Momentum Calculator (p = mv)
Solve p = mv for momentum, mass, or velocity. Enter any two values and get the third instantly with unit-labeled, step-by-step working shown.
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The momentum formula
Linear momentum measures how much "motion" a moving object carries — the product of its mass and velocity:
- p — momentum, in kilogram-metres per second (kg·m/s)
- m — mass, in kilograms (kg) — always positive
- v — velocity, in metres per second (m/s) — can be negative (direction matters)
Enter any two values and leave the third blank to solve for it.
Worked example
A 5 kg object moves at 4 m/s. What is its momentum?
- Formula: p = mv
- Substitute: p = 5 × 4
- Result: p = 20 kg·m/s
Solving in reverse
- Mass: m = p / v — enter p and v, leave m blank. Example: p = 20 kg·m/s at v = 4 m/s gives m = 5 kg.
- Velocity: v = p / m — enter p and m, leave v blank. Example: p = 20 kg·m/s with m = 5 kg gives v = 4 m/s.
Tip: Momentum is a vector — its sign shows direction, not just size. Two objects moving toward each other have momenta with opposite signs, which is why total momentum can cancel out even when both objects are moving fast.
Common mix-ups
- Confusing momentum with force. Force is mass × acceleration; momentum is mass × velocity — related but not the same quantity.
- Ignoring direction. Momentum's sign encodes direction; dropping it when adding momenta from multiple objects gives wrong totals.
- Mixing units. Speeds in km/h or mph must be converted to m/s before use.
Where this shows up
Momentum is central to collision analysis (cars, billiard balls, particles), rocket propulsion, and any scenario where mass and motion combine. It connects directly to the impulse and impulse–momentum theorem calculators, which describe how a force changes momentum over time, and to force via F = ma.
Frequently asked questions
- What is the formula for momentum?
- Linear momentum is p = mv, where p is momentum in kilogram-metres per second (kg·m/s), m is mass in kilograms (kg), and v is velocity in metres per second (m/s).
- How do I find velocity if I know momentum and mass?
- Rearrange the formula to v = p / m. Enter the momentum and mass values and leave velocity blank, and the calculator solves it for you.
- Can momentum be negative?
- Yes. Momentum has both magnitude and direction — a negative sign just means the object is moving in the direction you defined as negative. Only mass must stay positive.
- What units does the calculator use?
- SI units: kilograms (kg) for mass, metres per second (m/s) for velocity, and kilogram-metres per second (kg·m/s) for momentum. Convert other units before entering values.
- How is momentum different from force?
- Force is mass times acceleration (F = ma); momentum is mass times velocity (p = mv). They're linked by the impulse–momentum theorem, which describes how a force applied over time changes an object's momentum.
- Why does a heavier, slower object sometimes have more momentum than a lighter, faster one?
- Momentum depends on the product of mass and velocity, not either alone. A 100 kg object at 2 m/s (p = 200 kg·m/s) has more momentum than a 5 kg object at 30 m/s (p = 150 kg·m/s), even though the second object moves much faster.