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Momentum is a measure of how much motion an object carries — the product of its mass and velocity, p = m × v. A heavy truck at walking pace and a bullet at high speed can carry similar momentum, which is why momentum, not just speed, governs collisions.
Choose what you want to find, enter the two values you know, and get the result in kg·m/s, kg or m/s.
Momentum Calculator: step-by-step worked example
- Solve for
- Momentum (from mass & velocity)
- Mass (kg)
- 0.145
- Velocity (m/s)
- 40
- 1
Momentum
p = m × v
0.145 kg × 40 m/s = 5.8 kg·m/s
- 2
Impulse needed to stop it
J = Δp = F × t (e.g. to stop it in 0.01 s, F = p ÷ 0.01)
5.8 ÷ 0.01 = 580 N
- 3
Kinetic energy of the same object
KE = p² ÷ (2 × m)
5.8² ÷ (2 × 0.145) = 116 J
- 0.145 kg:0 kg·m/s → 11.6 kg·m/s
Good to know: Momentum is a vector — reversing direction flips its sign. A 145 g baseball at 40 m/s (≈ 90 mph) carries 5.8 kg·m/s; total momentum is conserved in collisions.
Momentum Calculator — how it works
The momentum relation
| Solve for | Formula |
|---|---|
| Momentum p (kg·m/s) | mass × velocity |
| Mass m (kg) | momentum ÷ velocity |
| Velocity v (m/s) | momentum ÷ mass |
Mass is in kilograms and velocity in metres per second, so momentum is in kg·m/s.
Momentum is conserved
In any collision or explosion with no outside forces, the total momentum before equals the total momentum after. This conservation law is what lets you predict the velocities after a crash, the recoil of a gun, or the push-back of a rocket. It holds even when kinetic energy is lost to heat and sound.
Momentum vs kinetic energy
Both depend on mass and velocity, but differently: momentum is m × v (linear in speed, and a direction matters) while kinetic energy is ½ m v² (grows with the square of speed, no direction). A collision conserves momentum always, but conserves kinetic energy only if it's perfectly elastic.
Where it helps
Collision and recoil problems, impulse calculations, and physics homework. For the energy the same object carries, use a kinetic energy calculator; for the force that changes its momentum, a force calculator.
Worked example
A 1,500 kg car moving at 20 m/s has momentum p = m × v = 1,500 × 20 = 30,000 kg·m/s. A 0.02 kg bullet at 400 m/s has p = 0.02 × 400 = 8 kg·m/s — far less, despite its speed, because its mass is tiny. To match the car's momentum, the bullet would need an impossible velocity, which is why the heavy, slow object still dominates a collision.
Frequently asked questions
What is momentum?+
Momentum is the quantity of motion of an object, the product of its mass and velocity: p = m × v. It is a vector, so direction matters.
What are the units of momentum?+
Kilogram-metres per second (kg·m/s), when mass is in kilograms and velocity in metres per second. There is no separate named unit for momentum.
What is conservation of momentum?+
In a system with no external forces, total momentum stays constant. The momentum before a collision equals the momentum after, which is how recoil and crash outcomes are predicted.
How is momentum different from kinetic energy?+
Momentum is m × v and is always conserved in collisions; kinetic energy is ½ m v² and is only conserved in perfectly elastic collisions. Energy grows with the square of speed, momentum only linearly.
How do I find velocity from momentum?+
Divide the momentum by the mass: v = p ÷ m. Choose "Velocity" mode and enter the momentum and mass.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
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