An impulse is what a force delivers by acting for a stretch of time, such as a foot on a ball or the floor on your feet as you land. The same impulse can come from a big force over a short time or a small force over a long one, and that trade-off is the idea behind airbags, helmets and bent knees. This calculator solves J = FΔt for impulse, average force or contact time, and turns the impulse into a velocity change if you give it a mass.
How to use the impulse calculator
- Under Solve for, choose Impulse, Average force or Contact time.
- Enter the two known values. Force accepts N, kN, lbf, kgf, dyn and ozf; contact time accepts milliseconds (the default), seconds, microseconds and minutes; impulse accepts N·s, kN·s, kg·m/s, lbf·s and dyn·s.
- Optionally fill in Mass of the object (optional) to see how much the impulse changes the object’s velocity.
- Pick the output unit under Show the result in. The result lists conversions, the change in momentum and, with a mass, the change in velocity in m/s, km/h and mph.
Impulse formula
The calculator rearranges it for whichever value is missing, and uses the mass when you supply one:
Impulse points the same way as the average force, so both are negative when the force acts against your chosen positive direction. Contact time and mass must be greater than zero. When solving for time, the force cannot be zero and must share the impulse’s sign; otherwise the time would be negative and the calculator rejects the inputs.
Worked example: kicking a ball
A player's foot pushes on a ball with an average force of 500 N for 20 ms.
Convert the time: 20 ms = 0.02 s.
Impulse: J = 500 N × 0.02 s = 10 N·s, about 2.248 lbf·s.
With a 0.45 kg ball entered as the mass: Δv = 10 ÷ 0.45 = 22.2 m/s, which is 80 km/h or about 49.7 mph.
A ball kicked from rest leaves the foot at roughly 80 km/h.
Longer contact time, smaller force
Someone weighing 70 kg who jumps down from a 1 m ledge hits the floor at about 4.43 m/s, so the floor must deliver roughly 310 N·s of impulse to stop them. That number is fixed by the fall. The only thing the jumper controls is how long the stop takes. Solving for average force with J = 310 N·s at a few illustrative contact times:
| How you land | Contact time | Average stopping force |
|---|---|---|
| Stiff legs on concrete | 10 ms | 31,000 N (about 6,969 lbf) |
| Knees bending | 100 ms | 3,100 N (about 697 lbf) |
| Deep squat or roll | 300 ms | 1,033 N (about 232 lbf) |
Thirty times the contact time means one-thirtieth of the force. During a landing the floor must also hold up the body’s weight, about 687 N here, so the floor’s actual push is the stopping force plus that weight. The weight matters little in a 10 ms jolt but adds a lot to a slow 300 ms landing.
The same reasoning runs through everyday safety design. Together, an airbag and a slightly stretchy seat belt extend the occupant’s stop from a few milliseconds against the dashboard to something closer to a tenth of a second. Helmet foam crushes, crumple zones fold, gym mats compress, and a catcher pulls the glove back toward the body. None of them reduce the impulse; they all buy time.
Average force versus peak force
The F in this calculator is the time-averaged force, and impulse is the area under the force–time curve: two impacts of very different shapes deliver the same impulse if their areas match. Real impacts climb to a peak and fall away, so the peak exceeds the average. For a smooth half-sine pulse the peak is π/2, or about 1.57 times the average; for a symmetric triangular pulse it is exactly twice the average. Force plates, crash sensors and drop-test rigs usually report the peak, so compare like with like: use the average for momentum bookkeeping and a pulse-shape factor when you need a design load.
A familiar benchmark
Model rocket motors are graded by total impulse in N·s, with each letter class doubling the range: a C motor delivers up to 10 N·s, the same impulse as the kick in the example above, spread over a burn lasting a second or two rather than 20 ms.
Related calculators
When you know the starting and ending velocities instead of the impulse, use the impulse-momentum calculator. The momentum calculator finds p = mv for a single object, and the free fall calculator gives the impact speed after a drop.
Frequently asked questions
Is impulse the same as change in momentum?
Yes, when the force is the net force on the object. Impulse is force multiplied by the time it acts, and Newton's second law makes that product equal to the change in momentum. That is why the calculator shows the same number in N·s and as a momentum change in kg·m/s.
Why is the calculator's force lower than the peak a sensor records?
The calculator gives the average force over the contact time. Real impacts rise and fall, so the peak is higher than the average: about 1.57 times higher for a smooth half-sine pulse and twice as high for a triangular one.
How do airbags and helmets help if the impulse stays the same?
The impulse needed to stop you is set by your mass and speed, so it cannot be reduced. What safety gear changes is the time: stretching the stop over ten times as long cuts the average force to a tenth. Padding also spreads the force over a larger area, which lowers the pressure on any one spot.
What does the optional mass field do?
If you enter the object's mass, the calculator divides the impulse by it to give the change in velocity, Δv = J ÷ m, shown in m/s, km/h and mph. Leave it empty when you only need the impulse, force or time.
What units is impulse measured in?
The SI unit is the newton second (N·s), which is identical to kg·m/s. The calculator also works in kN·s, pound-force seconds (1 lbf·s is about 4.448 N·s) and dyne seconds (1 dyn·s is 0.00001 N·s).