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Shaft torque from transmitted power

Torque describes the turning effort at a particular shaft speed. Use the power actually transmitted through that shaft; an electrical nameplate power may require a documented efficiency adjustment before it becomes shaft power.

Worked numbers are illustrative. Use your own operating conditions and documented material/process data.

Required inputs

  1. Transmitted mechanical power in W or kW.
  2. Rotational speed in rpm, greater than zero.
  3. Any specified transient or service load case, kept distinct from steady operation.

Governing equations

P = Tω

ω = 2πN / 60

T(N·m) = 60000P(kW) / (2πN)

Variables and units

  1. P: mechanical power; T: torque about the shaft axis.
  2. ω: angular speed in rad/s; N: revolutions per minute.

Assumptions

  1. Power and speed describe the same shaft and operating condition.
  2. The expression is a steady energy-rate relation, not a start-up torque model.

Calculation workflow

  1. Identify the shaft location and any upstream losses.
  2. Convert rpm to angular speed and divide power by angular speed.
  3. Check the answer against the reverse calculation P = Tω.

Worked example

  1. At 15 kW and 1440 rpm, T = 99.471839 N·m.
  2. At 720 rpm with the same 15 kW, T = 198.943679 N·m.
  3. Reverse check: 99.471839 × 150.796447 ≈ 15000 W.

Limitations

  1. At zero speed, this equation cannot determine static or stall torque. Use an actual motor/drive torque curve.
  2. Do not infer peak starting, braking or reversing torque from one steady rating.

Common mistakes

  1. Treating rpm as rad/s.
  2. Using electrical input power as transmitted mechanical power without stating losses.
  3. Presenting the rounded 9550 coefficient as exact.

Practical interpretation

A gearbox can raise torque while reducing speed; it does not create power. If efficiency is included, state whether it applies to power upstream or downstream of the gearbox. The common 9550 coefficient is rounded from 60000/(2π).

Related formulas

Power, speed and torque →

Engineering equation and unit reference tables →

Related workspace

Open Shaft Engineering →

Sources and reference basis

Equations and worked examples are independently explained here. References reviewed 2026-10-17; no copyrighted standard tables are reproduced.