What is the impulse-momentum theorem?

It states that the impulse applied to an object equals its change in momentum: J = F × Δt = Δp = m × Δv. Impulse is measured in newton-seconds (N·s), which is equivalent to kg·m/s.

What is the difference between impulse and force?

Force is the instantaneous push or pull (Newtons). Impulse is force multiplied by the duration it acts (N·s). Two impacts can have the same impulse with different forces if the contact time differs.

Can impulse be negative?

Yes. Impulse is a vector quantity. A negative value means the force acts in the direction opposite to the chosen positive direction, reducing the object's momentum.

What units does the calculator use?

SI units throughout: force in Newtons (N), time in seconds (s), mass in kilograms (kg), velocity in m/s, and impulse/momentum change in N·s (= kg·m/s).

How does this relate to Newton's second law?

Newton's second law (F = ma) is the instantaneous form. The impulse-momentum theorem is its time-integrated form: F × Δt = m × Δv. For constant force they are equivalent.

Impulse Momentum Theorem Calculator

Name: Impulse Momentum Theorem Calculator
Availability: InStock
Author: Nham Vu

Solve for impulse, force, or time using the impulse-momentum theorem (J = F × Δt = Δp = m × Δv).

Solve For

Choose an unknown, fill in the known values.

J = F × Δt = m × Δv

Force (F) N

Time Interval (Δt) s

Mass (m) kg

Velocity Change (Δv) m/s

Fill in the inputs and press Calculate

Example Presets

Summary

Solve for impulse, force, or time using the impulse-momentum theorem (J = F × Δt = Δp = m × Δv).

How it works

Select what you want to solve: impulse, force, or time interval.
Enter the known values with their units.
The calculator applies J = F × Δt = m × Δv to find the unknown.
Results show impulse in N·s and momentum change in kg·m/s (they are equal).
Switch solve mode at any time to explore different problem setups.

Use cases

Check answers to high-school and college physics homework problems.
Calculate the force a bat exerts on a baseball given contact time.
Determine how long an airbag must inflate to achieve a safe stopping force.
Verify braking force estimates from stopping distance and vehicle mass.
Solve rocket propulsion problems using exhaust impulse.
Explore the trade-off between force and contact time in sports collisions.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu