Conservation of Momentum Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

Share Print Save

A calculator saves arithmetic, but it should not hide the physics. For conservation of momentum, motion calculations become useful when the inputs and assumptions are kept explicit. A clean result can help you compare scenarios quickly, but the number only means what the underlying kinematic or drag model allows.

What this calculator does

The Conservation of Momentum Calculator evaluates the relationship behind conservation of momentum and reports final velocity (v₂) from the values entered on the page. Supporting values, where available, help you see the intermediate physics instead of treating the headline number as a black box.

How to use it

Start with the fields that drive the current calculation: Mass (m₁), Initial velocity (u₁), Final velocity (v₁), Mass (m₂). Enter values in the units shown beside each field; the page converts supported units before applying the formula. Keep signs and angles consistent with the labels, then read the headline result together with any supporting metrics rather than copying the number without its unit.

How the calculation works

The calculation enforces one-dimensional momentum conservation: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. With v₂ left as the unknown, it rearranges to v₂ = (m₁u₁ + m₂u₂ − m₁v₁)/m₂. Initial and final kinetic energies are also compared, but they are not used to force a particular collision type.

Example

Using the default example on the page (Mass (m₁) = 8 kg; Initial velocity (u₁) = 10 m/s; Final velocity (v₁) = 4 m/s; Mass (m₂) = 4 kg), the calculator returns final velocity (v₂) of 12 m/s. Change one input at a time and compare the direction of the change with the formula above; that is a quick way to catch a wrong unit, sign, or selected method before you rely on the number.

How to interpret the result

On the Conservation of Momentum Calculator, read the final velocity (v₂) together with the direction, time, or supporting trajectory values shown on the page. A physically reasonable result should respond consistently when you change speed, angle, height, drag, or mass according to the formula. Always keep the displayed unit attached to the number.

Limitations and notes

The visible collision-type selector does not change the current arithmetic. Momentum is conserved in the calculation, while kinetic energy is only reported for comparison. A ‘perfectly elastic’ or ‘perfectly inelastic’ label therefore does not impose the extra condition that such a collision would require.