DC Motor Torque Calculator and Formula

Calculate a DC motor’s torque by multiplying its torque constant by armature current: T = Kt × I. Enter the motor’s torque constant and current to get torque in newton-metres; this calculator also converts the result to pound-feet.

Formula

The ideal electromagnetic torque of a permanent-magnet DC motor, or a motor whose field flux is held constant, is:

T = Kt × I

• T is torque in newton-metres (N·m).
• Kt is the motor’s torque constant in newton-metres per ampere (N·m/A).
• I is armature current in amperes (A).

For the second calculator output, torque is converted using 1 N·m = 0.737562149 lb·ft. The calculator treats the entered current as a nonnegative magnitude. The signs of current and torque depend on the chosen direction convention; reversing current reverses torque in a fixed magnetic field.

Worked Example

Using the calculator’s defaults, Kt = 0.05 N·m/A and I = 2 A:

1. Multiply the torque constant by current: 0.05 × 2 = 0.10 N·m.
2. Convert to pound-feet: 0.10 × 0.737562149 = 0.0737562149 lb·ft.
3. Rounded to three decimal places, the outputs are 0.100 N·m and 0.074 lb·ft.

What the Torque Constant Means

A motor’s torque constant describes how much electromagnetic torque it produces per ampere under specified magnetic conditions. A larger Kt means more torque for the same current. Manufacturers may give the value in N·m/A, oz·in/A, or another unit, so convert it before using this calculator. For example, 1 N·m/A is approximately 141.612 oz·in/A.

In a permanent-magnet motor, the magnetic field is supplied by permanent magnets. In a separately excited or shunt-wound motor, field current can affect the magnetic flux; the simple formula applies when that flux is effectively constant. In a series-wound motor, flux changes with armature current, especially before magnetic saturation, so torque may not remain directly proportional to current over its full operating range.

Motor data sheets sometimes provide a torque constant, and sometimes provide speed and voltage information instead. In consistent SI units, the back-electromotive-force constant and torque constant have numerically equal values when expressed as V·s/rad and N·m/A, respectively. This relationship assumes the usual motor conventions and ideal electromagnetic conversion; check the manufacturer’s definitions and units.

When to Use This Calculation

Use the current-based equation to estimate a motor’s electromagnetic torque when its torque constant and operating current are known. It is useful for comparing operating points, estimating torque changes as current changes, and understanding why a motor controller’s current limit can limit available torque.

The result is not automatically the torque available at a particular shaft or wheel. Gearboxes can change output torque and speed, while friction and other losses reduce the torque delivered. If a gear reduction ratio is defined as motor speed divided by output speed, ideal output torque is motor torque multiplied by that ratio; actual output is lower by the transmission’s efficiency. Also distinguish motor-shaft torque from load torque and from starting, continuous, or peak torque ratings.

Current, Speed, and Real Motor Limits

For a fixed-field DC motor, torque is approximately proportional to armature current, but current is not simply the same as supply voltage. As the motor turns, it generates back EMF that opposes the applied voltage. At a given supply voltage, this generally leaves less voltage available to drive current as speed rises. At low speed or stall, back EMF is small, so current can rise sharply unless limited by the supply, winding resistance, or controller.

The equation estimates electromagnetic torque; it does not establish that a motor can safely sustain that torque. Continuous operation is limited by factors such as winding heating, cooling, commutation, mechanical strength, and the manufacturer’s ratings. Stall torque is often associated with stall current and should not be treated as a continuous operating point. Use the specified current and duty-cycle limits for the particular motor and drive rather than inferring safe operating limits from this calculator.

Common Errors and Formula Limits

• Mixing units: Current must be in amperes and Kt in N·m/A for the first output to be in N·m. Convert milliamperes to amperes by dividing by 1,000.
• Using the wrong current: The relevant value is armature current, not necessarily the power supply’s rated current or a controller’s maximum setting. Current varies with load and operating conditions.
• Confusing torque and power: Torque is a turning effect, measured in N·m or lb·ft. Mechanical power depends on both torque and rotational speed: P = T × ω, where ω is in radians per second and P is in watts.
• Assuming exact linearity: The simple equation assumes constant magnetic flux and a suitable torque constant. Temperature, magnetic saturation, brush and commutation effects, and measurement conventions can cause practical results to differ.
• Rounding too early: Keep the full value through conversions and round only the displayed answer. Small differences in a final digit can result from different rounding or conversion precision.

Frequently Asked Questions

How do you calculate DC motor torque from current?
Multiply armature current in amperes by the motor’s torque constant in N·m/A. For example, a 0.05 N·m/A constant at 2 A gives 0.10 N·m under the constant-field assumption.

Can I calculate torque from motor power and RPM?
Yes, if mechanical output power and speed are known: T = P/ω. In practical units, T in N·m is approximately 9,550 × power in kW divided by speed in rpm. Use mechanical output power, not electrical input power, unless losses are accounted for.

Is torque the same at every motor speed?
No. A fixed-field DC motor’s torque is tied mainly to current, but the current available at a given speed depends on voltage, back EMF, resistance, and the controller. A motor’s continuous and peak torque limits also vary with operating conditions.

What is the difference between stall torque and rated torque?
Stall torque is the torque when the rotor is not turning, generally associated with stall current. Rated torque refers to a specified operating condition and may be intended for continuous use. Consult the motor’s documentation; stall torque should not be assumed to be a continuous rating.

Why does my measured torque differ from the calculation?
The entered torque constant or current may not match the actual operating conditions. Flux variation, heating, measurement uncertainty, gearbox losses, and whether the measurement is taken at the motor shaft or after a transmission can all affect the comparison.

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in kt | Torque constant | N·m/A | 0.05 | 0
in i | Armature current | A | 2 | 0
out torque | Motor torque | N·m | kt * i | 3
out torque_lbf_ft | Motor torque | lb·ft | kt * i * 0.737562149 | 3