Measuring Motor Kv, Kt, and Ke: Bench Methods and Datasheet Conventions

Separate the Ideal Model from the Test

The Motor Electrical Design Guide introduces torque, back EMF, current, and power relationships. Here the engineering task is different: extract a usable constant from measured hardware without silently treating terminal voltage as internal EMF or measured shaft torque as ideal electromagnetic torque. Specify motor type, winding or brush connection, electrical drive state, shaft speed direction, ambient and winding temperature, and instrument calibration before collecting data.

Measure Back EMF Before Calling It Kv

For a brushed DC motor, drive the shaft mechanically with terminals open and measure generated terminal voltage at several stable RPM points. A high-impedance measurement avoids significant generator loading. Plot E against mechanical angular speed and fit a slope, rather than dividing one noisy point. Verify both rotation directions and subtract any instrument offset. A BLDC motor requires its own documented waveform and winding convention: line-to-line is not phase-to-neutral, and peak is not RMS. The simple Motor Kv & Kt Calculator is a conversion aid after those definitions have been reconciled, not a substitute for the phase/line conversion model.

For example, suppose an open-circuit DC-equivalent back EMF is 10.0 V at 1000 RPM after offset correction. Then Kv = 100 RPM/V, mechanical angular speed is 104.7198 rad/s, and Ke = 10/104.7198 ≈ 0.095493 V/(rad/s). The corresponding ideal Kt is 0.095493 N·m/A. At 2 A, the ideal electromagnetic torque estimate is 0.19099 N·m; do not present that as measured shaft torque. Repeat the slope check at several speeds and temperatures before using the fitted value in a driver design.

Use Loaded Tests to Expose the Voltage Error

A spinning motor under load draws current. Winding IR drop, brush contact or inverter drop, and source sag consume terminal voltage, so RPM divided by supply voltage generally underestimates ideal Kv. Measure terminals at the motor, current, winding resistance at the applicable temperature, and the drive-state voltage. A 12 V terminal reading, 2 A, and 0.5 Ω winding resistance already imply roughly 1 V of winding drop before other losses; if drive drop is negligible, E is nearer 11 V than 12 V. Resistance rises when a copper winding heats, so a cold bench estimate can miss the hot operating point. Use the DC Motor Back EMF Calculator to screen compatible electrical quantities, then compare with measured voltage and speed.

Estimate Kt from a Torque-Current Slope

Use a calibrated brake or dynamometer and measure shaft torque and current over a short, safe operating range. Fit the slope after accounting for no-load friction torque; one point near stall can overheat the winding and confound the result. For a brushed motor with approximately constant flux, changes in torque divided by changes in armature current can estimate an effective shaft torque constant over that range. The ideal electromagnetic Kt inferred from Ke need not equal this shaft slope because friction, iron loss, and other parasitics separate electromagnetic from delivered torque. For BLDC machines, specify whether reported current is phase, line, DC-bus, RMS, or peak, and whether torque is per-phase-model or shaft output before comparing values.

Reconcile Datasheet Conventions and Uncertainty

Record a unit ledger beside every imported constant. RPM/V, rad/s/V, V/krpm, and V/(rad/s) are different numeric scales. A BLDC line-to-line peak back-EMF rating cannot be substituted into a phase-neutral RMS model. If a datasheet omits the convention, request clarification or measure the motor. Compare constants at the same temperature and test method; manufacturer tolerances and thermal drift can be material. Treat disagreement as a prompt to inspect definitions, not automatic evidence that either the calculator or the device is defective. Use fitted slope uncertainty, tachometer resolution, voltage calibration, torque-fixture calibration, and temperature spread to form a realistic design range.

• Keep raw RPM, voltage, torque, current, and winding temperature measurements alongside fitted constants.
• Use a least-squares slope across multiple stable points; inspect curvature rather than forcing a linear model outside its valid region.
• Do not energize an unguarded spinning motor or hold it at stall for a constant measurement.
• Repeat cold and thermally stabilized tests when speed regulation, torque limit, or commutation margin is tight.
• Verify controller and datasheet phase-current conventions before copying Kt into a current-loop limit.

Common Mistakes

• Calling supply voltage back EMF in a loaded run.
• Using one noisy no-load point as the complete Kv curve.
• Mixing electrical and mechanical RPM or forgetting pole-pair count.
• Mixing BLDC line-to-line and phase-to-neutral voltage.
• Mixing peak and RMS current or voltage constants.
• Equating shaft torque with ideal electromagnetic torque.
• Comparing cold catalog constants to hot production measurements.
• Treating RPM/V as numerically reciprocal to N·m/A without 60/(2π).
• Measuring near stall without thermal or mechanical protection.
• Assuming a simple DC-equivalent model captures inverter harmonics and saturation.

Engineering Sources

maxon motor data and simulation guidance describes motor-constant tolerances and temperature-dependent speed-torque behavior. Microchip motorBench guidance documents why back-EMF measurements need phase/line and peak/RMS definitions. These sources inform the measurement boundaries; the equations above use the explicitly stated ECParts DC-equivalent convention.