Shaft (Mechanical) Power

Formula

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.