What is the formula for momentum?

Momentum p equals mass m times velocity v, written p = mv. Mass is in kilograms and velocity in metres per second, giving momentum in kilogram metres per second (kg m/s). It measures how much motion an object has and how hard it is to stop.

What is impulse and how does it relate to momentum?

Impulse J is the product of force and the time over which it acts: J = F times t. The impulse-momentum theorem states that impulse equals the change in momentum. So to stop a moving object, applying a larger force for a shorter time or a smaller force for a longer time both work, as long as the product equals the object's momentum.

Why do crumple zones reduce injury in crashes?

By extending the time over which the car decelerates, crumple zones reduce the average force on occupants. Since impulse equals change in momentum, the total change in momentum (the crash) is fixed, but spreading it over more time means a smaller force, which is what causes injury.

Momentum Calculator

Momentum is the product of an object's mass and velocity, written p = mv, and it is one of the most conserved and therefore most useful quantities in physics. A heavy lorry rolling slowly and a light car moving fast can carry the same momentum, which is why understanding both mass and speed is essential in collision analysis, safety engineering, and sport. This calculator covers three related calculations. In the basic momentum mode you enter mass in kilograms and velocity in metres per second and it returns momentum in kg m/s along with kinetic energy in joules. In the impulse mode you enter a force in newtons and the time over which it acts, and the calculator returns the impulse in newton-seconds, which by the impulse-momentum theorem equals the change in momentum produced. In the change in momentum mode you enter the same mass and two velocities, initial and final, and it returns the change in momentum directly. The default worked example uses a 5 kg object moving at 20 m/s, giving a momentum of 100 kg m/s and a kinetic energy of 1,000 J. All three modes update as you type. The impulse-momentum connection is physically important: it explains why airbags and crumple zones save lives (they extend the stopping time, reducing the peak force), why a cricket bat follows through (prolonging the contact increases the impulse and therefore the ball's change in momentum), and why it is easier to stop a slow object than a fast one of the same mass. Use this tool for physics homework, collision problems, or to build intuition for how mass and velocity interact.

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Calculation

Mass

Velocity

m/s

100 kg·m/s

momentum

Kinetic energy1,000 J

Velocity in km/h72.00 km/h

Velocity in m/s20.00 m/s

p = mv in kg m/s. Kinetic energy = 0.5 mv² in joules. Impulse = force x time = change in momentum. SI units, rounded for display.

How it works

Momentum is mass times velocity: p = mv. Kinetic energy is half of mass times velocity squared: KE = 0.5mv². Impulse equals force times time: J = Ft, and by the impulse-momentum theorem, J = Δp, the change in momentum. So if you apply an impulse to an object, its momentum changes by exactly that amount. Change in momentum is mass times the change in velocity: Δp = m(v - u).

Worked example

A 5 kg object moves at 20 m/s. Momentum = 5 times 20 = 100 kg m/s. Kinetic energy = 0.5 times 5 times 400 = 1,000 J. The velocity converts to 72.00 km/h. These match the default values pre-filled above.

Related calculators

Kinetic Energy Calculator: energy of a moving object.
Force Calculator: net force from mass and acceleration.
Average Velocity Calculator: velocity from displacement and time.
Work Calculator: work done by a force over a distance.

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