = 5,000, u = lbft gives hp = 285.599332, kw = 212.971385, torqueNm = 406.745384. Source: OpenStax University Physics Volume 1, §10.8, eq. 10.31: P = τω. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion; NIST SP 811 (2008) B.8: 1 hp = 550 ft·lbf/s.
2. tq = 100, rpm = 5,252.113122, u = lbft gives hp = 100. Source: OpenStax University Physics Volume 1, §10.8, eq. 10.31: P = τω, with 33,000 ÷ 2π = 5,252.11 rpm. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion.
3. tq = 400, rpm = 3,000, u = nm gives kw = 125.663706, p = 125,663.706144. Source: OpenStax University Physics Volume 1, §10.8, eq. 10.31: 400 N·m × 100π rad/s = 40,000π W. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion.
4. p = 223,709.961475, rpm = 6,000, u = lbft gives tq = 262.605656. Source: OpenStax University Physics Volume 1, §10.8, eq. 10.31, solved for τ = P ÷ ω. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion.

## FAQ

### How do you calculate horsepower from torque?

Multiply the torque in lb·ft by the rpm and divide by 5,252.11. 300 lb·ft at 5,000 rpm is 300 × 5,000 ÷ 5,252.11 = 285.6 hp.

### Where does 5,252 come from?

One horsepower is 550 ft·lbf per second, or 33,000 ft·lbf per minute. Power is torque times angular speed, and one turn is 2π radians, so hp = torque × rpm × 2π ÷ 33,000 = torque × rpm ÷ 5,252.11.

### Why do the torque and horsepower curves cross at 5,252 rpm?

Because hp = torque × rpm ÷ 5,252.11, the two numbers are equal at 5,252 rpm when torque is in lb·ft and power in hp. Below that speed the torque number is larger; above it the horsepower number is larger.

### How do I calculate power from torque in newton-meters?

Kilowatts = torque (N·m) × rpm ÷ 9,549.3. 400 N·m at 3,000 rpm is 125.7 kW, or 168.5 hp. Pick N·m as the torque unit and the calculator does it.

### What is the difference between hp and PS?

hp here is mechanical horsepower, 550 ft·lbf/s or 745.7 W. PS is metric horsepower, 75 kgf·m/s or 735.5 W, used in Europe and Japan. 100 hp is about 101.4 PS.

### Is this brake horsepower or wheel horsepower?

It is the power wherever the torque was measured. Torque from an engine dynamometer gives brake horsepower at the crankshaft. Wheel horsepower from a chassis dyno is lower, because the gearbox and driveline lose some power.

### Can it estimate horsepower from a quarter-mile time?

No. Quarter-mile formulas are rules of thumb fitted to race results, not physics. This calculator uses the exact relation between torque, speed, and power.

## Sources

- OpenStax, University Physics Volume 1, §10.8 Work and Power for Rotational Motion, equation 10.31: P = τω (CC BY 4.0), retrieved 2026-10-01. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion
- NIST SP 811 (2008), Guide for the Use of the International System of Units, Appendix B.8 (horsepower, 550 ft·lbf/s; foot, pound-force), retrieved 2026-10-01. https://www.nist.gov/pml/special-publication-811