PhysicsCalcs
Mechanics

Impulse Calculator

Calculate impulse (J = Ft), find average collision force with g-force and energy absorbed, 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 with g-force and energy absorbed, determine impact duration, or compute change in momentum.

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, crumple zones).
  • Average collision force = impulse / collision duration.
  • Impulse is a vector quantity with the same direction as the net force.
  • A bouncing object experiences greater impulse than one that stops on contact.

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.

Real-World Impact Forces

ScenarioTypical ForceDurationG-force
Baseball bat hit~8,000 N~1 ms~55 g
Car crash (30 mph, with airbag)~10,000 N~100 ms~15 g
Car crash (30 mph, no airbag)~100,000 N~10 ms~130 g
Tennis serve impact~1,500 N~5 ms~2,600 g (ball)
Bullet impact~4,000 N~1 ms~40,000 g (bullet)
Dropping a phone (1 m)~1,000 N~2 ms~450 g (phone)

Values are approximate order-of-magnitude estimates. Actual forces depend on materials, geometry, and deformation.

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, g-force, or energy 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 (≈ 4,075 g on the ball)

Car crash: 80 kg, 30 mph (13.4 m/s) to 0 in 0.1 s

F = 80 × 13.4 / 0.1 = 10,720 N (≈ 13.7 g), Energy = 7,178 J

Tennis bounce: 0.058 kg, 20→−15 m/s in 5 ms

J = 0.058 × (15+20) = 2.03 N·s, F = 406 N (ball bounces, so impulse > stopping case)

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 and therefore larger impulse).
  • Assuming peak force equals average force (peak is typically 1.5–2× average for many collisions).

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. Peak force estimates (~2× average) assume a roughly triangular pulse shape. 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 by the crash speed, a longer time means a smaller average force: F = Δp / Δt. Tripling the impact time cuts the force to one-third.

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.

How is impulse related to momentum?›

They are directly linked: J = Δp. The impulse delivered to an object equals its change in momentum. This means force × time = mass × change in velocity.

What is g-force in a crash?›

G-force is the deceleration expressed as a multiple of gravitational acceleration (9.81 m/s²). A 50 g impact means deceleration is 50 times gravity. Humans can typically survive brief impacts up to ~50 g with proper restraints.

Sources

  1. OpenStax University Physics – Impulse and Collisions
  2. HyperPhysics – Impulse
  3. NHTSA – Crash Test Data
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