Car Crash Calculator
Analyse the physics of inelastic collisions — calculate final velocity, kinetic energy lost, and impulse for any two-vehicle crash using conservation of momentum.
Enter the mass and initial velocity of two vehicles. Use negative velocity for a vehicle moving in the opposite direction (head-on collision). Supports kg/lb and m/s, km/h, mph units.
Car Crash Calculator
Analyse the physics of inelastic collisions — calculate final velocity, kinetic energy lost, and impulse for any two-vehicle crash using conservation of momentum.
Vehicle 1
Vehicle 2
Tip: Enter a negative velocity for a vehicle moving in the opposite direction (e.g. head-on collision).
Worked Examples
Click an example to load it into the calculator.
| Collision Scenario | Results | Physics Insight |
|---|---|---|
| Car 1: 1000 kg at +20 m/s; Car 2: 1200 kg at −15 m/s (head-on) | v_final ≈ +0.91 m/s, KE lost ≈ 334 kJ | Positive final velocity means combined mass moves in Car 1's original direction. Nearly all kinetic energy is dissipated as heat, sound, and deformation. |
| Car 1: 1500 kg at 30 m/s; Car 2: 1000 kg at 10 m/s (rear-end, same direction) | v_final = 22 m/s, KE lost = 120 kJ | Both vehicles move in the same direction after impact. Less energy is lost than in a head-on collision at comparable speeds. |
| Car 1: 2000 kg at 25 m/s; Car 2: 1500 kg at 0 m/s (stationary target) | v_final ≈ 14.3 m/s, KE lost ≈ 268 kJ | Hitting a stationary car transfers momentum to both vehicles. The moving car slows significantly; the stationary car begins to move. |
| Car 1: 3000 lb at 60 mph; Car 2: 2500 lb at −40 mph (imperial, head-on) | v_final ≈ 14.5 mph (Car 1's direction), KE lost ≈ 618 kJ | Demonstrates imperial unit support. At highway speeds, the energy released in a head-on collision is enormous — roughly equivalent to 150 grams of TNT. |
About the Car Crash Calculator
This calculator models a perfectly inelastic collision between two objects — the type of collision where the objects stick together after impact and move with a single combined velocity. While real-world car crashes involve complex deformation and partial rebounds, the perfectly inelastic model gives an excellent first approximation of the outcome and is widely used in accident reconstruction.
The physical principle underlying the calculation is conservation of momentum. Momentum is the product of mass and velocity (p = mv), and for a closed system with no external horizontal forces, total momentum before the collision equals total momentum after: m₁v₁ + m₂v₂ = (m₁ + m₂) × v_final. Solving for the final velocity gives v_final = (m₁v₁ + m₂v₂) / (m₁ + m₂). The sign convention is critical: velocities in the positive direction are positive, while a vehicle moving in the opposite direction must be entered as a negative velocity.
Kinetic energy is NOT conserved in an inelastic collision — this is what distinguishes it from an elastic collision (where KE is conserved, like billiard balls). The kinetic energy before the collision is KE_initial = ½m₁v₁² + ½m₂v₂². After the collision, KE_final = ½(m₁+m₂)v_final². The difference KE_lost = KE_initial − KE_final represents the energy that was converted to heat, sound, and permanent deformation. In a severe crash, this can be hundreds of kilojoules or more — equivalent to the chemical energy in a large explosive charge.
Impulse (change in momentum) measures the force-time product experienced by each vehicle. For Vehicle 1: J₁ = m₁(v_final − v₁). For Vehicle 2: J₂ = m₂(v_final − v₂). By Newton's third law, J₁ = −J₂. A larger impulse means a larger force was experienced over the collision duration, which relates directly to occupant injury risk. Modern crumple zones are engineered to extend the collision duration (increase Δt), thereby reducing the peak force F = J / Δt even though the impulse remains the same.
The quadratic relationship between speed and kinetic energy (KE ∝ v²) is why speed limits matter: doubling speed quadruples the kinetic energy that must be dissipated in a crash. A collision at 80 km/h involves four times more energy than the same collision at 40 km/h, dramatically increasing injury severity. This calculator helps visualise that relationship directly.
How to Use the Car Crash Calculator
- Enter the mass of Vehicle 1 in kilograms or pounds using the unit toggle. Use the vehicle's kerb weight plus passenger and cargo mass for accuracy.
- Enter the initial velocity of Vehicle 1. Choose the appropriate unit (m/s, km/h, or mph). If Vehicle 1 moves to the left, enter a positive value; if it moves to the right, enter negative — the key is consistency with Vehicle 2's sign.
- Repeat for Vehicle 2. For a head-on collision (vehicles approaching each other), one velocity must be positive and the other negative. For a rear-end collision (same direction), both velocities are positive.
- Click Calculate. The results show the final velocity after the perfectly inelastic collision, total initial and final kinetic energy, energy lost to deformation, and impulse on each vehicle.
- The sign of the final velocity tells you which direction the combined wreckage moves after impact, using the same convention as your input velocities.
Frequently Asked Questions
What is a perfectly inelastic collision?
A perfectly inelastic collision is one in which the colliding objects stick together after impact and move as a single combined mass. It represents the maximum possible kinetic energy loss for a given pair of objects and initial velocities. Real car crashes are not perfectly inelastic — there is some bouncing (coefficient of restitution > 0) — but the perfectly inelastic model is a conservative lower bound for final velocity and a useful approximation for severe crashes.
Why must I use a negative velocity for one car in a head-on collision?
Velocity is a vector — it has both magnitude (speed) and direction. The calculator uses a one-dimensional sign convention where positive values denote motion in one direction and negative values denote the opposite direction. In a head-on collision, both vehicles approach each other, so if Car 1's velocity is +20 m/s, Car 2 must be entered as a negative value (e.g. −15 m/s) to correctly represent the collision geometry. If you enter both as positive, the calculator models a rear-end collision instead.
What does the kinetic energy lost represent in real terms?
The kinetic energy lost is converted to other forms of energy during the crash: deformation of metal (plastic deformation energy), heat at contact surfaces, sound (the crash noise), and some vibration. In a severe collision at highway speed, the energy lost can be several hundred kilojoules to megajoules. Modern safety engineering (crumple zones, airbags) is designed to manage how quickly and through what mechanisms this energy is absorbed to minimise forces on occupants.
How is impulse related to injury risk?
Impulse J = F × Δt = m × Δv is the total change in momentum. The force experienced is F = J / Δt. For a given impulse (unavoidable from the momentum change), a longer collision duration Δt means a lower peak force. This is the principle behind crumple zones: they extend the crash duration from perhaps 50 ms (rigid car) to 100–150 ms, roughly halving the peak deceleration force on occupants, which dramatically reduces injury severity.
Does this model work for non-car objects?
Yes — the conservation of momentum applies to any two objects regardless of their nature. You can use this calculator for two football players colliding, a baseball bat hitting a ball (though that is closer to elastic), a spacecraft docking manoeuvre, or any other inelastic collision. Simply enter the masses and initial velocities in consistent units.
Why does a heavier car fare better in a collision?
In a perfectly inelastic collision, the final velocity v_final = (m₁v₁ + m₂v₂) / (m₁ + m₂). A heavier Car 1 has more momentum, so it shifts the final velocity closer to its own initial velocity. This means its occupants experience a smaller velocity change (Δv₁ = v_final − v₁), and therefore smaller impulse and deceleration. This is a well-documented statistical phenomenon — large vehicles generally impose more severe velocity changes on the smaller vehicle's occupants in mixed-mass crashes.