How to Calculate Momentum (p = mv): Impulse & Conservation

Calculate momentum with p = mv and impulse J = FΔt = Δp. Conservation in collisions, unit traps, worked examples, and a free momentum calculator.

What Momentum Asks

Momentum measures how much motion a mass has. A heavy object moving slowly can have the same momentum as a light object moving fast — mass and velocity both matter.

Linear momentum is p = m × v. Mass m in kilograms times velocity v in metres per second gives momentum in kg·m/s. Momentum is a vector: direction matches velocity.

If you have m and v (or p and one unknown), open the free momentum calculator first, then return here for impulse, conservation, and collision links.

The Formulas

p = mv — momentum from mass and velocity.

m = p / v — find mass.

v = p / m — find velocity.

J = F Δt = Δp — impulse equals change in momentum.

F = Δp / Δt — average force from a momentum change over time.

Impulse J has the same units as momentum (kg·m/s, also written N·s). A constant force acting for time Δt transfers impulse J = FΔt to the object.

Conservation of Momentum

When external forces are negligible during a short interaction (like a collision), total momentum before equals total momentum after.

Two objects: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.

Pick one direction as positive and keep signs consistent.

Kinetic energy is not always conserved — momentum usually is.

For final speeds after elastic, sticky, or partial-bounce collisions, use the collision calculator and the full

collisions guide.

Momentum vs Kinetic Energy

Kinetic energy is KE = ½mv² — it depends on v squared. Momentum is mv — linear in v. See kinetic energy when the question asks about energy loss in a crash, not just momentum balance.

Units

m → kg (convert g to kg).

v → m/s (divide km/h by 3.6).

p → kg·m/s (same as N·s).

F → N, Δt → s for J = FΔt.

Worked Examples

Example 1: 2.0 kg at 3.0 m/s

p = mv = (2.0)(3.0) = 6.0 kg·m/s in the direction of motion.

Example 2: find velocity

p = 12 kg·m/s, m = 4.0 kg. v = p/m = 12/4.0 = 3.0 m/s.

Example 3: impulse from a force

F = 50 N for Δt = 0.20 s. J = FΔt = (50)(0.20) = 10 N·s = 10 kg·m/s change in momentum.

Example 4: conservation check

m₁ = 2 kg at 4 m/s hits m₂ = 2 kg at rest and they stick. v = (2×4 + 2×0)/(2+2) = 2 m/s. Total p before = 8, after = (4)(2) = 8 kg·m/s.

Common Mistakes

Using grams with m/s without converting mass to kg.

Leaving km/h in p = mv without converting to m/s.

Treating momentum as always positive — direction and sign matter.

Assuming KE is conserved whenever momentum is (only elastic collisions conserve both).

Check It on the Calculator

Momentum calculator — p = mv and J = FΔt.

Collision calculator.

Kinetic energy calculator.

Force calculator.

Learn p = mv and confirm every homework number on the calculator.

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