Momentum p is the product of mass and velocity: p = m·v. It is a vector quantity, conserved in the absence of external forces.

Impulse J equals the change in momentum: J = Δp = m(v − u). It also equals the average force times the time interval: J = F·Δt.

Momentum and Impulse Calculator

Compute p = m·v, impulse J = Δp and the average force over a collision time.

Mass m (kg)

Initial velocity u (m/s)

Final velocity v (m/s)

Collision time Δt (s) — optional

Results

Formulas

Momentum: p = m · v
Change in momentum: Δp = m·(v − u)
Impulse: J = Δp = F·Δt
Average force during collision: F = Δp / Δt

How to use

Enter the object's mass and its initial and final velocities along the same axis.
Optionally enter the collision time Δt to compute the average force.
Click Calculate.

Physics behind momentum and impulse

Momentum is conserved in any closed system, making it one of the most powerful tools in physics. Collisions — elastic or inelastic — become simple to analyse when you track momentum because the total before equals the total after. Impulse is the practical form of Newton's second law: instead of F = ma, you use F·Δt = Δp. This is how engineers design car bumpers, crash barriers and airbags.

Worked example

m = 2 kg, u = 0, v = 5 m/s, Δt = 0.1 s

p (initial) = 2·0 = 0 kg·m/s
p (final)   = 2·5 = 10 kg·m/s
J = Δp = 10 kg·m/s
F = J/Δt = 10/0.1 = 100 N

Related tools

Newton's 2nd Law Work & Energy SUVAT Centripetal Force

FAQs

What is momentum?

Momentum p = m·v, a vector quantity conserved in the absence of external forces.

What is impulse?

Impulse is the change in momentum. Also equal to average force times collision time.

Why do airbags reduce injury?

They stretch Δt, which reduces the average force for the same Δp.