DC Motor Back-EMF & Torque Calculator (E=kω, T=kI)

DC Motor Back-EMF & Torque Calculator (E=kω, T=kI) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: number, select
Output type: json
Sample coverage: 4
API ready: Yes

Overview

Calculate a DC motor's back-EMF, electromagnetic torque, and mechanical power from the motor constant, angular speed, and armature current. Enter speed in rad/s or RPM and receive the results in JSON format.

When to use

Estimate back-EMF from a motor's machine constant and angular speed.
Calculate electromagnetic torque from the motor constant and armature current.
Check mechanical power using the relationship P = T·ω = E·I.

How it works

1Enter the motor constant k in V·s/rad or N·m/A.
2Enter angular speed in rad/s or select RPM and enter the rotational speed.
3Enter armature current in amperes and choose the number of decimal places.
4The calculator converts RPM to rad/s when needed, then computes E = k·ω, T = k·I, and P = T·ω.

Use cases

Motor design checks involving back-EMF and torque constants.
Electrical and mechanical calculations for DC motor experiments.
Quick verification of electromechanical power relationships.

Examples

1. Estimate back-EMF and torque at 100 rad/s

Electrical engineering student

Background

A student is checking the operating values of a DC motor with a known machine constant.

Problem

Calculate the motor's back-EMF, electromagnetic torque, and mechanical power.

How to use

Enter k = 0.1, speed = 100, select rad/s, and enter current = 5 A.

k: 0.1; speed: 100; speedUnit: rad_s; current: 5; decimalPlaces: 4

Outcome

The calculator returns E = 10 V, T = 0.5 N·m, and P = 50 W. The equivalent speed is approximately 954.9297 RPM.

2. Calculate motor values from 3000 RPM

Motor technician

Background

A technician needs to evaluate a DC motor using a datasheet speed in RPM rather than rad/s.

Problem

Convert 3000 RPM and calculate back-EMF, torque, and mechanical power.

How to use

Enter k = 0.05, speed = 3000, select RPM, and enter current = 10 A.

FAQ

What does the motor constant k represent?

In SI units, k is both the back-EMF constant and torque constant: k_e = k_t = k.

Can I enter speed in RPM?

Yes. Select RPM, and the calculator converts the value to rad/s for the calculations.

What formulas does the calculator use?

It uses E = k·ω for back-EMF, T = k·I for torque, and P = T·ω = E·I for mechanical power.

What units are used for the results?

Back-EMF is returned in volts, torque in N·m, speed in rad/s and RPM, and mechanical power in watts.

Can the armature current be zero?

Yes. A zero current produces zero torque and zero mechanical power, while back-EMF still depends on speed and k.

k: 0.05; speed: 3000; speedUnit: rpm; current: 10; decimalPlaces: 4

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Estimate back-EMF and torque at 100 rad/s

2. Calculate motor values from 3000 RPM

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