Motor Torque

τ = Kt × I

Quick answer

This calculator solves τ = Kt × I for Torque. With Torque Constant 2.2 N·m, Current 2 A, the result is 4.4 N·m. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Torque (N·m)
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Formula

τ = Kt × I

Description

The torque produced by a DC motor is directly proportional to the armature current, with the torque constant Kt as the proportionality factor. Kt is a fundamental motor parameter specified in the datasheet and depends on the motor's magnetic field strength, number of turns, and geometry. Interestingly, the torque constant Kt (in N·m/A) is numerically equal to the back-EMF constant Ke (in V/(rad/s)) when both are expressed in SI units. This duality arises from energy conservation in electromechanical conversion.

Variables

  • τ — Motor torque (N·m)
  • Kt — Torque constant (N·m/A)
  • I — Armature current (A)

Practical Notes

For BLDC motors, Kt usually refers to the peak torque per phase current. Stepper motors specify holding torque (at rated current with rotor locked) and detent torque (with no current). Motor current increases under load, so ensure the driver and wiring can handle the maximum expected current. Continuous torque rating is limited by thermal dissipation in the windings.

Symbols and units

Symbol Meaning Default unit Accepted units
tau Torque N·m N·m, mN·m
Kt Torque Constant N·m N·m, mN·m
I Current A pA, nA, µA, mA, A, kA

Step by step

  1. 1. What you know: Torque Constant 2.2 N·m, Current 2 A
  2. 2. The relation: τ = Kt × I
  3. 3. Substitute: Kt = 2.2 N·m, I = 2 A
  4. 4. Result: Torque = 4.4 N·m

Worked examples

Minimum range

Given: Torque Constant 11 mN·m, Current 2 mA

Result: Torque = 0.022 mN·m

Low range

Given: Torque Constant 110 mN·m, Current 20 mA

Result: Torque = 2.2 mN·m

Typical

Given: Torque Constant 2.2 N·m, Current 2 A

Result: Torque = 4.4 N·m

High range

Given: Torque Constant 110 N·m, Current 100 A

Result: Torque = 11000 N·m

Maximum range

Given: Torque Constant 1100 N·m, Current 1 kA

Result: Torque = 1.1 × 10⁶ N·m

Solving for each variable

Solve for Torque

Torque Constant 11 mN·m, Current 2 mA → 0.022 mN·m

Solve for Torque Constant

Torque 5 mN·m, Current 2 mA → 2.5 N·m

Solve for Current

Torque 5 mN·m, Torque Constant 11 mN·m → 0.4545 A

How Torque changes with Torque Constant

Torque Constant (input) Torque (result)
0.484 N·m 2.13 N·m
1.21 N·m 5.324 N·m
2.42 N·m 10.65 N·m
3.63 N·m 15.97 N·m
4.84 N·m 21.3 N·m
7.26 N·m 31.94 N·m
9.68 N·m 42.59 N·m
19.36 N·m 85.18 N·m
33.88 N·m 149.1 N·m
48.4 N·m 213 N·m

The same result in other units

Unit Value
N·m 4.4
mN·m 4400

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Frequently asked questions

How do you calculate Motor Torque?

Use τ = Kt × I. With Torque Constant 2.2 N·m, Current 2 A, Torque works out to 4.4 N·m.

What is the formula for Motor Torque?

The formula is τ = Kt × I. The torque produced by a DC motor is directly proportional to the armature current, with the torque constant Kt as the proportionality factor.

How do you find Torque Constant when you know the other values?

Rearrange for Torque Constant: with Torque 5 mN·m, Current 2 mA, Torque Constant is 2.5 N·m.

How do you find Current when you know the other values?

Rearrange for Current: with Torque 5 mN·m, Torque Constant 11 mN·m, Current is 0.4545 A.

What units does Motor Torque use?

Torque is shown in N·m, mN·m. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Motors & Mechanical formulas →
Motor Mechanical Power Motor Torque Motor Speed Gear Ratio Output Torque Back-EMF Voltage Motor Efficiency Rotational Dynamics Stepper Motor Step Angle

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