How do you estimate motor torque using a torque constant?

• A. Torque = Kt × current (accounting for gear ratio as needed).
• B. Torque = current / Kt.
• C. Torque is independent of current.
• D. Torque = Kt + current.

Answer: (B)

The key idea is that motor torque grows in direct proportion to the current, with the torque constant Kt telling you how much torque you get per amp. So the torque at the motor shaft is T = Kt × I. If you’re using a gearbox, you multiply by the gear ratio to get the output torque (assuming ideal gearing), so T_out = gear_ratio × (Kt × I).

Why the other forms aren’t right: dividing current by Kt would yield a quantity with the wrong units and contradicts the definition of the torque constant; torque changes with current, so it isn’t independent of current; and adding Kt to the current mixes unlike quantities.