Where does the formula for calculating torque come from?


I was wondering where the formula :arrow_down:️ comes from.


Cheers Stijn

The full formula is:

T = \frac{3}{2} \frac{1}{\sqrt{3}} \frac{60}{2\pi} \; \frac{I}{K_v}
  • Factor \frac{3}{2} is from the brushless motor torque equation (eqn 2.30 of this paper).
  • Factor \frac{1}{\sqrt{3}} is from converting line-line voltage (which is what is commonly used by hobby motor manufacturers in the determination of the Kv) to phase voltage (see here).
  • Factor \frac{2\pi}{60} is to convert from rpm to rad/s, which we need to do to get the torque constant from the voltage constant, due to the voltage constant being specified in units of RPM/V. (See here).

Thanks for the info

Cheers Stijn

Is the current I is Iq_measured in ODrive??


awesome! But why is there no factor of the pole pair or is this for a machine with 1 pole pair?

Thanks and with best regards

Pole pairs is included in the “velocity constant” or “voltage constant” Kv.
More poles = less RPM/volt = more Nm/A

As Oskar has just shown, the torque constant is proportional to the inverse of the velocity constant.

You need to know pole pairs to calculate Kv, of course, but the formula above assumes you already know that, from the spec of the hobby motor you are using.
Plus you can measure an approximate figure for Kv easily enough with a hobby ESC, a bench power supply and an optical tacho

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Okay, I understand now.

Thanks :slight_smile:

Hi, I’ve made some calculations to see where this formula comes from

Google Photos

(Tap picture to see it complete)

Carelsbergh Stijn


I trying to understand this formula and I’m bit confused. I don’t get why there is the “line-to-line” coefficient to Phase coefficient? During normal operation wouldn’t a phase be floating which would mean that the line-to-line current be equal to the phase current? I’ve tried looking at the number I got from a torque test I’ve done with a AXI 2814-16 motor. It’s given parameters are Kv: 1035 RPM/V, Internal Resistance: 0.033 Ohm and I0 of 1A. At full throttle with a source DC Voltage of 14.35V and a current consumption of 26.65A it had a torque of 0.24 N·m and a RPM of 11829. Using the following equation Kt = 60 / (Kv * 2 * pi) provides a Kt = 0.009 which matches 0.24 N·m / 26.65A = 0.009 while using the fomula Kt = 8.3/ Kv = 0.008 doesn’t match. I’m not sure what am I missing?

I think your calculations are equal if you would consider measurement and constants error, for example, Kv is not a perfectly constant value. Also, these are only basic calculations, I have a more complicated version but I couldn’t reach the end on those. If you want I will find them and send them.

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