About the Impulse Calculator
Impulse measures the total push a force delivers over time. This impulse calculator works it out two ways. If you know the average force and how long it acts, it multiplies them (J = F·Δt) and, given a mass, tells you how much the object's velocity changes. If you know an object's mass and its velocity before and after, it finds the change in momentum (J = m·Δv) and the average force needed to produce it in the contact time you enter.
The impulse–momentum theorem links the two: impulse always equals the change in momentum. That idea explains why airbags, crumple zones, bike helmets and soft landing mats save lives — stretching the stopping time lowers the average force for the same change in momentum. Sports scientists use the same physics to analyse kicks, bat swings and jumps, and engineers use it for impact loads.
Use SI units: newtons, seconds, kilograms and metres per second. Velocity is signed, so pick a positive direction and enter motion the other way as negative; a ball that reverses direction has a large change in velocity. The force is treated as an average over the contact time, which is how impulse is defined for real collisions where the force rises and falls quickly.
With the default inputs, the impulse j is 6 N·s. Change any value above to recalculate instantly.
How to use the impulse calculator
- 1Choose whether you know the force and time, or the mass and velocities.
- 2Enter the average force, or the velocities before and after (negative for the opposite direction).
- 3Enter the contact time and the mass of the object.
- 4Read the impulse, average force, change in velocity and g-load.
Formula and method
Impulse J is the product of a force and the time over which it acts. For a force that varies during a collision, J is the area under the force–time curve, and the average force is the constant force that would give the same area in the same time.
Newton's second law written in terms of momentum, F = Δp/Δt, rearranges into the impulse–momentum theorem: impulse equals the change in momentum, m(v_f − v_i). So knowing either the force and time or the mass and velocity change gives the impulse, and dividing it by the contact time gives the average force. Dividing the acceleration Δv/Δt by 9.80665 m/s² expresses it in g.
- J
- Impulse (N·s, equal to kg·m/s)
- F_avg
- Average force during contact (N)
- Δt
- Contact time (s)
- m
- Mass (kg)
- v_i, v_f
- Velocity before and after (m/s, signed)
- Δp
- Change in momentum (kg·m/s)
Worked examples
Kicking a football
A 500 N average force acting for 12 ms delivers an impulse of 500 × 0.012 = 6 N·s. Divided by the ball's 0.43 kg mass, that changes its velocity by about 13.95 m/s.
Baseball hit back toward the pitcher
The ball arrives at 40 m/s and leaves at 50 m/s the other way, so Δv = 90 m/s. Impulse is 0.145 × 90 = 13.05 N·s; over 0.7 ms of contact the average force is about 18,600 N.
Why airbags work: stopping a 70 kg occupant from 15 m/s
The occupant's momentum must change by 70 × 15 = 1,050 kg·m/s (the negative sign means the force opposes motion). Spread over 0.1 s by an airbag, the average force is 10,500 N, about 15 g; hitting a hard dashboard in 0.01 s would need ten times that.
Frequently asked questions
What is the formula for impulse?+
Impulse equals average force times the time it acts, J = F·Δt. It also equals the change in momentum, J = m·Δv. Both give units of newton-seconds (N·s), which are identical to kilogram-metres per second.
What is the impulse–momentum theorem?+
It states that the impulse applied to an object equals its change in momentum. It comes straight from Newton's second law, F = Δp/Δt, multiplied through by the time interval.
How do airbags and crumple zones use impulse?+
The impulse needed to stop you is fixed by your mass and speed. Airbags, crumple zones and helmets lengthen the stopping time, which reduces the average force for the same impulse and so reduces injury.
Can impulse be negative?+
Yes. Impulse is a vector with the direction of the force. If you choose the direction of travel as positive, a force that slows an object down produces a negative impulse and a negative change in momentum.
What units is impulse measured in?+
In SI units impulse is measured in newton-seconds (N·s), which equal kg·m/s, the unit of momentum. In US customary units it is pound-force seconds (lbf·s); 1 lbf·s ≈ 4.448 N·s.