# How to calculate the torque constant for a BLDC motor

I am designing a 12lb hobby robot with a 1000Kv BLDC motor at 14.8V nominal voltage and stall torque of 30A. How do I solve for the torque constant. I have seen equations where Kt(torque constant) = 1/Kv. And also equations where Kt = 30/pi(Kv). Which is the most accurate equation? Thank you,

• Kt = 1/Kv. If you are using SI units throughout. (As it must be : Torque * Speed = power = Voltage * Current). The other equation differs only in a constant factor : therefore it is equally accurate, if you can figure out which system of units it is in.
– user16324
Nov 9, 2020 at 14:57
• A word of caution on Kv. These equations work when Kv is measured correctly, which means that the actual back EMF is measured when the motor is being rotated by an external force. Sometimes people measure it other ways, such as by running the motor no-load with an ESC. In this method you divide no load speed in RPM/Battery voltage. That may be useful but it is not correct for calculating torque. Nov 9, 2020 at 18:08

The equation for the torque constant of a BLDC motor: $$\K_{\tau} = \frac{60}{2{\pi}K_{v(RPM)}} = \frac{1}{K_{v(SI)}} \$$, where $$\K_{\tau}\$$ is the torque constant in $$\\frac{N \cdot m}{A}\$$, and $$\K_v\$$ is the speed constant, in either rpm or rad/s.
EDIT: The answer above is guilty of a common misconception regarding the measurement of the motor torque constant. The Kv rating commonly provided by motor sellers is obtained with this method, but it differs from the true value by a factor of $$\ \sqrt{2}\$$ for Wye wound motors, and $$\ \sqrt{\frac{2}{3}} \$$ for delta wound motors. See this video for further details.