Free Momentum Calculator
Find the momentum of a moving object, model what happens when two objects collide, or calculate impulse and average force — all with instant, step-by-step results.
Understanding Momentum
Momentum measures how much motion a moving object carries, combining how heavy it is with how fast it’s going. It’s central to understanding everything from car crashes to rocket launches.
Key Concepts You Need
The physics behind every momentum problem
The Momentum Formula
Momentum equals mass multiplied by velocity (p = m × v), measured in kilogram-metres per second. Doubling either the mass or the velocity doubles the momentum.
Momentum Has Direction
Because velocity includes direction, momentum does too. A positive and negative velocity moving toward each other means their momenta can partly or fully cancel out.
Conservation of Momentum
In a closed system with no outside forces, total momentum before a collision always equals total momentum after it, even though individual objects change speed or direction.
Impulse and Force
Impulse is the change in momentum an object experiences, equal to force multiplied by the time it acts for — which is why airbags and padding reduce injury by extending contact time.
Momentum Calculator
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How to Calculate Momentum
Follow these steps to solve momentum problems by hand, or use the calculator above for an instant answer.
Identify Mass and Velocity
Write down the mass of the object in kilograms and its velocity in metres per second, including the direction it’s travelling in.
Apply the Momentum Formula
Multiply mass by velocity (p = m × v) to find the object’s momentum, keeping the sign consistent with your chosen positive direction.
For Collisions, Add Momenta Together
To find a combined velocity after a collision where objects stick together, add each object’s momentum before impact, then divide the total by the combined mass.
For Impulse, Find the Change in Momentum
Subtract initial momentum from final momentum to find the impulse, then divide by the time over which the change happened to find the average force involved.
Momentum vs Kinetic Energy
A side-by-side summary of how these two related, but different, physics quantities compare.
| Feature | Momentum | Kinetic Energy |
|---|---|---|
| Formula | p = m × v | KE = ½ × m × v² |
| Units | kg·m/s | Joules (J) |
| Has direction? | Yes, a vector quantity. | No, a scalar quantity. |
| Effect of doubling velocity | Doubles the value. | Quadruples the value. |
| Conserved in all collisions? | Always conserved in a closed system. | Only conserved in perfectly elastic collisions. |
| Which matters more in a crash? | Both matter — momentum determines the change in motion, kinetic energy determines the energy released as damage or heat. | |
Momentum FAQ
Answers to the most frequently asked questions about momentum, collisions, and impulse.
Momentum is a measure of an object’s mass in motion, calculated by multiplying an object’s mass by its velocity. It has both a size and a direction, since velocity itself is directional.
Momentum is calculated as p = m × v, where p is momentum, m is mass in kilograms, and v is velocity in metres per second, giving a result measured in kilogram-metres per second.
In any closed system with no external forces acting on it, total momentum before an event such as a collision always equals total momentum afterward, even though individual objects may speed up, slow down, or change direction.
Momentum describes how much motion an object has at a given moment, while force describes a push or pull that causes an object’s momentum to change over time, linked through the impulse-momentum theorem.
Impulse is the change in an object’s momentum, equal to the average force applied multiplied by the time over which it acts, which is why a longer contact time can reduce the force needed to produce the same change in momentum.