How much hp from torque and rpm?
Enter the torque and the engine speed, and the horsepower updates as you type. Fill any two of torque, rpm, and power, and the calculator finds the third.
- Power
- 285.599332 hp
300 lb·ft at 5,000 rpm is 285.599332 hp, or 212.971385 kW.
- Horsepower (hp)
- 285.599332
- Kilowatts (kW)
- 212.971385
- Metric horsepower (PS)
- 289.560499
- Torque (lb·ft)
- 300
- Torque (N·m)
- 406.745384
Power: 285.599332 hp. 300 lb·ft at 5,000 rpm is 285.599332 hp, or 212.971385 kW.
How to calculate
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.
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.
Formula: P = τ × ω, with ω = 2π × rpm ÷ 60; in US units hp = torque (lb·ft) × rpm ÷ 5,252.11
- 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
Each example is checked against the calculator on every build.
- Torque 300, Engine speed (rpm) 5,000, Torque unit lb·ft gives Horsepower (hp) 285.599332, Kilowatts (kW) 212.971385, Torque (N·m) 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
- Torque 100, Engine speed (rpm) 5,252.113122, Torque unit lb·ft gives Horsepower (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
- Torque 400, Engine speed (rpm) 3,000, Torque unit N·m gives Kilowatts (kW) 125.663706, Power 125,663.706144 W.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
- Power 223,709.961475 W, Engine speed (rpm) 6,000, Torque unit lb·ft gives Torque 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
How it works
Power is torque times angular speed (OpenStax, equation 10.31):
P = τ × ω, with ω = 2π × rpm ÷ 60 radians per second.
- With torque τ in newton-meters, P is in watts. Divided by 1,000 it is kilowatts: kW = τ (N·m) × rpm ÷ 9,549.30, where 9,549.30 = 60,000 ÷ 2π.
- With torque in pound-feet, first multiply by 1.3558179483 N·m per lb·ft (0.3048 m × 4.4482216152605 N). In horsepower this gives hp = τ (lb·ft) × rpm ÷ 5,252.11, where 5,252.11 = 33,000 ÷ 2π.
Fill any two of torque, rpm, and power, and the calculator solves the third:
- torque = P ÷ ω
- rpm = P ÷ (τ × 2π ÷ 60)
The result panel shows the power in horsepower, kilowatts, and metric horsepower, and the torque in both lb·ft and N·m.
Units
- 1 hp (mechanical horsepower) = 550 ft·lbf/s = 745.69987158 W, exactly from the foot and the pound-force (NIST SP 811).
- 1 PS (metric horsepower) = 75 kgf·m/s = 735.49875 W.
- 1 lb·ft = 1.3558179483 N·m.
Rules
- Torque and rpm must be more than 0. A power must be more than 0.
- The answer is the power at the shaft where the torque is measured, with no losses added or taken away.
Worked examples by hand
300 lb·ft at 5,000 rpm. In N·m: 300 × 1.3558179483 = 406.745 N·m. ω = 2π × 5,000 ÷ 60 = 523.599 rad/s. P = 406.745 × 523.599 = 212,971 W = 212.97 kW, and 212,971 ÷ 745.69987 = 285.60 hp. The shortcut gives the same: 300 × 5,000 ÷ 5,252.11 = 285.60 hp.
100 lb·ft at 5,252.113 rpm (33,000 ÷ 2π). 100 × 5,252.113 ÷ 5,252.113 = 100 hp. At 5,252.11 rpm, which rounds that speed, the page shows 99.999941 hp.
400 N·m at 3,000 rpm. ω = 2π × 3,000 ÷ 60 = 100π rad/s. P = 400 × 100π = 40,000π = 125,664 W = 125.66 kW.
Torque for 300 hp at 6,000 rpm. τ = 300 × 5,252.11 ÷ 6,000 = 262.61 lb·ft.
Other questions people ask
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.