Impulse and Momentum Calculator

Use our impulse and momentum calculator to compute impulse (J), momentum (p), and change in momentum (Δp). Includes what impulse and momentum are, the impulse–momentum theorem, the relationship between impulse and momentum, and whether impulse and momentum are the same thing (and their units).

Velocity change (Δv) (ft/s)
Can be negative.
Initial velocity (v₁) (ft/s)
Can be negative.
Mass (m) (lb)
Mass in lb (lbm). Must be > 0.
Force (F) (lbf)
Force in lbf. If F = 0, time interval is undefined.
Results
Final velocity (v₂) (ft/s)
v₂ = v₁ + Δv
ft/s
Time interval (sec)
t = J / F
s
Impulse (J) (lbf-s)
J = m·Δv / gₙ (with gₙ = 32.174 lbm·ft/(lbf·s²))
lbf•s
Initial momentum (p₁) (lbf-s)
p₁ = m·v₁ / gₙ
lbf•s
Final momentum (p₂) (lbf-s)
p₂ = m·v₂ / gₙ
lbf•s
v₂ = v₁ + Δv, J = m·Δv/gₙ, p = m·v/gₙ, t = J/F
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What Is Impulse and Momentum?

Momentum (p) describes how much “motion” an object has. It depends on mass and velocity. In one dimension, momentum is p = m·v.

Impulse (J) describes the effect of a force acting over a time interval. If a force acts for a time Δt, the impulse is J = F·Δt (for constant force).

Impulse and momentum are closely connected: impulse equals the change in momentum. That relationship is called the impulse–momentum theorem.

Impulse–Momentum Theorem

Impulse equals the change in momentum. This lets you connect forces and contact time to changes in velocity.

Momentum =
p = m · v

Momentum is a vector (direction matters).

Impulse (constant force) =
J = F · Δt

If force changes over time, impulse is the area under the force–time curve.

Impulse–momentum theorem =
J = Δp = p₂ p₁ = m·v₂ m·v₁

If mass is constant, Δp = m·Δv.

Relationship between impulse and momentum
Impulse causes momentum to change

A bigger force or longer contact time creates a bigger change in momentum.

Common use-case
Given m, v₁, v₂ → find impulse J

Or given J and m → find change in velocity.

How to Use the Impulse and Momentum Calculator

  1. 1

    Enter mass (m).

  2. 2

    Enter initial velocity (v₁) and final velocity (v₂).

  3. 3

    The calculator computes initial momentum p₁ = m·v₁, final momentum p₂ = m·v₂, and change in momentum Δp = p₂ − p₁.

  4. 4

    Impulse is returned as J = Δp.

Frequently Asked Questions

Are impulse and momentum the same thing?

No. Momentum is an object’s motion quantity (p = m·v). Impulse is the effect of a force over time. They are related because impulse equals the change in momentum (J = Δp).

What is the impulse momentum theorem?

The impulse–momentum theorem states that the net impulse on an object equals its change in momentum: J = Δp.

What is the relationship between impulse and momentum?

Impulse is what changes momentum. A net force acting over time produces an impulse, and that impulse equals the change in momentum.

Do impulse and momentum have the same units?

Yes. Impulse has units of newton-seconds (N·s). Momentum has units of kilogram-meters per second (kg·m/s). These are equivalent units.

Why does increasing contact time reduce force in collisions?

For a given change in momentum (fixed impulse), spreading the impulse over a longer time reduces the average force because J = Favg·Δt.