Torque to Power Calculator
Convert between torque, rotational speed (RPM), and power.
31,416 W · 42.13 hp
Power equals torque times angular speed: P = τ × 2πN ÷ 60, with torque in N·m and speed N in RPM. An engine making 100 N·m at 3000 RPM spins at ω = 314.159 rad/s, so P = 100 × 314.159 = 31,416 W = 31.42 kW (42.13 hp).
How torque becomes power
Torque is the twisting effort at the shaft; power is the rate at which that effort does work. Multiply torque by how fast the shaft turns and you get power. Because rotational speed is usually quoted in revolutions per minute (RPM), you first convert it to angular speed ω in radians per second, then multiply by torque. Knowing any two of torque, speed, and power gives you the third.
P = power (W), τ = torque (N·m), N = speed (RPM), ω = 2πN ÷ 60 (rad/s)
Worked example
A motor produces 100 N·m of torque at 3000 RPM. How much power is that?
- 1 Convert RPM to angular speed. ω = 2π × N ÷ 60 = 2π × 3000 ÷ 60 = 314.159 rad/s.
- 2 Multiply torque by angular speed. P = τ × ω = 100 × 314.159 = 31,416 W.
- 3 Express in kW and horsepower. 31,416 W ÷ 1000 = 31.42 kW; ÷ 745.7 = 42.13 hp.
Conversions used
The RPM-to-rad/s step and the horsepower definition.
| Quantity | Conversion | Notes |
|---|---|---|
| RPM → rad/s | ω = 2π × N ÷ 60 | One revolution = 2π radians; 60 s per minute |
| Power → kW | 1 kW = 1000 W | SI prefix |
| Power → hp | 1 hp = 745.7 W | Mechanical (imperial) horsepower |
| 1 RPM | ≈ 0.10472 rad/s | i.e. 2π ÷ 60 |
Why peak power and peak torque differ
Power is torque multiplied by angular speed, so a shaft can make more power at higher RPM even if its torque has started to fall. That is why an engine’s peak torque and peak power occur at different speeds: torque usually peaks in the mid-range, while power keeps climbing until torque drops faster than speed rises. Multiplying the two — P = τ × ω — traces the whole power curve from those torque figures.
Keep units consistent: torque in newton-metres and speed in RPM feed straight into P = τ × 2πN ÷ 60 to give watts. Mixing in lb·ft or leaving speed in rad/s without the 2π ÷ 60 factor is the most common source of error.