ConverterHub

Impulse Calculator

Find the impulse of a force over time.

How it is calculated

Impulse is a force applied over a time: J = F × t, in newton-seconds (N·s). By the impulse-momentum theorem it equals the change in momentum, J = m × Δv. When you also enter a mass greater than zero, the tool gives the velocity change Δv = J / m in m/s; without a mass it shows a dash. Force is in newtons and time in seconds. The calculation treats the force as constant, so for a force that varies during a collision enter the average force. The result is the change in velocity, not the final velocity unless the object started at rest.

Worked example

A kick applies an average force of 500 N for 0.02 s to a 0.16 kg ball. Impulse = 500 × 0.02 = 10.00 N·s. The velocity change is 10 / 0.16 = 62.50 m/s. If the ball started at rest, its speed after the kick is 62.50 m/s. Doubling the contact time with the same force would double both numbers.

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Common mistakes

  • Entering the contact time in milliseconds without converting; 20 ms must be 0.02 s.
  • Using the peak force of a collision instead of the average force over the contact time.
  • Entering the mass in grams instead of kilograms, which makes Δv 1000 times too large.
  • Reading Δv as the final speed even when the object was already moving.
  • Forgetting direction: a rebound reverses the velocity, so the change can be more than the speed.

About this calculator

Impulse is the product of a force and the time interval over which it acts, J = F·t, and by the impulse-momentum theorem it equals the resulting change in momentum, Δp = m·Δv — this is why a larger impulse — a bigger force, or the same force applied for longer — produces a larger velocity change on a given mass.

Physicists and engineers use impulse to explain why airbags, crumple zones, and padded landing surfaces reduce injury — they extend the time over which a collision's momentum change happens, which lowers the peak force involved even though the total impulse is the same — and to calculate rocket thrust, the recoil of a fired projectile, or the force from a bat or club striking a ball. Enter the force and time (and optionally mass) to find the impulse and resulting velocity change.

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