Motor Control Tools

Ke / Kt Constant Converter

Convert between the back-EMF constant (Ke) and torque constant (Kt) of a PMSM or BLDC motor.

Convention matters

Ke and Kt are frequently misquoted because manufacturers, textbooks and firmware libraries all define them differently — RMS vs. peak, phase vs. line-to-line, mechanical vs. electrical speed. Select exactly how your value is defined below. Guessing wrong silently scales the result by √2, √3, the pole pair count, or some combination of the three.

Quantity
V RMS (LL) / krpm

Required for this convention (poles ÷ 2).

Flux linkage

Weber0.01Wb
Volt-seconds / radian0.01V·s/rad

Ke representations

Peak, phase-neutral / elec. rad/s0.01V/(rad/s)
RMS, line-line / krpm5.13V/krpm
RMS, phase-neutral / krpm2.962V/krpm
Peak, line-line / krpm7.255V/krpm
Peak, phase-neutral / krpm4.189V/krpm

Kt representations

Per peak phase amp0.06N·m/A
Per RMS phase amp0.085N·m/A

Ke / Kt relationship

Canonical form

Kt = 1.5 · P · Ke

Kt
Torque constant, per peak phase amp [N·m/A]
P
Pole pairs [—]
Ke
Back-EMF constant, peak, phase-neutral, per electrical rad/s [V/(rad/s)]

Kt = Ke (no 1.5·P factor) is a common shortcut, but only holds for a single-phase actuator. For a 3-phase PMSM under vector control the 1.5 × P factor above the calculator applies is required — datasheet Ke/Kt values almost never arrive in this exact convention, which is why they need converting first rather than compared directly.

Worked example

A motor datasheet quotes Ke = 5.13 V RMS (line-to-line) / krpm, pole pairs = 4:

  • Convert to peak, phase-neutral, per electrical rad/s (the canonical form above) using the converter.
  • That canonical Ke is numerically equal to the flux linkage λm in Wb (same relation used throughout this toolkit).
  • Kt (per peak phase amp) = 1.5 × 4 × λm — computed automatically once pole pairs are entered.

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