Machines & Drives
Induction Motor Equivalent Circuit Solver
Stator current, torque, efficiency, and power factor from R1, X1, R2', X2', Xm at a given slip.
About this calculator
The IEEE approximate per-phase equivalent circuit models an induction motor as a stator impedance (R1 + jX1) in series with the parallel combination of the magnetizing reactance (jXm) and the rotor branch referred to the stator (R2'/s + jX2'), where s is slip. Solving this circuit at a given slip gives the stator current, rotor current, air-gap power, developed torque, and efficiency — the standard analysis taught in every electric machinery course and used to predict how a motor performs away from its nameplate rated point.
Enter the five equivalent-circuit parameters (typically from a manufacturer datasheet, a locked-rotor/no-load test, or a machines textbook problem), the supply voltage and its connection, and the slip you want to evaluate. The calculator solves the circuit with complex (phasor) arithmetic and shows the intermediate impedances so you can check the work by hand.
This is the approximate circuit — it neglects core-loss resistance and places the magnetizing branch directly across the input terminals rather than between the stator and rotor impedances, which introduces a small error at high slip but is standard practice for hand analysis. Rotational losses (friction, windage, and stray load loss) are not modeled, so the torque and efficiency shown are developed (air-gap-derived) values, slightly higher than the true shaft values a dynamometer would measure.
Assumptions
- IEEE approximate equivalent circuit: magnetizing branch placed directly across the input terminals, core-loss resistance neglected.
- Balanced three-phase sinusoidal steady-state operation at the stated slip.
- Rotational losses (friction, windage, stray load loss) are not modeled — torque and efficiency shown are developed (air-gap) values, not shaft values.
- Equivalent-circuit parameters are treated as constant (no deep-bar or temperature-dependent rotor resistance effects).
When to use this calculator
Appropriate for
- Estimating steady-state torque, current, losses, and efficiency of a three-phase induction motor from its equivalent-circuit R/X parameters
- Studying how a parameter change (rotor resistance, slip, voltage) shifts performance
- Preliminary machine analysis where the single-cage equivalent circuit is an adequate model
Not suitable for
- Deep-bar or double-cage rotors, where a single rotor branch misrepresents the starting region
- Transient events — starting inrush dynamics, reacceleration, or drive-fed operation with non-sinusoidal supply
- Nameplate certification or thermal/derating decisions for a specific installed machine
What this calculator does not cover
- Steady-state, per-phase model with constant parameters — deep-bar (skin) effect, saturation, and temperature all change R2′ and the reactances with slip and load.
- Stray-load loss and friction/windage are not modeled separately, so the efficiency figure is approximate.
- Assumes a balanced sinusoidal supply — results do not apply directly on a PWM drive waveform with significant harmonic content.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What is the difference between developed torque and shaft torque?
Developed torque is derived from air-gap power and represents everything the rotor produces electromagnetically. Shaft (output) torque is developed torque minus the mechanical losses from friction, windage, and stray load loss, which this calculator does not model since they require additional test data.
Where do R1, X1, R2', X2', and Xm come from?
They're typically derived from a DC test (R1), a locked-rotor test (R2', X1, X2' via the standard IEEE split), and a no-load test (Xm), or provided directly on a manufacturer datasheet or in a textbook problem.
Why is the calculator's efficiency higher than the nameplate efficiency?
The approximate equivalent circuit doesn't include core loss or rotational losses, so the efficiency computed here (developed power / input power) will read a few points higher than the nameplate efficiency, which includes those losses.
References
- Chapman, S., Electric Machinery Fundamentals, 5th ed., Ch. 6
- Fitzgerald, Kingsley, Umans, Electric Machinery, 6th ed., Ch. 6
- IEEE Std 112 — Test Procedure for Polyphase Induction Motors and Generators
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