Momentum Calculator
Calculate linear momentum (p = m·v) from mass and velocity, with the kinetic energy — the conserved quantity behind collisions, recoil, and propulsion.
How to use this calculator
- 1Enter the object's mass in kilograms.
- 2Enter its velocity in metres per second (negative for the opposite direction).
- 3Read the momentum and the kinetic energy.
- 4Use the impulse figure to see the force-over-time needed to stop it.
How it works
Linear momentum
p = m × v p = momentum (kg·m/s), m = mass, v = velocity impulse = force × time = change in momentum kinetic energy = ½ m v²
Momentum is the quantity of motion an object carries, defined simply as its mass times its velocity. A heavy object moving slowly and a light object moving quickly can have the same momentum. Because velocity is a vector, momentum has direction as well as magnitude, which matters when objects interact. The deep importance of momentum comes from its conservation: in any isolated system, with no external forces, the total momentum stays constant. When objects collide or push apart, momentum simply redistributes between them, so the total before equals the total after. Changing an object's momentum requires an impulse — a force applied over a time — and the change in momentum exactly equals that impulse. Momentum should not be confused with kinetic energy: momentum is proportional to speed, while kinetic energy is proportional to speed squared, so the two behave very differently as speed rises.
Worked example
A 1,000 kg car travelling at 20 m/s (72 km/h) has a momentum of 1,000 × 20 = 20,000 kg·m/s. Its kinetic energy is ½ × 1,000 × 20² = 200,000 joules. To bring it to a stop, brakes must supply an impulse of 20,000 N·s — say 20,000 newtons for one second, or 10,000 newtons for two.
Momentum Calculator: the complete guide
Conservation of momentum
The reason momentum is one of the most important quantities in physics is that it is conserved. In any system free of outside forces, the total momentum — adding up mass times velocity for everything, with direction taken into account — remains exactly the same over time. This is not an approximation but a fundamental law, rooted in the symmetry of space itself. It means that whenever objects interact, whatever momentum one gains, another must lose, so the books always balance.
This conservation principle explains a huge range of phenomena that would otherwise seem unrelated. A rifle recoils backward because the forward momentum given to the bullet must be matched by equal backward momentum in the gun. A rocket accelerates in the vacuum of space, with nothing to push against, because it hurls exhaust gas backward and gains equal forward momentum in return. Ice skaters push off each other and glide apart in opposite directions. In every case, the total momentum started at zero and stays at zero, with the pieces sharing it out. Once you learn to look for conserved momentum, these seemingly diverse situations reveal themselves as the same law at work.
Impulse: changing momentum over time
To change an object's momentum, you must apply a force, and the effect depends not just on how strong the force is but on how long it acts. This product of force and time is called impulse, and it equals exactly the change in momentum produced. A small force applied for a long time can change momentum as much as a large force applied briefly. This relationship is why the same change in motion can be achieved gently or violently, a fact with enormous practical consequences for safety.
Consider stopping a moving car, or catching a fast ball. The momentum that must be removed is fixed, so the impulse required is fixed — but you can deliver that impulse over a short time with a huge force, or over a longer time with a gentler force. Crumple zones in cars, airbags, padded landing surfaces, and a boxer rolling with a punch all work on this principle: they extend the time over which momentum changes, reducing the peak force and therefore the damage. Understanding impulse turns momentum from an abstract quantity into a guide for how to make collisions survivable, which is why it underpins so much of engineering for safety.
Momentum versus kinetic energy
Momentum and kinetic energy are both measures of motion, and both are conserved in certain circumstances, but they are not the same and confusing them leads to errors. Momentum is mass times velocity, growing in direct proportion to speed. Kinetic energy is one-half mass times velocity squared, growing with the square of speed. This difference in how they scale with speed is profound: doubling an object's speed doubles its momentum but quadruples its kinetic energy.
The squared relationship for energy is why speed is so dangerous. A car travelling at 60 mph has twice the momentum of one at 30 mph, but four times the kinetic energy — and it is the energy that must be dissipated to stop, so the braking distance and the destructive potential of a crash rise far faster than speed alone suggests. The two quantities also behave differently in collisions: total momentum is always conserved, but total kinetic energy is only conserved in perfectly elastic collisions; in real, inelastic collisions some energy is lost to heat and deformation while momentum is still perfectly conserved. Keeping the two concepts distinct — momentum for the exchange of motion, energy for the capacity to do damage or work — is essential to reasoning about anything that moves and collides.
Frequently asked questions
How do I calculate momentum?
Multiply mass by velocity: p = m × v. A 1,000 kg car at 20 m/s has a momentum of 20,000 kg·m/s. Momentum is a vector, so its direction matters — use a negative velocity for motion in the opposite direction.
What is conservation of momentum?
In a system with no external forces, total momentum stays constant. When objects collide or push apart, momentum redistributes but the total is unchanged. This explains gun recoil, rocket propulsion, and how colliding objects exchange motion — the total before always equals the total after.
What's the difference between momentum and kinetic energy?
Momentum (m·v) grows in proportion to speed; kinetic energy (½mv²) grows with speed squared. Doubling speed doubles momentum but quadruples energy. Momentum is always conserved in collisions; kinetic energy only in perfectly elastic ones. The energy scaling is why crashes get so much worse with speed.
What is impulse?
Impulse is force times the time it acts, and it equals the change in momentum. To stop a moving object you deliver a fixed impulse — either a big force briefly or a gentler force over longer. Crumple zones and airbags extend the time to reduce the peak force, which is how they protect you.