Physics · Mechanics · Motion & Energy

Momentum and impulse calculator

Calculate momentum, force impulse, average force or momentum change. Use signed components along one common axis.

Created Sep 30, 2026v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

Mechanics · Motion & Energy

Results

Momentum

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Mass times signed final velocity.

Impulse

—

Signed change in momentum, equal to net force integrated over time.

Net force

—

Signed net force along the chosen axis.

Initial momentum

—

Momentum before the specified velocity change.

Relation and numerical substitutionp = m × v

—

Signed one-axis quantities; m > 0; inverse force requires Δt > 0.

01Formulas and symbols

Formulas used

pp = m × vMass times signed final velocity.

JJ = F × ΔtSigned change in momentum, equal to net force integrated over time.

FF = J / ΔtSigned net force along the chosen axis.

p₀p₀ = m × v₀Momentum before the specified velocity change.

JJ = m × (v − v₀)Signed change in momentum, equal to net force integrated over time.

02Assumptions and limits

Scope of validity

Signed one-axis quantities; m > 0; inverse force requires Δt > 0.

03Validation example

Reference numerical case

m = 2 kg, v = 3 m/s: p = 6 kg·m/s. F = 10 N for Δt = 0.5 s: J = 5 N·s. For m = 2 kg from v₀ = 3 to v = 5.5 m/s, J = 2 × (5.5 − 3) = 5 N·s.

04References

Technical references

University Physics Volume 1, §9.2 Impulse and Collisions — OpenStax

FAQ

What is the difference between momentum and impulse?

Momentum p = mv describes the motion state of a mass at an instant. Impulse J = ∫F dt describes the accumulated effect of a net force over time, and the impulse–momentum theorem gives J = Δp.

Why does the same impulse produce the same change in momentum?

Because net impulse equals the change in momentum directly: J = Δp. The same impulse therefore gives the same Δp, although the resulting velocity change still depends on the mass.

05How it works

Momentum p describes motion at an instant. Impulse J describes its change over an interval: J = Δp. For a constant mass, the change mode uses both initial and final velocities. The force mode gives average net force over the specified duration.

06Limits of the model

Classical mechanics with constant positive mass. FΔt is valid for a constant net force or its time average; a varying force requires its integral for exact impulse. This is not a collision or momentum-conservation solver.

07Common mistakes

N·s and kg·m/s are equivalent, but neither is a joule. Initial momentum need not be zero; J is not generally final momentum. To test the change oracle, set final velocity to 5.5 m/s.