Impulse Calculator
Calculate impulse from force and time, or from mass and velocity change.
Enter any two variables to find the third using the impulse-momentum theorem.
Impulse is the product of force and the time over which it acts. It equals the change in momentum of the object the force acts on.
J = F x Δt = Δp = m x Δv
This is the impulse-momentum theorem, one of the most practically useful relationships in mechanics. It tells you that the same change in momentum can be produced by a large force over a short time, or a small force over a long time.
Engineers exploit this constantly. A car airbag does not reduce the change in momentum during a crash — the occupant still decelerates from 60 mph to 0. What the airbag does is extend Δt from ~0.01 seconds to ~0.05 seconds, cutting the peak force by a factor of five.
A baseball pitcher throwing at 95 mph exerts roughly the same impulse per pitch as a slow-pitch softball thrower, but the mechanics look completely different. The fast pitcher applies less force over more time during the windup; the delivery itself is just the release.
Units: impulse is measured in newton-seconds (N·s) or kilogram-meters per second (kg·m/s). These are the same unit — 1 N·s = 1 kg·m/s.
This calculator solves for:
- Impulse J: given force (F) and time (Δt), or mass (m) and velocity change (Δv)
- Force F: given impulse and time
- Time Δt: given impulse and force
- Velocity change Δv: given impulse and mass
Select what you want to calculate, enter the known values.