Momentum Calculator: p = m × v
Solve momentum, mass or velocity with p = m·v. Choose kg·m/s, N·s or lb·ft/s and see the formula with each step. Free and private, runs in your browser.
Fill in all but one field: the empty field is the one you solve for.
About the Momentum Calculator
The Momentum Calculator solves p = m × v for momentum, mass or velocity. Enter any two of Momentum, Mass and Velocity and the third appears as you type, with the formula in standard notation, the solved symbol highlighted and a one-line substitution such as 1,500 kg × 20 m/s = 30,000 kg·m/s.
Momentum describes how hard it is to stop a moving object. A truck rolling slowly and a bullet flying fast can have similar momentum, even though they differ enormously in mass and speed. Unlike kinetic energy, momentum has a direction, and in a closed system with no outside forces the total momentum is conserved, which is the key to analysing collisions.
How to use the momentum calculator
Steps
- Fill in two fields and leave the one you want to find empty.
- Choose units. Momentum offers kg·m/s, N·s, g·cm/s and lb·ft/s, mass offers kg, g and lb, and velocity offers m/s, km/h, mph, ft/s and knots.
- Read the answer under the formula, then change the unit of the empty field to convert it.
- Press Clear all to reset.
Mass must be greater than zero. Velocity and momentum can be negative: a negative sign marks motion in the opposite direction. Negative values appear in brackets in the substitution line, for example 2 kg × (−3 m/s) = −6 kg·m/s.
Formula
p is momentum in kg·m/s, m is mass in kilograms and v is velocity in metres per second. The unit newton-second is the same as kilogram-metre per second, so 1 N·s = 1 kg·m/s.
Worked examples
Example 1: find the momentum
A 1,500 kg car moves at 20 m/s. Its momentum is p = 1,500 × 20 = 30,000 kg·m/s.
Example 2: find the velocity
A 3 kg cart has a momentum of 12 kg·m/s. Its velocity is v = 12 ÷ 3 = 4 m/s.
Example 3: find the mass
A vehicle with 30,000 kg·m/s of momentum moves at 15 m/s. Its mass is m = 30,000 ÷ 15 = 2,000 kg.
Example 4: opposite direction
A 2 kg ball moves at −3 m/s, which is 3 m/s to the left. Its momentum is p = 2 × (−3) = −6 kg·m/s.
Momentum and impulse
A force changes momentum by acting over time. That quantity is impulse, and the impulse-momentum theorem says it equals the change in momentum. The Impulse Calculator works out both J = F × Δt and J = m(v₂ − v₁), so you can go from a change in momentum to the average force of a collision.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
The Momentum Converter converts between momentum units, the Kinetic Energy Calculator finds the energy of the same motion, and the Speed Converter prepares a velocity in km/h or mph.
Frequently asked questions
What is momentum?
Momentum is mass times velocity, p = m × v. It measures how hard it is to stop a moving object, and it has a direction because velocity does.
How do I calculate momentum?
Enter the mass and the velocity and leave the momentum field empty. A 1,500 kg car moving at 20 m/s has a momentum of 30,000 kg·m/s.
How do I find mass or velocity from momentum?
Leave that field empty. Velocity is momentum divided by mass, and mass is momentum divided by velocity. A 3 kg cart with 12 kg·m/s moves at 4 m/s, and 30,000 kg·m/s at 15 m/s means 2,000 kg.
What is the unit of momentum?
The SI unit is the kilogram-metre per second, kg·m/s, which is the same as the newton-second, N·s. The calculator also offers g·cm/s and lb·ft/s as options.
Can momentum be negative?
Yes. A negative velocity means motion in the opposite direction, and it gives a negative momentum. For example, 2 kg at −3 m/s has −6 kg·m/s. Mass must always be greater than zero.
What is the difference between momentum and kinetic energy?
Momentum is mass times velocity and has a direction, and it is conserved in collisions. Kinetic energy is half mass times speed squared and has no direction. The Kinetic Energy Calculator handles the second.
Is my data private?
No. The mass, velocity and momentum you enter are calculated locally in your browser, and nothing is uploaded, stored or shared with a server, so private numbers stay on your device.