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How to use
Use the momentum calculator to find momentum from mass and velocity with p=mv, or rearrange the same equation to solve for mass or velocity. Signed values preserve the chosen one-dimensional direction. Worked example: a 1,200 kg car at 72 km/h moves at 20 m/s, giving momentum 24,000 kg·m/s, also 24,000 N·s. To solve velocity, divide momentum by mass: 60 kg·m/s with a mass of 3 kg gives 20 m/s.
- Choose momentum p, mass m or velocity v as the unknown.
- Enter known values and units; velocity or momentum may be negative for the opposite direction.
- Calculate the result and SI equivalent.
How it is calculated
Example
Example: a 0.15 kg object at -30 m/s has momentum -4.5 kg·m/s relative to the chosen sign axis.
Important notes
The calculator handles one signed linear component only; it is not a 2D/3D vector or multi-body collision solver.
Worked examples and interpreting results
In one dimension, linear momentum is mass times velocity. A 2 kg object moving at 3 m/s has momentum 6 kg·m/s; reversing velocity reverses the momentum sign.
| Case | Calculation | Result |
|---|---|---|
| Motion in the positive direction | 2 × 3 | 6 kg·m/s |
| Motion in the negative direction | 2 × (−3) | -6 kg·m/s |
How to check the result
Momentum is a vector quantity. Use consistent direction signs when combining momenta in one dimension. Do not confuse it with kinetic energy, which depends on velocity squared and is non-negative.
Momentum formula p = mv: mass, speed and direction
Linear momentum equals mass multiplied by velocity. Convert speed to metres per second and mass to kilograms for SI results. To solve for velocity, divide momentum by mass; a negative sign identifies the opposite chosen direction.
- 1200 kg at 20 m/s: 1200 × 20 = 24000 kg·m/s
- Velocity from momentum 90 and mass 3: 90 ÷ 3 = 30 m/s
- 0.4 kg moving at −5 m/s: 0.4 × (−5) = −2 kg·m/s
Important distinction
Momentum has direction, unlike kinetic energy. A negative momentum is not an error: it indicates motion opposite the positive axis. Use consistent units in every calculation.
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Frequently asked questions
How do I calculate momentum?
Multiply mass by velocity: p = mv. Use kilograms and metres per second for momentum in kg·m/s.
Is N·s equal to kg·m/s?
Yes. They are dimensionally and numerically equivalent in SI.
Why can momentum be negative?
The sign represents direction along your chosen axis; mass itself remains positive.
When is momentum conserved?
Total momentum is conserved for an isolated system when the net external impulse is negligible. During a collision each object’s momentum may change while the system total remains constant.
What is the difference between momentum and kinetic energy?
Momentum p = mv has a direction; kinetic energy K = ½mv² is nonnegative. At constant mass, doubling speed doubles momentum magnitude and quadruples kinetic energy.