Momentum Calculator — p = mv
Calculate linear momentum from mass and velocity. Covers conservation of momentum, impulse, collisions, and practical examples in sports and physics.
Momentum is what makes a freight train dangerous at low speed and a bullet dangerous despite tiny mass. It's the product of mass and velocity, and unlike kinetic energy, it's a vector — direction matters. The conservation of momentum is one of the most powerful tools in physics, holding even when forces between objects are unknown.
The CalcHub momentum calculator computes momentum and also handles collision scenarios using conservation laws.
The Formula
p = m × v- p = momentum (kg·m/s)
- m = mass (kg)
- v = velocity (m/s)
Conservation of Momentum
In a closed system (no external forces), total momentum is conserved:
p_before = p_afterFor a two-object collision: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
This works regardless of whether the collision is elastic or inelastic — which is what makes it so useful.
Momentum vs. Kinetic Energy
| Property | Momentum | Kinetic Energy |
|---|---|---|
| Formula | p = mv | KE = ½mv² |
| Type | Vector | Scalar |
| Conserved in ALL collisions? | Yes | Only elastic |
| Units | kg·m/s | Joules |
Worked Example
A 0.16 kg hockey puck moves at 40 m/s and collides with a 75 kg goalie who is stationary. They move together. What's the final velocity?
Using conservation of momentum:
(0.16 × 40) + (75 × 0) = (0.16 + 75) × v_f
6.4 = 75.16 × v_f
v_f = 6.4 / 75.16 ≈ 0.085 m/s
The goalie barely moves — all that momentum from the puck is absorbed by the much larger mass. Makes sense intuitively.
Why can't I just use kinetic energy for collisions?
KE is not always conserved. Inelastic collisions convert some KE to heat, sound, or deformation. Momentum is always conserved as long as no external forces act on the system, making it the more reliable conservation law for collision problems.
What is angular momentum?
Linear momentum (p = mv) describes straight-line motion. Angular momentum (L = Iω) describes rotational motion. They're separate but analogous concepts, each independently conserved when the respective net torque or force is zero.
How does momentum relate to force?
Newton's second law in its original form: F = Δp/Δt — force equals rate of change of momentum. F = ma is a special case where mass is constant. The more general form handles rockets and variable-mass systems.