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.
Required for this convention (poles ÷ 2).
Flux linkage
Ke representations
Kt representations
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.
Related calculators
Motor Constant Converter
Convert Ke, Kt and flux linkage across RMS/peak, phase/line-line and speed-basis datasheet conventions, with every assumption stated explicitly.
Electrical Speed Calculator
Convert mechanical speed to electrical speed and frequency using the motor's pole pair count.
PMSM Electromagnetic Torque
Compute electromagnetic torque from d/q-axis currents, flux linkage and inductances.