The momentum formula
Linear momentum is the product of mass and velocity: p = m·v, where m is mass in kilograms and v is velocity in meters per second. A 10 kg object at 5 m/s gives 50 kg·m/s. Momentum is a vector, so direction matters. If you need the energy of a moving object, try the work calculator.
Momentum measures how hard an object is to stop. Newton originally framed his second law in these terms: a force changes an object's momentum, and the change equals the force multiplied by the time it acts. That product, force times time, is called impulse.
How to use this calculator
Enter the mass in kilograms and the velocity in meters per second. The result is momentum in kg·m/s, the SI unit. Use a negative velocity if the object moves in the opposite direction. For the force in circular motion, see the centripetal force calculator.
Convert other units before entering them: divide km/h by 3.6 to reach m/s, and use kilograms rather than grams or pounds. Pick one direction as positive and stay with it throughout a problem, so the signs of several momenta can be added meaningfully.
Worked example
Suppose a 10 kg cart rolls at 5 m/s. Multiply: 10 × 5 = 50 kg·m/s. Double the speed to 10 m/s and the momentum doubles to 100 kg·m/s, because momentum scales linearly with velocity.
Now let a second identical cart travel the other way at the same speed. Its momentum is −50 kg·m/s, so the pair together has zero total momentum. If they collide and stick, the combined wreck must sit still — a direct application of conservation of momentum, and the reason head-on collisions are so destructive. Momentum is linear in speed while kinetic energy rises with its square, which is why the two behave so differently in a collision.
Frequently asked questions
- How do I calculate momentum?
- Multiply the object's mass by its velocity: p = m·v.
- What are the units of momentum?
- Kilogram-meters per second (kg·m/s) in SI units.
- Is momentum a vector?
- Yes. It has both magnitude and direction, matching the direction of velocity.
- What is conservation of momentum?
- In a closed system with no external force, total momentum stays constant before and after a collision.
- How is momentum different from kinetic energy?
- Momentum is proportional to speed and keeps its direction, while kinetic energy depends on speed squared and has no direction. Momentum is conserved in every collision; kinetic energy is only conserved in perfectly elastic ones.