Electric Motor Torque Calculator

The electric motor torque calculator provides the relation between rotational speed, power, and torque in the shaft.

Shaft torque49.3929 N·mP/ω, and the handy form is 9550 × kW / rpm which gives 49.3966 N·m — the 9550 is just 60000/2π

In pound-feet36.4303 lb·ft

Angular velocity151.8436 rad/s

Torque at half the speed, same power98.7858 N·mDOUBLE — torque and speed trade off exactly at constant power, which is the whole purpose of a gearbox

Synchronous speed1,500 rpm120f/poles — the speed of the rotating field, which an induction motor can approach but never reach

Slip3.3333%an induction motor MUST slip, because without relative motion there is no changing flux, no induced rotor current and therefore no torque at all

Slip speed50 rpm

Rotor frequency1.6667 Hzthe frequency the rotor actually sees

Electrical input power8.427 kWat 89% efficiency

Losses as heat0.927 kWall of it ends up warming the motor and its surroundings

Line current, three phase14.3097 AP/(√3 V pf) — the √3 is what distinguishes a three-phase calculation from a single-phase one, and omitting it is the classic error

Apparent power9.9141 kVAwhat the supply must be sized for, which exceeds the real power by the power factor

The formula

τ = P/ω = 9550 P_kW/rpm; slip = (n_s − n)/n_s

Torque and speed trade at constant power

Power is torque times angular velocity, so at a fixed power halving the speed doubles the torque exactly. That is the entire purpose of a gearbox: it cannot create power, only redistribute it between the two. The convenient engineering form is 9550 times kilowatts over rpm, where the 9550 is simply 60000/2π.

An induction motor must slip

The rotating field turns at 120f/poles, but the rotor can never quite reach it. If it did, there would be no relative motion, no changing flux through the rotor, no induced current and therefore no torque at all. The motor would immediately fall back. Slip of a few percent under load is not inefficiency — it is the mechanism.

Drive the rotor ABOVE synchronous speed and the slip reverses sign: the machine becomes a generator and feeds power back into the supply, which is how wind turbines using induction generators work.