Inelastic Collision Calculator
Enter two masses and their initial velocities to find the shared final velocity after they collide and stick together (a perfectly inelastic collision). A live 3D scene shows the objects merge into one, and charts show the kinetic energy lost to heat, sound and deformation.
Reviewed by the ToolNestr Editorial Team — July 2026
Two ideas that trip students up
1. The objects merge into one
The blue and red spheres collide and stick together, becoming the single green combined body moving at v' — unlike an elastic collision, they never separate again.
2. Kinetic energy is lost, not conserved
Two stacked blocks compare total kinetic energy before and after. The shorter after-block shows energy that vanished into heat, sound and deformation — momentum still balances, but KE does not.
Collision graphs
How it works
The core idea in one line: in a perfectly inelastic collision the objects stick together, so momentum conservation alone determines the single shared final velocity — kinetic energy is not conserved.
v' = (m1·u1 + m2·u2) / (m1+m2)
shared final velocity (objects stick together)
p_before = p_after
momentum is conserved
KE lost = KE_before − ½(m1+m2)v'²
kinetic energy is NOT conserved
Because the objects share one final velocity, momentum conservation m1u1 + m2u2 = (m1+m2)v' has only one unknown, making it the simplest collision to solve. The kinetic energy that vanishes — always the largest possible loss consistent with momentum conservation — goes into heat, sound and permanent deformation, which is exactly what car crumple zones and packaging are designed to absorb safely.
Worked example 1 — bullet embeds in a block
Given: A 0.010 kg bullet moving at 400 m/s embeds in a stationary 2.0 kg wooden block. Find the final velocity and the kinetic energy lost.
Worked example 2 — train cars coupling
Given: A 20,000 kg train car moving at 3.0 m/s couples with a stationary 15,000 kg car. Find the combined final velocity.
Elastic vs inelastic vs perfectly inelastic collisions
All three conserve momentum. What changes is kinetic energy and whether the objects stick together.
| Collision type | Momentum | Kinetic energy | After collision |
|---|---|---|---|
| Elastic | Conserved | Conserved | Objects separate, bounce apart |
| Inelastic (general) | Conserved | Some KE lost to heat/sound/deformation | Objects separate, may deform |
| Perfectly inelastic | Conserved | Maximum KE lost (but not necessarily all) | Objects stick together, move as one |
Momentum conservation holds for every closed collision — a perfectly inelastic collision loses the most kinetic energy possible while still conserving momentum.
Where inelastic collisions actually matter
🚗 Car crash analysis
When vehicles crumple together in a crash, accident investigators often model the impact as perfectly inelastic to estimate impact speeds from the wreckage — momentum conservation gives a lower bound on how fast the vehicles were moving.
🚂 Train and freight coupling
Rail cars are designed to couple and move together after impact — an intentionally inelastic collision. The kinetic energy "lost" is absorbed by couplers and buffers so it does not damage the cargo or cars.
🏈 Tackles and impacts in sport
A football tackle where two players end up moving together is a real-world perfectly inelastic collision. The kinetic energy lost is why such impacts feel much harder than a glancing, more elastic collision.
Common misconceptions
"Inelastic collisions don't conserve anything."
Momentum is still conserved — it is conserved in every closed collision regardless of type. Only kinetic energy fails to be conserved in an inelastic collision.
"Perfectly inelastic means all kinetic energy is lost."
Not necessarily all — just the maximum amount possible while momentum is still conserved. If both objects end up at rest (e.g. equal and opposite momenta), then yes, all KE is lost; otherwise, some kinetic energy typically remains in the combined motion.
"Objects only stick together if they are sticky or soft."
Stickiness is one way to get a perfectly inelastic collision, but any mechanism that leaves both objects with the same final velocity qualifies — a latching coupler, a tackle, or a bullet embedding in wood all count.
"The heavier object always ends up moving faster."
The combined velocity is a mass-weighted average of the initial velocities — it depends on both masses and both velocities together, not on which object is heavier alone.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §9.4 "Types of Collisions" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 9, Center of Mass and Linear Momentum, perfectly inelastic collisions.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 9, Linear Momentum and Collisions.
Formulas assume a 1D (head-on) collision with no external forces, and that the objects merge into one body. Results are rounded for display.
How to use this calculator
Enter the masses
Type m1 and m2 — any consistent mass unit works since it cancels in the ratio.
Enter the velocities
Type u1 and u2 in m/s; use negative signs for objects approaching from opposite directions.
Check the energy loss
Read the shared final velocity v', then see exactly how much kinetic energy was lost to heat, sound and deformation.
Related tools
Frequently asked questions
What is a perfectly inelastic collision?
A perfectly inelastic collision is one where the two objects stick together after impact and move with a single common final velocity. Momentum is still conserved, but kinetic energy is not — some is converted to heat, sound and permanent deformation.
What is the formula for the final velocity?
For masses m1 and m2 with initial velocities u1 and u2 colliding and sticking together, v' = (m1u1 + m2u2) / (m1+m2). This comes directly from conservation of momentum: m1u1 + m2u2 = (m1+m2)v'.
How much kinetic energy is lost in an inelastic collision?
KE lost = KE_before − KE_after = [½m1u1² + ½m2u2²] − ½(m1+m2)v'². For a perfectly inelastic collision this loss is the maximum possible while still conserving momentum — no other outcome loses more kinetic energy.
Is momentum conserved in an inelastic collision?
Yes. Momentum conservation holds for any closed collision, elastic or not, because it follows from Newton's third law alone. Only kinetic energy conservation is special to the elastic case.
What are real examples of perfectly inelastic collisions?
A bullet embedding in a wooden block, two train cars coupling together, a football tackle where players end up moving as one, or a ball of wet clay hitting the floor and sticking — anywhere two objects end up moving with a single shared velocity.