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Torque of a DC Motor

Torque is the turning force a motor produces at its shaft. For a DC motor, it equals a constant times the magnetic flux times the armature current. In simple terms: more current means more torque, and a stronger magnet also means more torque. Think of tightening a bolt: the harder you push (more current), the more turning force you get. This is why a motor draws a big surge of current when it first starts or when it is heavily loaded.

Written by the Vorzep Team

Electric Machines DC Motors

DC Motor Torque Calculator

Torque, armature current, flux and machine constant, with power, back EMF and gearbox output.

k · Φ · IaWinding constantSeries & fixed fluxPower & gearbox
T = k · Φ · Ia

Inputs

Results

Variables

Symbol Quantity Unit
T Torque N·m
k Motor constant N·m/(Wb·A)
Φ Flux per pole Wb
I_a Armature current A

What it means

The torque T of a DC motor is given by T = k·Φ·I_a, where k is a constant depending on motor construction, Φ is the magnetic flux per pole, and I_a is the armature current. Torque is proportional to the product of flux and armature current. In a shunt motor, Φ is nearly constant, so torque is directly proportional to armature current. In a series motor, Φ is proportional to I_a, so torque is proportional to I_a². This is used in traction applications where high starting torque is needed. The torque equation is derived from the Lorentz force on the armature conductors. Example: A motor with k=0.5, Φ=0.02Wb, and I_a=10A produces T = 0.5 * 0.02 * 10 = 0.1 N·m. To increase torque, either increase flux or armature current.

Worked example

DC Motor Torque – Practical Example

Real‑World
Scenario: A DC motor has a torque constant k·Φ = 0.05 N·m/A. If armature current is 4 A, find the torque.
ParameterValue
k·Φ0.05 N·m/A
Ia4 A
FormulaT = k·Φ·Ia
1T = 0.05 × 4 = 0.2 N·m
Final Design T = 0.2 N·m ✓ Torque
Why: Torque in a DC motor is proportional to armature current – more current means more torque.

Common mistakes

Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.

Applications

Torque of a DC motor T = k·Φ·I_a is proportional to the product of flux and armature current. This shows how torque is produced by the interaction of the magnetic field and the current. Engineers use it to design motors, to select ratings, and to control torque by adjusting current or field flux. This formula is fundamental to motor design and performance analysis.

  • DC motor sizing and torque requirement calculation
  • Field‑weakening control for high‑speed operation
  • Torque control in servo systems
  • Motor performance optimisation
  • Educational understanding of electromechanical torque

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  • Published July 10, 2026
  • Last updated September 10, 2026