HesapHanem

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.

Try this example →

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.

Sources

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.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    The same impulse can come with a big force over a short time or a small force over a long time, which is why padding and bending knees work. Stopping a 0.16 kg ball at 25 m/s needs 4.00 N·s: try 400 N for 0.01 s, then 40 N for 0.1 s. Both give 4.00 N·s and a 25.00 m/s change. Which situation are you modelling, sport, safety gear or a collision problem?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators