Impulse Calculator (J = F·Δt)

Compute impulse from force and contact time, or use it to find the change in velocity for a given mass.

Inputs

In newtons.

How long the force acts.

Only used when computing Δv.

Result

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General calculation reads

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How to use this calculator

  • Pick a mode. "Impulse" computes J = F·t. "Δv" computes the velocity change a given impulse produces on a given mass.
  • Enter the force in newtons and contact time in seconds.
  • For Δv mode, also enter the object's mass.
  • Read impulse (N·s) — equivalent to change in momentum (kg·m/s).

About this calculator

Impulse is the integral of force over time: how much push, multiplied by how long. For a constant force, J = F·Δt. The impulse-momentum theorem says impulse equals change in momentum, J = Δp, which has the practical consequence that you can change an object's velocity by either applying a large force briefly or a small force for longer. That is the engineering principle behind crumple zones, airbags, catcher's mitts, and even how you bend your knees when landing — extending the contact time reduces the peak force for the same Δp. Units: 1 N·s = 1 kg·m/s.

Frequently asked

Why are airbags effective?+
They extend the time over which the body decelerates, lowering peak force for the same change in momentum. The Δp the body experiences is the same with or without an airbag, but spreading it over 100 ms instead of 10 ms drops peak force by 10×.
How is impulse related to momentum?+
Impulse-momentum theorem: J = Δp. The impulse on an object equals its change in momentum.
What is the difference between J·s and N·s?+
J·s is the unit of action (Planck constant). N·s is the unit of impulse, equal to kg·m/s. Don't confuse them — only the latter is impulse.
Can impulse be negative?+
Yes — if the force opposes the motion. Braking applies negative impulse and reduces forward momentum.
Does this work for a varying force?+
For a constant force, J = F·Δt. For a varying force, J = ∫F dt — the area under the F-vs-t curve. This calculator uses the constant-force form.

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