Momentum
Handle momentum and impulse calculations in one place. Free online calculator with formulas and step-by-step solutions.
Key formula
p = mv, J = F delta t
How do you calculate momentum?
Linear momentum is p = m × v. Multiply mass (kg) by velocity (m/s) to get kg·m/s. Rearrange to m = p/v or v = p/m. Impulse J = FΔt equals the change in momentum Δp. Average force F = Δp/Δt over contact time.
About this tool
Momentum combines mass and velocity into one measure of motion. This page keeps p = mv and impulse J = FΔt = Δp visible so you can solve for momentum, mass, velocity, or force without mixing kg·m/s with wrong units.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: 2.0 kg at 3.0 m/s
p = m v = (2.0)(3.0) = 6.0 kg·m/s in the direction of motion.
Example 2: find velocity from momentum
p = 12 kg·m/s, m = 4.0 kg. v = p/m = 12/4.0 = 3.0 m/s.
Example 3: impulse from a constant force
F = 50 N for Δt = 0.20 s. J = FΔt = (50)(0.20) = 10 N·s — the momentum changes by 10 kg·m/s.
Frequently asked questions
What is the momentum formula?
p = m v for linear momentum. Mass in kg, velocity in m/s, momentum in kg·m/s. It is a vector pointing the same way as velocity.
What is impulse?
Impulse J = F Δt is the momentum transferred by a force over time. It equals Δp. Units are N·s, the same as kg·m/s.
When is momentum conserved?
In an isolated system or during a brief collision when external forces are negligible, total momentum before equals total after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
What is the difference between momentum and kinetic energy?
Momentum is p = mv (linear in v). Kinetic energy is KE = ½mv² (depends on v²). Collisions conserve momentum but usually not KE unless elastic.
How does momentum relate to collisions?
Start every 1D collision with momentum conservation. Use the collision calculator for elastic, inelastic, or partial restitution final speeds after you understand p = mv.