Shaft (Mechanical) Power

P = τ × 2π × n / 60

Quick answer

This calculator solves P = τ × ω = τ × 2π × n/60 for Mechanical Power. With Torque 1 N·m, Speed (RPM) 0.5, the result is 52.36 mW. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Mechanical Power (W)
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Formula

P = τ × ω = τ × 2π × n/60

Description

Mechanical shaft power is the product of torque and angular velocity. Since speed is commonly given in RPM rather than rad/s, the 2π/60 factor converts RPM to rad/s. This formula applies to any rotating machine: motors, generators, pumps, fans, compressors, and turbines. For motor sizing, calculate the required shaft power from the load torque and speed, then select a motor with rated power exceeding this value, accounting for motor efficiency. A 1 hp motor produces 746 W of mechanical power.

Variables

  • P — Mechanical shaft power (W)
  • τ — Torque at the shaft (N·m)
  • n — Rotational speed (RPM)

Practical Notes

1 horsepower (hp) = 746 W. A motor rated at 1 hp and 1750 RPM produces τ = 746 × 60/(2π × 1750) = 4.07 N·m of torque. At startup, motors typically produce 2-6× rated torque (locked-rotor torque). Variable frequency drives (VFDs) can maintain constant torque over a wide speed range, with power proportional to speed. Above base speed, field weakening reduces torque while maintaining constant power.

Symbols and units

Symbol Meaning Default unit Accepted units
P Mechanical Power W µW, mW, W, kW
tau Torque N·m N·m, mN·m
n Speed (RPM) — —

Step by step

  1. 1. What you know: Torque 1 N·m, Speed (RPM) 0.5
  2. 2. The relation: P = τ × ω = τ × 2π × n/60
  3. 3. Substitute: tau = 1 N·m, n = 0.5
  4. 4. Result: Mechanical Power = 52.36 mW

Worked examples

Minimum range

Given: Torque 5 mN·m, Speed (RPM) 0.025

Result: Mechanical Power = 13.09 µW

Low range

Given: Torque 50 mN·m, Speed (RPM) 0.25

Result: Mechanical Power = 1.309 mW

Typical

Given: Torque 1 N·m, Speed (RPM) 0.5

Result: Mechanical Power = 52.36 mW

High range

Given: Torque 50 N·m, Speed (RPM) 0.8

Result: Mechanical Power = 4.189 W

Maximum range

Given: Torque 500 N·m, Speed (RPM) 8

Result: Mechanical Power = 0.4189 kW

Solving for each variable

Solve for Mechanical Power

Torque 5 mN·m, Speed (RPM) 0.025 → 13.09 µW

Solve for Torque

Mechanical Power 10 mW, Speed (RPM) 0.025 → 3.82 N·m

Solve for Speed (RPM)

Mechanical Power 10 mW, Torque 5 mN·m → 19.1

How Mechanical Power changes with Torque

Torque (input) Mechanical Power (result)
100 mN·m 5.236 mW
0.25 N·m 13.09 mW
0.5 N·m 26.18 mW
0.75 N·m 39.27 mW
1 N·m 52.36 mW
1.5 N·m 78.54 mW
2 N·m 104.7 mW
4 N·m 0.2094 W
7 N·m 0.3665 W
10 N·m 0.5236 W

The same result in other units

Unit Value
µW 52360
mW 52.36
W 0.05236

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Frequently asked questions

How do you calculate Shaft (Mechanical) Power?

Use P = τ × ω = τ × 2π × n/60. With Torque 1 N·m, Speed (RPM) 0.5, Mechanical Power works out to 52.36 mW.

What is the formula for Shaft (Mechanical) Power?

The formula is P = τ × ω = τ × 2π × n/60. Mechanical shaft power is the product of torque and angular velocity.

How do you find Torque when you know the other values?

Rearrange for Torque: with Mechanical Power 10 mW, Speed (RPM) 0.025, Torque is 3.82 N·m.

How do you find Speed (RPM) when you know the other values?

Rearrange for Speed (RPM): with Mechanical Power 10 mW, Torque 5 mN·m, Speed (RPM) is 19.1.

What units does Shaft (Mechanical) Power use?

Mechanical Power is shown in µW, mW, W. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Motors & Mechanical formulas →
Motor Mechanical Power Motor Torque Motor Speed Gear Ratio Output Torque Back-EMF Voltage Motor Efficiency Rotational Dynamics Stepper Motor Step Angle

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