Induction Motor Torque-Speed Curve Generator

An induction motor's torque varies with slip across its entire operating range, from locked rotor (s = 1) through breakdown (pull-out) torque down to the light-load region near synchronous speed. Using the Thevenin equivalent of the stator circuit as seen from the rotor branch, torque at any slip is T(s) = 3·V_th² · (R2'/s) / [ω_sync · ((R_th + R2'/s)² + (X_th + X2')²)] — the standard closed-form result derived from the induction motor equivalent circuit.

This calculator sweeps that formula across the full slip range to plot the complete torque-speed curve, and marks three points every machines engineer looks for: starting (locked-rotor) torque, breakdown (maximum, pull-out) torque and the slip it occurs at, and the rated torque at the slip you specify. The breakdown slip has a closed-form solution too — s_maxT = R2' / √(R_th² + (X_th + X2')²) — shown in the worked steps alongside the Thevenin parameters.

Use this to evaluate whether a motor's starting torque clears a load's breakaway torque, whether there's enough margin between rated and breakdown torque for transient overloads, or to compare how changing rotor resistance (a common wound-rotor or NEMA design-class question) reshapes the curve. Like the equivalent-circuit calculator, this uses the standard approximate circuit and does not include rotational losses or deep-bar rotor effects, so it represents developed torque, not measured shaft torque.