Calculate Km from torque constant and equivalent winding resistance, Kt from torque/current, or Ke and Kv from generated back EMF and speed. Use consistent permanent-magnet DC-equivalent measurements.

Torque per square root of winding copper loss.

Use consistent permanent-magnet DC-equivalent measurements. BLDC phase/line and RMS/peak ratings require the manufacturer’s conversion. Use generated back EMF, not loaded terminal voltage.

The resistance must use the same current and copper-loss basis as Kt.

Motor Constant Formula

The following formula is used to calculate the motor constant (also called a motor “figure of merit” based on copper loss).

Kₘ = (Kₜ) / (√(R)) = (T) / (√(Pcu)), Pcu = I²R, T = Kₜ I

Variables:

  • Km is the motor constant (Nm/√W)
  • Kt is the torque constant (Nm/A)
  • R is the equivalent winding resistance (Ω), using the same current and copper-loss basis as Kt
  • Pcu is the copper (I2R) loss in the windings (W)
  • T is torque (N·m), and I is current (A)

To calculate the motor constant, divide the torque constant by the square root of the winding resistance. Equivalently, if you know the copper loss at a given operating point, you can compute Km = T / √Pcu. Note: This definition uses copper loss (I2R), not mechanical output power (Tω). BLDC phase/line and RMS/peak conventions can require manufacturer-specific conversion; raw line-to-line resistance cannot always be inserted directly.

What is a Motor Constant?

The motor constant (Km) is a value that represents how much torque a motor can produce per square root of copper loss in the windings. A higher motor constant means the motor can produce more torque for the same I2R heating, assuming similar operating conditions. This figure of merit does not include other losses (iron/core loss, windage, friction, controller losses), so it is not a complete measure of overall system efficiency.

How to Calculate Motor Constant?

The following steps outline how to calculate the Motor Constant.

  1. Determine the torque constant (Kt) of the motor (for example, from a datasheet or from torque/current measurements using Kt = T/I).
  2. Determine equivalent winding resistance R in ohms (Ω), matching the datasheet current convention used for Kt. For Ke/Kv modes, enter generated back EMF, not uncorrected loaded terminal voltage.
  3. Calculate the motor constant using Km = Kt / √R.
  4. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Torque Constant (Kt) = 0.10 Nm/A

Winding Resistance (R) = 0.50 Ω

With a consistent current basis, Km = 0.10 / √0.50 ≈ 0.1414 N·m/√W. The ideal DC-equivalent relation Kt = Ke = 60/(2πKv) requires compatible SI definitions; it is not a universal BLDC conversion.