Momentum Change & Impulse Calculator
Find the change in momentum of a mass, the impulse delivered and the average force from the contact time — the impulse–momentum theorem worked out.
How it works
Δp = m·(v_f − v_i) · Impulse J = Δp = F_avg·t · F_avg = Δp ÷ t
The impulse–momentum theorem says the impulse delivered to an object equals its change in momentum: J = F·t = Δp = m·Δv. That is why crumple zones, airbags and follow-through in sport all work by stretching out the time t — for the same change in momentum, a longer contact time means a smaller average force. Momentum is a vector, so a sign change in velocity (a bounce) counts as a large Δv.
Worked example
A 2 kg mass speeds up from 3 m/s to 8 m/s. Δp = 2 × (8 − 3) = 10 kg·m/s, so the impulse is 10 N·s. If the push lasts 0.5 s, the average force is 10 ÷ 0.5 = 20 N.
Sources: Impulse (physics) — Wikipedia
Frequently asked questions
Is impulse the same as momentum change?
Yes. The impulse–momentum theorem states that the net impulse on an object (force multiplied by the time it acts) equals the change in the object’s momentum, J = Δp. They have the same units, kg·m/s, also written N·s.
Why does a longer contact time reduce the force?
For a fixed change in momentum, F = Δp ÷ t. Increasing t while Δp stays the same lowers F. Airbags, landing by bending your knees and catching an egg on a soft cloth all exploit this.
What if the object reverses direction?
Treat velocity as a signed quantity along your chosen axis. A ball hitting a wall at +5 m/s and rebounding at −5 m/s has Δv = −10 m/s, so the momentum change is twice what a simple stop would give.
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This calculator is for educational purposes. Double-check important results before acting on them.