Momentum Calculator

Linear momentum, impulse, and kinetic energy from mass and velocity.

About this calculator

This calculator starts from the basic definition of linear momentum, p = mv, and kinetic energy, KE = ½mv², for an object's current mass and velocity, then layers on an impulse scenario: apply a given force for a given duration and see how the object's motion changes. Impulse is computed as J = F·Δt, and by the impulse-momentum theorem that impulse equals the object's change in momentum, so dividing by mass gives the resulting velocity change (Δv = J/m), which is added to the initial velocity to produce a final velocity and a final momentum. The calculator then double-checks its own physics by reporting momentum change directly and noting that it should equal the impulse you specified — if the two figures match, the impulse-momentum theorem checked out as expected.

One subtlety: velocity is signed, so a force applied in the same direction as motion increases speed, while the same force could just as easily represent a braking force if you interpret negative values as opposing the object's direction — the calculator itself always adds the impulse-driven velocity change in the positive direction, so decelerating scenarios need to be modeled with careful sign choices on your part. The included "de Broglie" output computes a quantum-mechanical wavelength, λ = h/p (using Planck's constant), purely as a curiosity — it applies to any object with momentum in principle, but the wavelength is only physically meaningful (detectable via interference effects) for particles at atomic scales or smaller; for a macroscopic mass and everyday velocity it will compute as an almost inconceivably tiny, physically irrelevant number.

Inputs

Mass (kg)

Velocity (m/s)

Applied Force (N)

Force Duration (s)

Tab to move between fields

Results

Momentum (kg·m/s)

Kinetic Energy (J)

250

Impulse (N·s)25

Velocity Change (m/s)5

Final Velocity (m/s)15

Final Momentum (kg·m/s)75

Momentum Change (kg·m/s)25

De Broglie0

How to Use This Calculator

Enter mass (kg) and current velocity (m/s) of the object.
Enter applied force (N) and force duration (s) for the impulse calculation.
Read momentum (kg·m/s) and kinetic energy (J).
Review impulse (N·s), velocity change (m/s), and final velocity (m/s) after the impulse.
Confirm that momentum change equals the applied impulse.

How the result changes with Mass (kg)

Mass (kg)	Momentum (kg·m/s)	Kinetic Energy (J)
2.5	25	125
3.75	37.5	187.5
7.5	75	375
13	130	650

What each input means

Mass (kg): Mass of the object in kilograms.
Velocity (m/s): Current velocity (positive direction).
Applied Force (N): Force applied for impulse calculation.
Force Duration (s): Duration the force is applied.

What each result means

Momentum (kg·m/s): p = mv. Linear momentum.
Kinetic Energy (J): KE = ½mv².
Impulse (N·s): J = F·Δt. Change in momentum from applied force.
Velocity Change (m/s): Δv = J/m.
Final Velocity (m/s): v_f = v_i + Δv.
Final Momentum (kg·m/s): Momentum after impulse.
Momentum Change (kg·m/s): Δp = J. Should equal impulse.

How this is calculated

Worked example, using the default values

Identify Input Parameters
4 parameters
Mass (kg) = 5, Velocity (m/s) = 10, Applied Force (N) = 50, Force Duration (s) = 0.5 = 4 input(s) provided
Calculate Momentum
Momentum = massKg * velocityMs
50 = 50
Calculate Kinetic Energy
Kinetic Energy = 0.5 * massKg * velocityMs * velocityMs
250 = 250
Calculate Impulse
Impulse = forceN * timeDurationS
25 = 25
Calculate Velocity Change
Velocity Change = forceN * timeDurationS / massKg
5 = 5

Engine last updated September 1, 2026. Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does momentum change end up equal to impulse — is that a coincidence?

No, it's a direct check built into the math: the calculator computes velocity change as Δv = J/m (from impulse J = F·Δt), then adds that to the initial velocity to get a final velocity and final momentum. Momentum change is then simply final momentum minus initial momentum, which by construction equals J — so seeing the two figures match is confirmation the impulse-momentum theorem was applied correctly, not an independent verification of different physics.

Can I model a braking or decelerating force with this calculator?

Only indirectly — the engine always adds the impulse-driven velocity change (Δv = F·Δt/m) in the positive direction to your initial velocity, since force is entered as a non-negative magnitude (clamped to a minimum of 0). To model deceleration, you need to enter a negative initial velocity yourself so that adding a positive Δv effectively slows the object down relative to its direction of motion; the calculator won't infer a 'braking' interpretation on its own.

What does the de Broglie wavelength output actually mean for an everyday object?

It's computed as λ = h/p, Planck's constant divided by momentum, which is a genuine quantum-mechanical formula that applies to any object with momentum in principle. But for a macroscopic mass moving at ordinary velocities, momentum is so large that the resulting wavelength is an inconceivably tiny number — far too small to produce any observable wave effect — so the output is included as a physics curiosity rather than something with practical meaning outside atomic-scale particles.

Why is kinetic energy computed from velocity rather than from the momentum value shown above it?

The engine calculates kinetic energy directly as ½mv² using your entered mass and velocity, the same two inputs used for momentum (p = mv) — it doesn't derive KE from momentum via KE = p²/(2m), even though that would give an equivalent result. Both formulas are mathematically consistent for the same mass and velocity, so the displayed KE will always agree with what you'd get from either approach.

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