Mechatronics & Robotics

DC Motor Torque and Angular Speed Calculator — Current, Voltage, Resistance and Motor Constant Model

Calculate DC motor torque and angular speed using current, torque constant, supply voltage, resistance and back EMF constant.

Unit-aware inputs Deterministic calculation Engineering interpretation
Calculation workspace

Enter the known values and review the calculated result

Deterministic calculation
01
Parameters

Input parameters

Use consistent values and select the intended engineering units.

Electrical parameters

Motor constants

02
Output

Results

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Engineering reference

Method, application and limitations

Review the calculation method, intended application and engineering assumptions before using the result in a design decision.

01
Method

Formula and calculation method

Torque formula:

T = Kt · I

Angular speed formula:

ω = (V − I · R) / Ke,used

Back EMF constant used by the model:

Ke,used = Ke when Ke > 0, otherwise Ke,used = Kt

where:

  • T — Torque (N·m)
  • ω — Angular speed (rad/s)
  • I — Current (A)
  • Kt — Torque constant (N·m/A)
  • Ke,used — Back EMF constant used in calculation (V·s/rad)
  • Ke — Back EMF constant (V·s/rad)
  • V — Supply voltage (V)
  • R — Armature resistance (Ω)
02
Application

When to use this calculator

Torque formula:

T = Kt · I

Angular speed formula:

ω = (V − I · R) / Ke,used

Back EMF constant used by the model:

Ke,used = Ke when Ke > 0, otherwise Ke,used = Kt

where:

  • T — Torque (N·m)
  • ω — Angular speed (rad/s)
  • I — Current (A)
  • Kt — Torque constant (N·m/A)
  • Ke,used — Back EMF constant used in calculation (V·s/rad)
  • Ke — Back EMF constant (V·s/rad)
  • V — Supply voltage (V)
  • R — Armature resistance (Ω)
03
Decision support

How to interpret the result

Torque is defined as the motor output torque calculated from current and torque constant.

Angular speed is defined as the effective motor voltage divided by the back EMF constant used by the model. Effective voltage depends on supply voltage minus the voltage drop caused by current and armature resistance.

Torque depends on current and torque constant. Increasing current increases torque.

Angular speed depends on supply voltage, current, armature resistance and back EMF constant used by the model. Increasing supply voltage increases angular speed. Increasing current or armature resistance decreases angular speed because effective voltage becomes lower.

  • Safe — when speed ratio exists and is from 0.05 to 0.95, while no warning or unsafe condition is active.
  • Limit — when speed ratio is below 0.05 or above 0.95.
  • Unsafe — when mechanical power is greater than electrical input power by more than 1%.
  • Warning — when voltage balance error is greater than 1e-6 · max(1, supply voltage), when the back EMF constant used differs from the torque constant by more than 20%, or when armature resistance equals zero.
  • Invalid — when current is below zero, torque constant is not greater than zero, armature resistance is below zero, voltage is not valid, effective voltage is below zero, angular speed is invalid, efficiency is negative, or efficiency is greater than 1.01.
  • Info — when only torque is calculated and the voltage-resistance speed model is not active.

The result is used to evaluate motor operating torque, angular speed, effective voltage, speed ratio, torque ratio and power consistency.

04
Worked case

Calculation example

Example:

A user wants to estimate the operating torque and angular speed of a DC motor from measured current and known motor constants.

  • I = 5 A
  • Kt = 0.08 N·m/A
  • Ke = 0.08 V·s/rad
  • V = 24 V
  • R = 0.6 Ω

T = 0.4 N·m

ω = 262.5 rad/s

05
Model boundaries

Assumptions and limitations

  • Torque is calculated as a linear product of torque constant and current.
  • Angular speed is calculated only when supply voltage and armature resistance are provided and the back EMF constant used by the model is greater than zero.
  • If the back EMF constant is not provided or is not greater than zero, the torque constant is used as the back EMF constant.
  • Effective voltage is calculated as supply voltage minus current multiplied by armature resistance.
  • No-load speed and stall torque are calculated only when armature resistance is greater than zero.
  • Efficiency is calculated only when electrical input power is greater than zero.
06
Questions

Frequently asked questions

How to calculate torque?
Torque is calculated using T = Kt · I. It depends on current and torque constant. Increasing current increases torque.
How to calculate angular speed?
Angular speed is calculated using ω = (V − I · R) / Ke,used. It depends on supply voltage, current, armature resistance and back EMF constant used by the model.
What affects torque and angular speed the most?
Torque increases with current and torque constant. Angular speed increases with effective voltage and decreases when current or armature resistance increases, because the voltage drop I · R becomes larger.
When is the torque and angular speed formula not valid?
The calculation is invalid when current is below zero, torque constant is not greater than zero, armature resistance is below zero, voltage is not valid, effective voltage is below zero, angular speed is negative, efficiency is negative, or efficiency is greater than 1.01.
Can this calculator be used without a back EMF constant?
It can be used without a provided back EMF constant because the model uses the torque constant as the back EMF constant when the back EMF constant is not provided or is not greater than zero.
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Engineering notice. Verify input data, assumptions, applicable standards and required safety factors before using results for design release or safety-critical decisions.