# What is the impulse?

Computes impulse from an average force and the time it acts (J = FΔt), or from a mass and its change in velocity (J = mΔv), with the average force of an impact, in N·s and lbf·s.

- Page: https://www.acalculator.org/physics/impulse-calculator
- JSON spec: https://www.acalculator.org/physics/impulse-calculator.json
- Version: 5ed863da9fad

## Default answer

Example with the default inputs (Impulse from Force × time, Average force 112.404471549855 lbf, Contact time 100 ms): The impulse is 50 N·s (11.2404 lbf·s).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | Impulse from | Work out the impulse from an average force and a time, or from a mass and its change in velocity. |
| F | Average force | The average force during the contact; negative if it pushes backward. |
| m | Mass | The mass of the object. |
| v1 | Initial velocity | The velocity before the impact; negative for the opposite direction. |
| v2 | Final velocity | The velocity after the impact; negative for the opposite direction. |
| t | Contact time | How long the force acts. Optional when you start from the change in momentum. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| impulse | Impulse (N·s) | The impulse J in newton-seconds, the same as kg·m/s of momentum change. |
| lbfs | Impulse (lbf·s) | The same impulse in pound-force seconds. |
| average | Average force (N) | The impulse ÷ the contact time. |
| averageLbf | Average force (lbf) | The average force in pounds-force. |
| dv | Change in velocity (m/s) | In the momentum mode: v₂ − v₁. |

## Method

J = F_avg × Δt; J = Δp = m × (v₂ − v₁); F_avg = J ÷ Δt.

## Assumptions

- Motion along one line: a positive velocity or force points one way, a negative one the other way.
- The mass stays the same during the impact. Exact unit sizes: 1 lbf = 4.4482216152605 N; 1 lb = 0.45359237 kg; 1 mph = 0.44704 m/s; 1 km/h = 1/3.6 m/s; 1 ft/s = 0.3048 m/s.

## Worked examples

1. from = force, F = 500, t = 0.1 gives impulse = 50, average = 500. Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions.
2. from = momentum, m = 0.145, v1 = -40, v2 = 50, t = 0.001 gives impulse = 13.05, dv = 90, average = 13,050. Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions.
3. from = momentum, m = 1,000, v1 = 20, v2 = 0 gives impulse = -20,000, dv = -20. Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions.
4. from = force, F = 4.448222, t = 1 gives lbfs = 1, impulse = 4.448222. Source: OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; impulse-momentum theorem J = Δp), https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions; NIST SP 811 (1 lbf = 4.4482216152605 N), https://www.nist.gov/pml/special-publication-811.

## FAQ

### What is the formula for impulse?

Impulse is the average force times the time it acts: J = F × Δt. An average force of 500 N for 0.1 s gives an impulse of 50 N·s.

### How is impulse related to momentum?

By the impulse-momentum theorem, the impulse equals the change in momentum: J = Δp = m (v₂ − v₁). A 0.145 kg baseball that goes from 40 m/s toward the bat to 50 m/s away has J = 0.145 × 90 = 13.05 N·s.

### How do I find the average force of an impact?

Divide the impulse by the contact time: F = J ÷ Δt. The baseball’s 13.05 N·s delivered in 1 ms is an average force of 13,050 N.

### Why does a negative impulse appear?

Impulse has a direction. If the object slows down or turns back, the change in velocity is negative along the direction you chose as positive. A car stopping from 20 m/s takes an impulse of −20,000 N·s per 1,000 kg.

### Why do airbags and crumple zones help?

The impulse to stop you is fixed by your mass and speed. Spreading it over a longer time lowers the average force, F = J ÷ Δt.

### What are the units of impulse?

Newton-seconds (N·s), which are the same as kg·m/s, the unit of momentum. 1 lbf·s = 4.4482216152605 N·s.

## Sources

- OpenStax, University Physics Volume 1, §9.2 Impulse and Collisions (J = F_ave Δt; the impulse-momentum theorem J = Δp). https://openstax.org/books/university-physics-volume-1/pages/9-2-impulse-and-collisions (retrieved 2026-10-03)
- NIST SP 811, Appendix B.8 (1 lbf = 4.4482216152605 N; 1 lb = 0.45359237 kg). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-03)