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Calculators/Momentum
Classical Mechanics

Momentum Calculator

Calculate momentum (p = mv), or solve for mass or velocity. Includes a full collision solver for elastic, inelastic and perfectly inelastic collisions.

Momentum p = mv

Enter values to calculate.

Collision Solver

1D collision — enter masses, velocities and coefficient of restitution (e)

Object 1
Object 2

Momentum equations

Momentum
p = mv
Impulse
J = F·Δt = Δp
Conservation
m₁v₁ + m₂v₂ = const
Elastic collision v₁'
v₁' = (m₁−m₂)v₁/(m₁+m₂) + 2m₂v₂/(m₁+m₂)
Inelastic v_combined
v_f = (m₁v₁+m₂v₂)/(m₁+m₂)
KE from momentum
KE = p²/(2m)

What is momentum?

Momentum is the product of an object's mass and velocity: p = mv. It is a vector quantity — it has both magnitude and direction. The law of conservation of momentum states that the total momentum of a closed system remains constant unless an external force acts on it.

Impulse J = FΔt is the change in momentum caused by a force applied over time. This is why airbags save lives — they increase the time of impact, reducing the force even though the change in momentum (from moving to stationary) is the same. For the full treatment see Momentum and Impulse.

What is the difference between momentum and kinetic energy?↓
Momentum p = mv is linear in velocity; kinetic energy KE = ½mv² is quadratic. Momentum is always conserved in collisions; kinetic energy is only conserved in perfectly elastic collisions. They measure different aspects of motion.
Why is momentum conserved?↓
Conservation of momentum follows directly from Newton's third law: if object A exerts a force on object B, then B exerts an equal and opposite force on A. Over any time interval, these forces produce equal and opposite impulses — equal and opposite changes in momentum. The total change is zero.
CalcKinetic Energy CalculatorCalcNewton's Second Law CalculatorArticleMomentum and ImpulseArticleNewton's Laws of Motion