Quick answer
Impulse is J = F Δt = m Δv. An average force of 500 N applied for 0.02 s delivers 10 N·s of impulse.
Enter the average force and duration, and optionally mass. The calculator returns the impulse and the change in velocity.
Related tools: Force Calculator: Force from mass and acceleration (Newton's second law). Centripetal Force Calculator: Force and acceleration for circular motion. Normal Force Calculator: Normal force on an object resting on a flat or inclined surface.
How to use the Impulse Calculator
- Enter average force (N) (above 0).
- Enter duration (s) (above 0).
- Optionally, enter mass (optional) (kg) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Average force | A number, in N | > 0 |
| Duration | A number, in s | > 0 |
| Mass (optional) (optional) | A number, in kg | > 0 |
Formula and method
Formula
J = F Δt = m Δv
IEEE-754 double precision; shown to the decimals indicated.
Impulse equals change in momentum.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Average force = 500; Duration = 0.02.
| Result | Value |
|---|---|
| Impulse | 10 N·s |
| Change in velocity | — |
Example 2
Inputs: Average force = 1200; Duration = 0.5; Mass (optional) = 80.
| Result | Value |
|---|---|
| Impulse | 600 N·s |
| Change in velocity | 7.5 m/s |
The first line is the headline result (impulse). Below it the impulse Calculator lists change in velocity, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Impulse–momentum theorem
The impulse equals the change in momentum. If the 10 N·s acted on a 0.5 kg ball, its speed changes by 10 ÷ 0.5 = 20 m/s. With the mass blank the velocity change is not shown.
Why it matters
Airbags and crumple zones lengthen the time Δt, lowering the force for the same impulse. A kick lasting 0.02 s at 500 N gives the same impulse as 50 N for 0.2 s.
How the result changes with average force
Holding every other input at the first worked example, this table changes only average force. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Average force | Impulse | Change in velocity |
|---|---|---|
| 250 | 5 N·s | — |
| 500 | 10 N·s | — |
| 1000 | 20 N·s | — |
| 2000 | 40 N·s | — |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Average force: entering "0" shows "Average force must be greater than 0." beside that field and no result.
- Duration: entering "0" shows "Duration must be greater than 0." beside that field and no result.
Choosing between the Impulse Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Force Calculator](/science/force-calculator/) | mass and acceleration | Force |
| [Centripetal Force Calculator](/science/centripetal-force-calculator/) | mass, speed and radius | Centripetal force |
| [Normal Force Calculator](/science/normal-force/) | mass, incline angle and gravitational acceleration | Normal force |
| [Momentum Calculator](/science/momentum-calculator/) | mass and velocity | Momentum |
| [Net Force Calculator](/science/net-force-calculator/) | force magnitudes and direction of each force | Net force |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Mass is optional
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for average force and duration to confirm this.
Frequently asked questions
What are the units?
Newton-seconds, the same as kg·m/s.
Is impulse a vector?
Yes. Impulse has the direction of the force, just like the change in momentum it produces.
How do helmets help?
They extend the impact time.
What does the Impulse Calculator calculate?
Impulse from force and time, and the change in velocity if the mass is known. It returns Impulse and Change in velocity.
What formula does the Impulse Calculator use?
J = F Δt = m Δv. Impulse equals change in momentum.
What do I need to enter in the impulse Calculator?
You enter Average force (N) and Duration (s). Optional: Mass (optional) (kg).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Mass is optional.
What is an example of a impulse result?
With average force 500 and duration 0.02, the impulse is 10 N·s.
Related calculators
- Force Calculator — Force from mass and acceleration (Newton's second law).
- Centripetal Force Calculator — Force and acceleration for circular motion.
- Normal Force Calculator — Normal force on an object resting on a flat or inclined surface.
- Momentum Calculator — Linear momentum from mass and velocity.
- Net Force Calculator — Resultant of several forces at different angles.
- Friction Force Calculator — Friction force from the coefficient of friction and the normal force.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.