# Motor torque calculation, about the units

This link shows a motor torque, power, and speed relationship, as shown below: With regards to its units, how does kW and RPM become equivalent to N.m?

It's quite a simple calculation, especially if you're used to dealing with metric units:

$$Power=Torque \times angular Speed$$ (rotational equivalent of $$force \times speed$$)

$$Power [kW]= Torque [Nm] \times Speed [\frac{rev}{min}] \times \frac{1}{60} [\frac{min}{seconds}] \times 2π [\frac{rad}{rev}] \times 10^{-3} [\frac{kW}{W}]$$

RPM= rev/min

Finally you clear torque and get the result:

$$Torque [Nm]=\frac{(60 \times \frac{1000}{2π})\times Power[kW]}{ Speed [rpm]}$$

And 60,000/2*π is actually 9.5488.

• Equivalent explanation with different constants for the other units shown, if you are familiar and as engineers even if you are not... – Solar Mike May 20 '19 at 6:15
• @Sam Thanks. Thinking of it as Power = Force x Speed also helped, (physics.nist.gov/cuu/Units/units.html), where I can see the units [Nm] x [1/s] being the same as [N] x [m/s] = [W], based on their SI-derived units. – plu May 21 '19 at 19:51
• @SamFarjamirad Yes, [m kg s^{-2}] x [ m s^{-1}] works out to be [m^{2} kg s^{-3}] = [W]. – plu May 21 '19 at 20:37

With regards to its units, how does kW and RPM become equivalent to N.m?

Power = force * speed. When you're dealing with rotary motion, power = torque * rotation rate. Their calculation of torque from HP and RPM is just a matter of getting the units consistent, and solving for torque (noting that for the power as a function of torque and rotation rate, the rotation rate must be in radians/second).