Impulse Calculator

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, because the occupant still decelerates from 60 mph to zero either way. What the airbag does is extend Δt from around 0.01 seconds to around 0.05 seconds, cutting the peak force by a factor of five.

A 145 g baseball leaving the hand at 95 mph (42.5 m/s) has been given an impulse of 0.145 × 42.5 = 6.2 N·s. The pitcher builds that up over roughly 0.15 seconds of arm acceleration, so the average force is only about 41 N, less than the weight of a full kettle. The catcher takes the identical 6.2 N·s back out in maybe 0.02 seconds as the mitt compresses, which puts the average force at that end nearer 310 N. Same impulse, same ball, seven and a half times the force, purely because one end of the trip is slower than the other.

Units: impulse is measured in newton-seconds (N·s) or kilogram-meters per second (kg·m/s). These are the same unit, since 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.