# Horsepower calculator: torque, rpm and quarter-mile

> Horsepower from torque and rpm (hp = lb-ft × rpm ÷ 5252) or from quarter-mile ET and trap speed, with crank vs wheel horsepower and drivetrain loss.

Version interactive : https://www.calcopenly.com/fr/science/horsepower-calculator
Sujet : Calculatrices scientifiques

Power is torque times rotational speed. In US units that is horsepower = torque (lb-ft) × rpm ÷ 5,252, where 5,252 is 33,000 ft·lbf per minute divided by 2π; in metric units kW = torque (N·m) × rpm ÷ 9,549. The calculator also runs the formula backwards to get torque from a power figure, and shows the result in hp, kW and metric PS.

From a drag strip time slip it estimates engine horsepower with four published empirical formulas that link race weight, power and the quarter mile: Hale, Huntington, Fox and Jeff Lucius's best fit to 243 Road & Track tests. A 3,500 lb car trapping at 105 mph works out to about 316 hp by Hale's trap-speed formula and 324 hp by the Lucius fit.

Quarter-mile figures are estimates: traction, gearing, weather and the driver all move the time slip. Trap speed tracks power more closely than elapsed time. Wheel and crank horsepower differ by the drivetrain loss, entered here as a percentage.

## Données

- **Calculate** (options : From torque, Torque from hp, From trap speed, From ET)
- **Couple**
- **Puissance**
- **Engine speed**
- **Race weight with driver**: Car, fuel and driver as it sits on the start line.
- **Quarter-mile trap speed**
- **Quarter-mile elapsed time**
- **Formule** (options : Hale (1986), Huntington (1958), Fox (2001), Lucius best fit)
- **The torque or power figure is** (options : At the crank (engine), At the wheels (chassis dyno))
- **Drivetrain loss**: Share of crank power lost before the wheels. Garrett Motion's rule of thumb: 10% FWD, 15% RWD, 20% AWD, more with an automatic.

## Résultats

- cheval mécanique (hp) — résultat principal
- Puissance (kW)
- Metric horsepower (PS)
- Couple (lb-ft)
- Couple (N·m)
- Crank horsepower (hp)
- Wheel horsepower (hp)
- Weight per horsepower (lb/hp)
- Predicted ET at this power (s)
- Predicted trap speed at this power (mph)

## Formule

$$
\text{hp} = \frac{\tau_{\text{lb-ft}} \times \text{rpm}}{5252},\qquad \text{kW} = \frac{\tau_{\text{N·m}} \times \text{rpm}}{9549},\qquad \text{hp}_{\text{Hale}} = W\left(\frac{\text{mph}}{234}\right)^{3}
$$

## Exemples détaillés

### 350 lb-ft at 5,600 rpm

- Calculate: From torque
- Couple: 350 lbf·ft
- Engine speed: 5600 rpm
- The torque or power figure is: At the crank (engine)
- Drivetrain loss: 15%
- **cheval mécanique: 373.2 hp**
- **Puissance: 278.3 kW**
- **Metric horsepower: 378.4 PS**
- **Couple: 474.5 N·m**
- **Wheel horsepower: 317.2 hp**
- Source de vérification : Python decimal with 2π exact: 350 × 5600 × 2π / 33000 = 373.183 hp (Inch Calculator's worked example gives 373.19 with the rounded 5,252); × 0.85 = 317.206

### 400 N·m at 3,000 rpm

- Calculate: From torque
- Couple: 400 N·m
- Engine speed: 3000 rpm
- The torque or power figure is: At the crank (engine)
- Drivetrain loss: 15%
- **Puissance: 125.7 kW**
- **cheval mécanique: 168.5 hp**
- Source de vérification : Python decimal: 400 × 3000 × 2π / 60000 = 125.6637 kW; ÷ 0.74569987 = 168.5178 hp

### Torque from 300 PS at 6,000 rpm

- Calculate: Torque from hp
- Puissance: 300 PS
- Engine speed: 6000 rpm
- The torque or power figure is: At the crank (engine)
- Drivetrain loss: 15%
- **cheval mécanique: 295.9 hp**
- **Couple: 351.2 N·m**
- **Couple: 259.0 lb-ft**
- Source de vérification : Python decimal: 300 × 735.49875 W = 220,649.6 W; ÷ (6000 × 2π/60) = 351.175 N·m = 259.013 lb-ft

### Edge: 300 hp measured at the wheels, 15% loss

- Calculate: Torque from hp
- Puissance: 300 hp
- Engine speed: 6000 rpm
- The torque or power figure is: At the wheels (chassis dyno)
- Drivetrain loss: 15%
- **Wheel horsepower: 300.0 hp**
- **Crank horsepower: 352.9 hp**
- Source de vérification : Hand calculation: crank = 300 ÷ (1 − 0.15) = 352.941 hp

### calculator.net: 3,000 lb at 117 mph (Hale)

- Calculate: From trap speed
- Race weight with driver: 3000 lb
- Quarter-mile trap speed: 117 mph
- Formule: Hale (1986)
- Drivetrain loss: 15%
- **cheval mécanique: 375.0 hp**
- **Predicted ET at this power: 11.65 s**
- Source de vérification : calculator.net engine horsepower calculator gives 375 hp; 3000 × (117/234)³ = 375 and 5.825 × (3000/375)^(1/3) = 11.65 s by hand

### Inch Calculator: 3,750 lb running 13 s (Hale ET)

- Calculate: From ET
- Race weight with driver: 3750 lb
- Quarter-mile elapsed time: 13 s
- Formule: Hale (1986)
- Drivetrain loss: 15%
- **cheval mécanique: 337.4 hp**
- Source de vérification : Inch Calculator engine horsepower calculator worked example: 337.4 hp

## Questions

### How do you convert torque to horsepower?

Multiply torque in lb-ft by rpm and divide by 5,252. An engine making 350 lb-ft at 5,600 rpm produces 350 × 5,600 ÷ 5,252 = 373 hp. The constant comes from James Watt's horsepower of 33,000 foot-pounds per minute: a 1 lb-ft torque does 2π foot-pounds of work per revolution, and 33,000 ÷ 2π = 5,252.1. In metric units, kW = N·m × rpm ÷ 9,549.

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

At 5,252.1 rpm the conversion factor is exactly 1, so the number of horsepower equals the number of lb-ft. Below that speed the torque figure is larger, and above it the horsepower figure is larger. On a dyno chart drawn in hp and lb-ft on the same scale, the two curves always meet at 5,252 rpm; drawn in kW and N·m they cross at 9,549 rpm instead.

### How do you estimate horsepower from a quarter-mile time?

Hale's formulas give hp = weight × (trap mph ÷ 234)³ or hp = weight ÷ (ET ÷ 5.825)³, with weight in pounds including the driver. A 3,500 lb car trapping at 105 mph comes out at 3,500 × (105 ÷ 234)³ = 316 hp. Jeff Lucius's comparison of 243 Road & Track tests found trap speed predicts power better than ET, because launch and traction affect the time far more than the speed.

### What is the difference between wheel and crank horsepower?

Crank (brake) horsepower is measured at the engine's output shaft; wheel horsepower is what reaches the tires on a chassis dynamometer after the transmission, driveshaft and differential take their share. Garrett Motion's rule of thumb is a 10% loss for front-wheel drive, 15% for rear-wheel drive and 20% for all-wheel drive. Road & Track measured a 500 hp Mustang at 421 to 465 wheel hp on four different dynos.

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

Mechanical horsepower is 550 ft·lbf per second, or 745.7 watts (NIST SP 811). Metric horsepower (PS, CV or ch) is 75 kgf·m per second, 735.5 watts, so 1 hp = 1.0139 PS. European makers quote PS or kW: 300 PS is 296 hp or 220.6 kW. Electric horsepower, used for motors, is defined as exactly 746 watts.

### Quelle est la précision de « Horsepower calculator: torque, rpm and quarter-mile » ?

La précision dépend de vos données et des hypothèses de la méthode. Le calcul décimal utilise 50 chiffres significatifs, mais les estimations, méthodes numériques et données sources peuvent être moins précises ; l’arrondi affiché ne supprime pas ces limites. Exemples résolus vérifiés à partir de sources indépendantes : 9. Par exemple, « 350 lb-ft at 5,600 rpm » est vérifié à l’aide de Python decimal with 2π exact: 350 × 5600 × 2π / 33000 = 373.183 hp (Inch Calculator's worked example gives 373.19 with the rounded 5,252); × 0.85 = 317.206.

### D’où vient cette méthode ?

NIST SP 811 Appendix B.8 — horsepower (550 ft·lbf/s) = 745.6999 W; metric horsepower = 735.4988 W; Jeff Lucius, stealth316.com — Calculate horsepower, ET and MPH (Huntington, Fox, Hale and LRT formulas with fit to 243 Road & Track tests); G. T. Fox, “On the physics of drag racing”, American Journal of Physics 41, 311 (1973); Garrett Motion — Crank vs wheel horsepower (drivetrain loss rule of thumb).

## Sources

- [NIST SP 811 Appendix B.8 — horsepower (550 ft·lbf/s) = 745.6999 W; metric horsepower = 735.4988 W](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8)
- [Jeff Lucius, stealth316.com — Calculate horsepower, ET and MPH (Huntington, Fox, Hale and LRT formulas with fit to 243 Road & Track tests)](https://www.stealth316.com/2-calc-hp-et-mph.htm)
- [G. T. Fox, “On the physics of drag racing”, American Journal of Physics 41, 311 (1973)](https://doi.org/10.1119/1.1987216)
- [Garrett Motion — Crank vs wheel horsepower (drivetrain loss rule of thumb)](https://www.garrettmotion.com/news/newsroom/article/turbo-tech-crank-vs-wheel-horsepower-and-why-it-matters-for-your-turbo/)