Momentum Calculator
Momentum measures how hard something is to stop: mass times velocity, the quantity of motion it carries. A peloton, a freight wagon and a fired bullet all owe their impact force to it, and collisions are momentum being shared. The number is easy to compute but easy to misread across unit systems — ballistics uses g·cm/s, rail planning tonne·m/s — so this calculator returns all three from one pair of inputs.
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Results
- Momentum
- 10 kg·m/s
- In gram·centimetres per second
- 1,000,000 g·cm/s
- In tonne·metres per second
- 0.01 tonne·m/s
How is the Momentum calculated?
Two number fields: the mass in kilograms and the speed in metres per second. Multiplying them gives the momentum in kg·m/s, the SI unit. The page then restates the same quantity in g·cm/s by multiplying by 100,000 and in tonne·m/s by dividing by a thousand. A negative speed is allowed and simply flips the sign, marking motion in the opposite direction rather than an error.
Formula
p = m × v, where p is the momentum in kg·m/s, m the mass in kilograms and v the speed in m/s. Multiplying by 100,000 converts to g·cm/s, since a kilogram is 1,000 grams and a metre 100 centimetres. Dividing by 1,000 converts to tonne·m/s. The sign of v carries direction: opposite travel shows as negative momentum of the same size.
Example
A 2 kg object moving at 5 m/s carries p = 2 × 5 = 10 kg·m/s. In ballistics units that is 10 × 100,000 = 1,000,000 g·cm/s, and in rail units 10 ÷ 1,000 = 0.01 tonne·m/s. Scale up to a 1,500 kg car at 20 m/s: 30,000 kg·m/s, which is exactly 30 tonne·m/s — one tonne moving at 1 m/s each — showing why heavy, slow trains deserve the same caution as light, fast cars.
Things to remember
Momentum is conserved in every collision — the total before and after never changes, only its distribution — so track it in every impact. Keep units honest: the g·cm/s figure looks enormous, both its units are small. For force and impact duration, the force converter picks up.
Frequently Asked Questions
How do you calculate momentum?
Multiply mass by velocity. A 2 kg mass at 5 m/s carries 10 kg·m/s of momentum. Double either input and the momentum doubles, which is why a slow truck can be harder to stop than a fast motorcycle despite similar energies.
What units are momentum measured in?
The SI unit is kg·m/s. Ballistics historically use g·cm/s, which is 100,000 times larger — 10 kg·m/s equals 1,000,000 g·cm/s — and railway work uses tonne·m/s, a thousandth of the SI value. This calculator shows all three together.
Can momentum be negative in practice?
Yes, when velocity is negative, meaning travel in the chosen opposite direction. A 3 kg mass moving at −2 m/s carries −6 kg·m/s: the same difficulty to stop, just headed the other way. Only the direction changes; the magnitude of the effect is identical.
Why does momentum matter in collisions?
Because the total momentum of a closed system never changes — before an impact it equals the total after, redistributed between the objects. That conservation law is what lets accident reconstructions and billiard-shot predictions work from nothing but masses and speeds.
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