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.
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
The two relations this converter uses
Back-EMF
Epeak,phase = ωe · λf
- Epeak,phase
- Peak, phase-to-neutral back-EMF [V]
- ωe
- Electrical angular speed [rad/s]
- λf
- Peak permanent-magnet flux linkage [Wb]
Standard result for a sinusoidal PMSM. This is also why Ke expressed as peak, phase-neutral, per electrical rad/s equals λf exactly — it's the same relation solved for λf.
Torque
T = 1.5 · P · λf · Iq
- T
- Electromagnetic torque [N·m]
- P
- Pole pairs [—]
- Iq
- Peak q-axis current (Id = 0, MTPA) [A]
Amplitude-invariant Park transform convention. Solving for Kt = T / Iq gives Kt = 1.5 · P · λf — every Kt and per-krpm Ke output on this page is this pair of relations applied algebraically forward or backward, nothing else.
Why Ke and Kt values often look inconsistent in datasheets
A popular rule of thumb says "Kt equals Ke in consistent SI units." For a 3-phase PMSM under vector control, that is only true for one specific pair of definitions: Kt as newton-meters per peak phase amp, and Ke as peak, phase-to-neutral volts per electrical rad/s. In that specific pairing, Kt = 1.5 × P × Ke — not Kt = Ke — because torque production sums contributions from all three phases (the 1.5 factor) and because Ke is usually reported against a different speed and current basis than Kt.
Datasheets almost never use that pairing. Ke is typically given in volts per 1000 mechanical RPM (not electrical rad/s), and as often as not it's the RMS, line-to-line value read straight off an oscilloscope — because that's what's easy to measure by spinning the shaft and probing two motor leads. Kt, meanwhile, is usually quoted per RMS phase amp, since that's what a current sensor or multimeter reads. Converting mechanical RPM to electrical rad/s needs the pole pair count; converting line-to-line to phase-neutral needs √3; converting RMS to peak needs √2 — and each of those factors is a completely separate correction from the 1.5 × P that relates Kt to Ke in the first place. Skip any one of them, or apply the "Kt = Ke" shortcut to values that were never in that convention, and the result is quietly wrong by a factor that looks plausible enough to miss.
This calculator never applies that shortcut. It converts every input back to permanent-magnet flux linkage (λf, in Wb) using only the two relations above, then derives every output from that same λf — so every representation you see is mutually consistent, and pole pairs are only requested when a relation actually needs them.
Worked example
A datasheet quotes Ke = 5.13 V RMS (line-to-line) / krpm, pole pairs = 4:
- Flux linkage λf ≈ 0.01 Wb (the canonical pivot every other value is derived from)
- Kt, per peak phase amp: 1.5 × 4 × 0.01 = 0.06 N·m/A
- Kt, per RMS phase amp: 0.06 × √2 ≈ 0.085 N·m/A
Related calculators
Ke / Kt Constant Converter
Convert between the back-EMF constant (Ke) and torque constant (Kt) of a PMSM or BLDC motor.
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.