Rotational mechanics tool

Angular Impulse Calculator

Solve angular impulse, torque, or time using J = τt = ΔL.

Enter two known values

Solve an angular impulse problem

Free tool
N·m·s

This is the value being calculated.

N·m

Average torque acting during the time interval.

s

Positive duration for which the torque acts.

Use newton-seconds for angular impulse, newtons for torque, and seconds for the time interval.

Try an example:

Your angular impulse result will appear here

Choose the missing variable and enter the other two known values.

Physics overview

What is angular impulse?

Angular impulse describes the effect of torque acting over a time interval. It equals the resulting change in angular momentum.

Formula

Angular impulse formula

Angular ImpulseJ = τt = ΔL

  • J is angular impulse in N·m·s.
  • τ is torque in N·m.
  • t is time in seconds.
  • ΔL is the change in angular momentum.

Worked example

A torque of 8 N·m acts for 3 seconds

  1. Write the formula: J = τt.
  2. Substitute the values: J = 8 × 3.
  3. Calculate angular impulse: J = 24 N·m·s.

Rearranged equations

Solve for torque or time

Torque

τ = J ÷ t

Divide angular impulse by time.

Time

t = J ÷ τ

Divide angular impulse by torque.

Angular momentum relationship

Angular impulse equals ΔL

The angular impulse applied to an object equals its change in angular momentum. A larger torque or a longer application time produces a larger rotational momentum change.

Units

Standard SI units

Use newton meter seconds for angular impulse, newton meters for torque, and seconds for time.

Real-world applications

Where angular impulse is used

  • Starting and stopping rotating machinery.
  • Applying torque to wheels and flywheels.
  • Sports involving rotational motion.
  • Motor and turbine performance analysis.
  • Studying changes in angular momentum.

Calculation limits

Important assumptions

  • All entered values must be greater than zero.
  • Torque is treated as constant during the time interval.
  • The torque direction is not represented.
  • Units are not converted automatically.

Related tools

Use the Torque Calculator to calculate torque, force, or lever arm distance.

Use the Angular Momentum Calculator to calculate angular momentum, moment of inertia, or angular velocity.

Questions and answers

Angular impulse calculator FAQ

What formula does the angular impulse calculator use?

It uses J = τt = ΔL, where angular impulse equals torque multiplied by time and also equals the change in angular momentum.

What is angular impulse?

Angular impulse measures the rotational effect of torque acting over a time interval.

How do you calculate torque from angular impulse?

Divide angular impulse by time using τ = J ÷ t.

What units are used for angular impulse?

Angular impulse is measured in newton meter seconds, written as N·m·s.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the Science Lab Tools Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Learn more about our formula-review and correction process, or read about Science Lab Tools.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently