Impulse Calculator
Find impulse and speed change from force, time, and mass.
What it does
Impulse links force, time, and motion in one product. Push with 20 newtons for half a second and you deliver 10 newton seconds of impulse. That impulse becomes momentum change, so a 2 kg object gains 5 m/s from rest.
The tool above takes average force, contact time, and mass and returns impulse, speed change, and time in milliseconds. The defaults 20 N, 0.5 s, and 2 kg match the worked example, so the page opens showing 10 N-s. Switch to imperial for pounds and feet.
The core is the impulse momentum theorem: change in momentum equals average net force times time. Seat belts, airbags, and catching a ball with soft hands all stretch time to cut peak force while delivering the same impulse. Rocket total impulse uses the same idea over a burn.
Average force is the key phrase. Real impacts spike and fade, but the area under the force time curve equals average force times time. Use measured averages or estimates, and keep mass constant during the push for the simple form.
This page shows the formula, one full hand checked example at 20 N for 0.5 s on 2 kg, a reference table, and practice checks that run through the tool in both unit systems.
How to use
- Pick Metric (N, kg) or Imperial (lbf, lb).
- Type the average force during contact.
- Type the contact time in seconds.
- Type the mass of the object.
- Read Impulse as force times time.
- Read Speed change as impulse divided by mass, starting from rest.
Formula
- F
- Average net force in N or lbf.
- dt
- Contact time in seconds.
- m
- Mass in kg or lb, assumed constant.
With varying force, J is the area under the force time curve. The tool uses the average form. For mass that changes a lot, such as a firing rocket, use the full variable mass form instead.
Worked example
Example: 20 N for 0.5 s on 2 kg
A 2 kg block gets a steady 20 N push for half a second, starting from rest.
- Write the inputs: F = 20 N, dt = 0.5 s, m = 2 kg.
- Impulse: J = 20 x 0.5 = 10 N-s.
- Speed gain: dv = 10 / 2 = 5 m/s.
- Time in ms: 0.5 x 1000 = 500 ms.
- Imperial mirror: 4.5 lbf for 0.5 s gives 2.25 lbf-s.
- Imperial speed: same push on 4.4 lb gives about 16.45 ft/s.
Reference table
| Push | Time | Impulse |
|---|---|---|
| 20 N | 0.5 s | 10 N-s |
| 10 N | 2 s | 20 N-s |
| 5 N | 0.2 s | 1 N-s |
| 4.5 lbf | 0.5 s | 2.25 lbf-s |
Limits
- Average force form. Sharp spikes need the full force time integral.
- Constant mass assumed. Burning fuel or picking up mass needs more terms.
- Straight line push. Angled forces need components first.
- Ignores friction and air drag during contact unless included in F.
Common mistakes
- Using peak force instead of average, which overstates impulse.
- Mixing grams with newtons without converting to kilograms.
- Dividing by weight in pounds as if it were mass in slugs without care. This tool converts lb mass correctly.
- Forgetting seconds to milliseconds, so 0.5 s is read as 0.5 ms.
- Applying dv as final speed when the object already moves. It is change in speed.
Try it yourself
Quick checks. Answers sit tucked under each question.
10 N for 2 s on 4 kg?
Impulse 20 N-s, speed change 5 m/s, time 2,000 ms.
5 N for 0.2 s on 1 kg?
Impulse 1 N-s, speed change 1 m/s, time 200 ms.
Questions
What is impulse?
Force times time. It equals change in momentum.
Impulse or momentum?
Momentum is mv at a moment. Impulse is F times dt, the change delivered.
What are impulse units?
N-s in SI, equal to kg m/s. In imperial, lbf-s.
Why do airbags help?
Same momentum change over longer time means lower average force.
Can impulse be negative?
Sign follows force direction. This tool uses magnitudes for speed gain from rest.
What if force varies?
Use average force, or integrate the force time curve for exact J.