Engineering Mechanics

Momentum Calculator

Calculate linear momentum from mass and velocity, or back-solve for the mass or velocity needed to produce a target momentum using p = m × v.

Formula p = m × vReviewed Sep 8, 2026

Linear momentum is a measure of how difficult it is to stop a moving object. It depends on two things: how much mass the object has and how fast it is moving. The relationship is simply p = m × v - momentum equals mass times velocity. Momentum is a vector quantity, but this calculator works with magnitudes (speed), which covers the vast majority of engineering and physics problems. Use it to find momentum, to determine what mass moves at a given speed with a known momentum, or to find the velocity that produces a specific momentum for a given mass.

Calculation Bench

Solve for

01Mass

m · The mass of the moving object. Mass is a scalar - it does not depend on direction.

02Velocity

v · Speed magnitude of the object. This calculator uses the scalar (speed) form, so enter the magnitude only - direction is not needed.

Solution

Enter the required values to calculate momentum.

p = m × v

Formula Sheet

p = mv

m = \dfrac{p}{v}

v = \dfrac{p}{m}

pMomentum
mMass
vVelocity

Variables & Units

Symbol	Variable	Description	Common Units
p	Momentum	Linear momentum of the object - the product of its mass and velocity. Also equal to the impulse (force × time) needed to bring the object from rest to that state of motion.	kg·m/s, N·s, g·cm/s, lb·ft/s, slug·ft/s
m	Mass	The mass of the moving object. Mass is a scalar - it does not depend on direction.	g, kg, lb
v	Velocity	Speed magnitude of the object. This calculator uses the scalar (speed) form, so enter the magnitude only - direction is not needed.	m/s, km/h, mph, ft/s

How to Use This Calculator

01Select what you want to calculate: Momentum, Mass, or Velocity.
02Enter the two known values and select the correct units for each.
03Click Calculate to see the result, the active formula, and the substitution in SI base units.
04Use Load example to pre-fill a real-world scenario for the selected mode. Use speed magnitude here; if direction matters, track signs or vector components separately outside this scalar calculator.

How the Formula Works

Momentum is defined as the product of mass and velocity: p = m × v. In SI units, mass is in kilograms and velocity in meters per second, giving momentum the unit kilogram-meters per second (kg·m/s), also written as newton-seconds (N·s) because 1 N·s = 1 kg·m/s.

Momentum is conserved in a closed system - the total momentum before and after a collision or interaction remains the same (Newton's third law consequence). This makes it one of the most powerful tools in dynamics: if you know the combined momentum of two objects before a collision, you know their combined momentum afterward, even without knowing the forces involved.

The impulse-momentum theorem extends this: a net force applied over a time interval changes momentum by F × Δt = Δp. This links momentum directly to force and time, making it essential for impact, crash, and propulsion analysis.

Worked Example 01

Momentum of a moving car

Known

Mass (m): 1,500 kg
Velocity (v): 20 m/s

Formula

p = m × v

Substitution

p = 1,500 × 20

Result

p = 30,000 kg·m/s

A 1,500 kg car traveling at 20 m/s (72 km/h) carries 30,000 kg·m/s of momentum - the same impulse a braking force must overcome to bring it to rest.

Worked Example 02

Finding mass from momentum and speed

Known

Momentum (p): 500 kg·m/s
Velocity (v): 25 m/s

Formula

m = p / v

Substitution

m = 500 / 25

Result

m = 20 kg

An object moving at 25 m/s with a momentum of 500 kg·m/s has a mass of 20 kg - useful when momentum is known from an impulse measurement but mass is not directly given.

Worked Example 03

Finding velocity from momentum and mass

Known

Momentum (p): 750 kg·m/s
Mass (m): 60 kg

Formula

v = p / m

Substitution

v = 750 / 60

Result

v = 12.5 m/s

A 60 kg person with a momentum of 750 kg·m/s is moving at 12.5 m/s (45 km/h) - a speed that highlights the importance of protective equipment in cycling or skating.

Applications

01Calculating the momentum of vehicles, projectiles, or machinery in impact and safety analysis
02Solving textbook dynamics and impulse-momentum problems
03Checking momentum conservation before and after a collision
04Estimating the force needed to stop or redirect a moving mass within a given time (impulse = Δp)
05Sizing buffers, shock absorbers, and arresting systems based on expected incoming momentum

Assumptions

01The calculation is purely kinematic - it does not model forces, collisions, or energy dissipation.
02Velocity is treated as a speed magnitude; direction is not modeled (scalar form).
03Mass is constant - relativistic mass increase at speeds near the speed of light is not accounted for.
04Motion is translational (linear); rotational (angular) momentum is a separate quantity.

Where This Model Stops

01Does not solve conservation of momentum across two bodies - only computes one body's momentum at a time.
02Not valid for relativistic speeds (approaching the speed of light), where momentum is p = γmv.
03Does not compute impulse or the force-time history needed to produce a momentum change.
04Does not calculate kinetic energy automatically; compare with the Kinetic Energy Calculator when stopping distance, damage, or work-energy matters.

References

[1]
9.1 Linear Momentum - University Physics Volume 1
OpenStax
Defines linear momentum as p = mv, discusses its vector nature, and connects it to Newton's second law.
[2]
Engineering Mechanics: Dynamics, 14th Edition - §15-1 Principle of Linear Impulse and Momentum
Hibbeler / Pearson
Primary engineering-dynamics reference for momentum, impulse, and conservation - the standard undergraduate text.

Frequently Asked Questions

What unit is momentum measured in?

The SI unit of momentum is the kilogram-meter per second (kg·m/s). This is equivalent to the newton-second (N·s) because 1 N = 1 kg·m/s². Both names appear in engineering and physics texts; this calculator uses kg·m/s as the base unit.

Is momentum a vector or a scalar?

Momentum is a vector - it has both magnitude and direction. This calculator computes the magnitude only (using speed rather than velocity with direction). For problems involving direction (e.g. head-on collisions, 2D momentum conservation), you must resolve momentum into components separately.

How is momentum related to force?

Newton's second law in its most general form states that net force equals the rate of change of momentum: F = dp/dt. For constant mass, this simplifies to F = ma. The impulse-momentum theorem follows: F × Δt = Δp, meaning a force applied for a time interval produces a change in momentum equal to F × Δt.

What is conservation of momentum?

In a closed system (no external net force), the total momentum before an event equals the total momentum after it. This holds for all types of collisions - elastic, inelastic, and perfectly inelastic - and is one of the most reliable conservation laws in classical mechanics. This calculator computes a single body's momentum; to apply conservation you would compare the sum of momenta before and after.

How is this different from the Kinetic Energy Calculator?

Both use mass and velocity, but momentum (p = mv) is linear in velocity while kinetic energy (KE = ½mv²) is quadratic. Doubling velocity doubles momentum but quadruples kinetic energy. In collisions, momentum is always conserved; kinetic energy is only conserved in perfectly elastic collisions. Use momentum when analyzing force and time effects (impulse); use kinetic energy when analyzing work and energy transfer.

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