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Momentum Calculator

Computes linear momentum from mass and velocity, the matching kinetic energy, and, when a stopping time is given, the average force needed to bring the object to rest (impulse–momentum theorem).

When to use

You need an object's momentum, or the average force involved in stopping or launching it over a known time (collisions, braking, catching a ball).

Do not use when: You need the outcome of a two-body collision (conservation of momentum between two objects is not implemented), or only the energy of motion (use kinetic-energy).

Formula

p = mass_kg × velocity_m_s; KE = ½ × mass_kg × velocity_m_s²; average_stopping_force_n = |p| / stop_time_s (impulse F·Δt = Δp)

Inputs

Parameter	Type	Unit	Required	Description
`mass_kg`	number	kg	yes	Mass of the object in kilograms. Range: > 0
`velocity_m_s`	number	m/s	yes	Velocity in metres per second; sign indicates direction along the line of motion.
`stop_time_s`	number	s	no	Optional time over which the object is brought to rest; enables the average force output. Range: > 0

Outputs

Output	Type	Unit	Description
`momentum_kg_m_s`	number	kg·m/s	p = m × v (same sign as the velocity).
`kinetic_energy_j`	number	J	½ × m × v² for the same object.
`average_stopping_force_n`	number	N	\|p\| / stop_time_s: mean force to remove all momentum in the given time (only when stop_time_s is given).

Example

1200 kg car at 25 m/s stopped in 3 s: {"mass_kg":1200,"velocity_m_s":25,"stop_time_s":3} → {"momentum_kg_m_s":30000,"kinetic_energy_j":375000,"average_stopping_force_n":10000}

57 g tennis ball at 50 m/s: {"mass_kg":0.057,"velocity_m_s":50} → {"momentum_kg_m_s":2.85,"kinetic_energy_j":71.25}

GET https://tttkmbb.com/api/v1/calculate/momentum?mass_kg=1200&velocity_m_s=25&stop_time_s=3

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/momentum (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/momentum · Markdown: https://tttkmbb.com/physics/momentum.md · JSON definition: https://tttkmbb.com/physics/momentum.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="momentum"
OpenAPI operationId: calculate_momentum
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

HyperPhysics – Momentum (reference)
Wikipedia – Momentum (reference)

FAQ

What is the unit of momentum?

Kilogram-metres per second (kg·m/s), equivalent to newton-seconds (N·s), the unit of impulse.

Why does a longer stopping time reduce the force?

The impulse (force × time) needed equals the momentum change, so spreading it over more time (crumple zones, airbags, bending the knees) lowers the average force.

Related calculators

Kinetic Energy Calculator — Energy of the same moving object.
Force Calculator — Force from mass and acceleration.