⚙️ Torque & Power Calculator

Calculate mechanical power from torque and rotational speed.

Inputs

Torque (τ)

Rotational Speed (N)

RPM

Results

Mechanical Power (P)

0.00 hp

Power-Torque Relationship

Calculator Description

Torque represents rotational force, while power is the rate of doing work. In rotating machinery torque and speed combine into power, and understanding this relation lets you select rated motors, engines and turbines.

What this calculator finds

Enter the torque τ and rotational speed N (RPM) to compute the mechanical power P. Both metric (W, N·m) and imperial (HP, lb-ft) bases are handled.

Why it matters

Selecting motor/engine ratings and checking overload
Gear-ratio design exploiting the torque–speed trade-off
Driving-power sizing for pumps, compressors and fans

Formula

Power & Torque Equation

Power equals torque times angular speed ω (with ω = 2πN/60 in rad/s). The power unit differs by unit system.

Metric (SI)

P\,(\text{W}) = \tau\,(\text{N·m}) \times \dfrac{2\pi N(\text{RPM})}{60}

Imperial (US)

P\,(\text{HP}) = \dfrac{\tau\,(\text{lb-ft}) \times N(\text{RPM})}{5252}

P — Mechanical power [W or HP]
τ — Torque [N·m or lb-ft]
N — Rotational speed [RPM]

How the formula works

Power P is proportional to torque τ → at the same speed, more torque means more output.
Power is proportional to speed N → at the same torque, higher speed gives more output.
The constant 5252 arises from 33000/(2π) in the HP·lb-ft·RPM system.

Worked example

At 1750 RPM and 100 N·m: ω = 2π×1750/60 ≈ 183.3 rad/s, so P = 100 × 183.3 ≈ 18,300 W ≒ 18.3 kW. The equivalent in HP is about 24.5 HP.

Useful Tips

Practical tips

Use a reducer to raise torque and lower speed (power conserved) when low-speed high-torque is needed.
Motor ratings distinguish continuous vs short-time duty — consider the duty cycle.
Account for efficiency: input power = output power ÷ efficiency.

Limitations & cautions

This is shaft power (lossless); motors differ by input electrical power and efficiency.
Starting and peak torque differ from rated average — review starting conditions separately.