PhysicsCalcs
Mechanics

Impulse Calculator

Calculate impulse (J = Ft), find average collision force, determine impact duration, or compute change in momentum. Step-by-step solutions with unit conversions.

Interactive calculator

Impulse Calculator

Calculate impulse (J = Ft), find average collision force, determine impact duration, or compute change in momentum using the impulse\u2013momentum theorem.

Try an example

Average force during interaction

Duration of force application

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose what to find: impulse, force, time, or collision force.
  • Enter known values with units.
  • Click Calculate for the result and formula breakdown.

Table of Contents

Key Takeaways

  • Impulse J = FΔt measures the total effect of a force over time.
  • Impulse equals the change in momentum: J = Δp.
  • The SI unit of impulse is N·s (equivalent to kg·m/s).
  • Longer contact time reduces impact force (airbags, padding).
  • Average collision force = impulse / collision duration.
  • Impulse is a vector quantity with the same direction as the net force.

What Is Impulse?

Impulse measures the total effect of a force applied over a time interval. It connects force (what you apply) with momentum change (what results). The longer and harder you push, the greater the impulse.

J = Ft (Impulse Definition)

J=F×ΔtJ = F \times \Delta t

For a constant force, impulse is simply force times time. For a variable force, impulse is the area under the force-vs-time curve (integral of F dt).

Impulse–Momentum Theorem

J=Δp=m(v2−v1)J = \Delta p = m(v_2 - v_1)

This theorem states that impulse equals the change in momentum. It’s one of the most useful relationships in collision analysis and sports biomechanics.

Collision Force Analysis

Favg=Δp/ΔtF_{avg} = \Delta p / \Delta t

Rearranging the impulse equation gives the average force during a collision. This explains why crumple zones, padding, and nets work: they increase Δt, reducing F for the same momentum change.

How to Use the Calculator

  1. Select the calculation mode for your known values.
  2. Enter force, time, mass, or velocities with units.
  3. Click Calculate.
  4. Review impulse, force, or time results.

Example Calculations

500 N for 0.02 s

J = 500 × 0.02 = 10 N·s

Baseball: 0.145 kg, 40→0 m/s in 1 ms

F = 0.145 × 40 / 0.001 = 5,800 N

80 kg person: 5→0 m/s

Δp = 80 × 5 = 400 N·s

Common Mistakes

  • Confusing impulse (N·s) with energy (joules).
  • Forgetting that velocity direction matters (signs).
  • Using instantaneous force instead of average force.
  • Not accounting for rebound (ball bouncing back has larger Δv).

Accuracy and Limitations

This calculator uses the average force approximation. Real collisions have complex force-time profiles. Deformable bodies, multi-stage impacts, and material properties affect actual forces. Results are educational estimates, not engineering-grade analysis.

FAQ

What is impulse?›

Impulse is the product of average force and the time interval over which it acts: J = FΔt. It represents the total ‘push’ delivered to an object, measured in N·s.

How is impulse related to momentum?›

Impulse equals the change in momentum: J = Δp = mΔv. This is the impulse–momentum theorem.

Why do airbags reduce injury?›

Airbags increase the time of impact. Since impulse (momentum change) is fixed, a longer time means a smaller average force: F = Δp / Δt.

Can impulse be negative?›

Yes. Negative impulse means the force acts opposite to the chosen positive direction, reducing momentum in that direction.

Is impulse the same as force?›

No. Force is instantaneous (newtons). Impulse is force integrated over time (newton-seconds). A small force applied for a long time can produce the same impulse as a large force applied briefly.

How do I find the average force during a collision?›

Measure or calculate the impulse (Δp), then divide by the collision duration: F_avg = Δp / Δt.

Sources

  1. OpenStax University Physics – Impulse and Collisions
  2. HyperPhysics – Impulse
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish