Person out for a walk
A 70.0 kg walker moving at 1.4 m/s (about 5 km/h).
Momentum Calculator
Momentum is mass times velocity: a measure of how hard something is to stop. Two numbers in, one honest answer out.
Speed change while braking: decelerated motion. Height energy: potential energy.
Result
Enter values — the result shows up here.
How it works
Why does a freight train need a mile to stop while a cyclist halts in a few yards? Momentum: mass multiplied by velocity. It measures the quantity of motion. The more of it, the harder a body is to stop or steer. The second law of motion says exactly that: force is the rate of change of momentum, not only the "mass times acceleration" shortcut from school.
Momentum has one gorgeous property: in collisions it is conserved. The total before equals the total after, always, no exceptions. Billiards runs on it, but so does crash reconstruction. Forensic investigators work out pre-impact speeds from skid marks and final positions using conservation of momentum, essentially reading the equation off the asphalt.
Intuition struggles here because momentum mixes two things. A person out for a walk carries about 100 kg·m/s. A soccer ball off a hard strike: barely 13 kg·m/s, despite flying at 30 m/s. A mosquito? Effectively zero, which is why hitting one feels like a tickle rather than a punch. At the other end, a freight train at just 60 km/h hauls around 30 million kg·m/s. Hence mile-long stopping distances and crossing gates that do not negotiate.
Enter the mass in your chosen unit ({{mass}}). The header toggle switches systems. Enter the speed in the unit shown next to the field. The result comes out in kg·m/s regardless, since momentum is an SI quantity.
Mind the direction, too: momentum is a vector. Two identical carts rolling toward each other at equal speeds have a combined momentum of zero; couple them together and they stop dead. This calculator gives you the magnitude; signs and directions stay on your side of the notebook.
How to use
- Enter the mass in your chosen unit ({{mass}}).
- Enter the speed in the unit shown next to the field.
- Read the momentum in kg·m/s.
Formula
p = m · v
m is the mass and v is the velocity in m/s. The result p comes out in kg·m/s. Momentum is a vector, so direction matters when you add momenta together.
Real-life examples
Cyclist on the road
Rider plus bike, 85.0 kg total, at 6.9 m/s (about 25 km/h).
Car in city traffic
A 1400 kg car rolling at 13.9 m/s (about 50 km/h).
Soccer ball off a strike
A 0.43 kg ball flying 30 m/s after a hard shot.
Tennis ball after a serve
A 0.06 kg ball at 55 m/s (a 193 km/h serve).
Semi truck on the interstate
A 40000 kg rig cruising at 22.2 m/s (about 80 km/h).
Speed skater
A 75.0 kg skater on the straight: 12 m/s.
Freight train
A 2000000 kg consist rolling at 16.7 m/s (about 60 km/h).
Mosquito in flight
A 0.00 kg mosquito cruising at 0.5 m/s: for scale.
Basketball pass
A chest pass: a 0.62 kg ball at 7 m/s.
Frequently asked questions
How do I calculate momentum?
Multiply mass by speed: p = m·v. A 70 kg person walking at 1.4 m/s carries 98 kg·m/s of momentum.
What unit is momentum measured in?
kg·m/s. It never got its own name, though you will also see N·s (newton-seconds), which is exactly equivalent.
Can I enter the mass in pounds?
Yes. The unit toggle in the page header switches between kilograms and pounds, and the calculator converts behind the scenes. The result stays in kg·m/s, the SI unit.
What is the difference between momentum and kinetic energy?
Momentum is m·v; kinetic energy is ½mv²: speed enters once versus squared. In practice: momentum tells you how hard something is to stop, energy tells you how much damage it does when it stops.
Why is momentum conserved in collisions?
Because the forces two colliding bodies exert on each other are equal and opposite, so their momentum changes cancel out. The total before and after is identical: one of the most ironclad laws in physics.
How much momentum does a car have in town?
A typical car at 50 km/h (13.9 m/s) carries about 19500 kg·m/s, two hundred times more than a pedestrian. That imbalance is the entire physics of road safety in one number.
Why does a train take over a mile to stop?
A freight consist at 60 km/h holds around 30 million kg·m/s, and steel wheels on steel rails offer limited friction. Hence the iron rule: the car yields at the crossing, never the train.
Can momentum be negative?
Yes. Momentum is a vector, so the sign depends on your chosen direction. Two carts heading toward each other with equal momenta total zero, and coupled together they stop on the spot.
How do crash investigators use momentum?
They measure skid marks and where the vehicles ended up, then apply conservation of momentum to compute pre-impact speeds. It is routine evidence in court cases.
What is impulse?
Force multiplied by the time it acts, and that product exactly equals the change in momentum. This is why airbags work: they stretch out the stopping time, so the same momentum change needs far less force.
How much momentum does a tennis serve carry?
At 55 m/s with a 58-gram ball, only about 3.2 kg·m/s, less than a strolling cat. The kinetic energy is substantial though, since speed gets squared there.