Car Crash Calculator
Learn how momentum and energy work in a two-vehicle collision: final velocities, delta-v, energy dissipated and the equivalent fall height.
🚗 What is a Car Crash Calculator?
A car crash calculator, in the sense used on this page, is a physics teaching tool that applies conservation of momentum and the coefficient of restitution to a collision between two vehicles moving along a straight line. Given the two masses, the two velocities and how bouncy the impact is, it finds the velocities right after the impact, the change of velocity (delta-v) of each vehicle, the kinetic energy that was turned into deformation, heat and sound, and an equivalent speed against a rigid barrier or an equivalent drop height. It also has a barrier mode that converts one vehicle's speed into a drop height and an average deceleration.
Important: this is an educational tool only. It is not for accident reconstruction, insurance claims, legal work or safety certification. Real crashes involve angled impacts, rotation, crush stiffness, tyre friction, braking before impact and structural details that a one-dimensional model ignores, and professional reconstruction uses measured evidence and validated methods. Use this page to understand the physics, for example in a school project, a lecture demonstration or simple curiosity about why speed matters so much.
Several ideas become clear when you play with it. Momentum is always conserved in the collision, whatever the impact type. Kinetic energy is not conserved unless the impact is perfectly elastic, and the energy lost depends on the closing speed squared, so doubling the closing speed quadruples the energy dissipated. The vehicle with the smaller mass always suffers the larger velocity change, since the impulses on the two vehicles are equal and opposite. Finally, a barrier impact at a given speed has the same energy as dropping the vehicle from a height of v squared divided by 2g, which gives an intuitive feel for what a speed means: about 9.84 m, roughly three storeys, for 50 km/h.
The two modes cover the two main situations. The collision mode handles two vehicles and uses a chart of final velocities against restitution so you can see how the outcome shifts from sticking together to bouncing apart. The barrier mode uses a crush distance to estimate the average deceleration in g and the stopping time, with a chart of deceleration against crush distance showing why longer crumple zones reduce the load on occupants. For related ideas see the conservation of momentum calculator.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Rear-End Collision, Vehicles Stick Together
1500 kg at 50 km/h hits a 1200 kg vehicle at 20 km/h in the same direction, e = 0
Example 2 — Head-On, Equal Cars
Two 1500 kg cars, one at +50 km/h and one at −50 km/h, e = 0
Example 3 — Head-On, Light Car Against Heavy Vehicle
1000 kg at +60 km/h meets 2000 kg at −40 km/h, e = 0
Example 4 — Elastic Bumper Cars
200 kg bumper car at 4 m/s hits an identical car at rest, e = 1
Example 5 — Partly Elastic Impact
1000 kg at 30 km/h hits an identical stationary 1000 kg vehicle, e = 0.3
Example 6 — Rigid Barrier at 50 km/h
1500 kg vehicle hits a fixed barrier at 50 km/h and crushes 0.6 m
Example 7 — Low-Speed Barrier Contact
1200 kg vehicle at 30 km/h into a barrier with 0.5 m of crush
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the final velocity after a car collision?
Use conservation of momentum with the restitution coefficient e: v1' = (m1 v1 + m2 v2 + m2 e (v2 - v1)) / (m1 + m2), and v2' = (m1 v1 + m2 v2 + m1 e (v1 - v2)) / (m1 + m2). For a perfectly inelastic crash e = 0 and both vehicles move together.
What is delta-v in a collision?
Delta-v is the change in a vehicle's velocity caused by the collision. For e = 0 it equals (m other / (m1 + m2)) times the closing speed, so the lighter vehicle always has the larger delta-v. For two equal cars head-on at 50 km/h each, delta-v is 50 km/h for both.
How much energy is lost in a car crash?
The kinetic energy dissipated is 0.5 x mu x (1 - e^2) x closing speed squared, where mu = m1 m2 / (m1 + m2) is the reduced mass. It goes into deformation, heat and sound. A perfectly elastic collision (e = 1) loses none.
What is a perfectly inelastic collision?
It is a collision in which the objects stick together and move with a common velocity afterwards, so e = 0. Momentum is still conserved but the maximum possible kinetic energy for the given momentum is dissipated.
What is the coefficient of restitution?
It is the ratio of the separation speed to the approach speed along the line of impact, e = (v2' - v1') / (v1 - v2). It is 0 for objects that stick together and 1 for a perfectly elastic bounce. Real vehicle crashes are near the low end.
What does barrier-equivalent speed mean?
It is the speed at which a vehicle would have to hit a rigid barrier to absorb the same energy as it did in the collision. In this calculator it is the square root of 2 E / m for the energy share assigned to each vehicle.
How is a crash speed related to a fall height?
The speed gained in a fall is v = sqrt(2 g h), so the equivalent height is h = v^2 / (2 g). A barrier impact at 50 km/h (13.89 m/s) matches a fall from 9.84 m, about three storeys.
Why does the lighter car feel a bigger change in speed?
Both vehicles experience equal and opposite impulses, so m1 times delta-v1 equals m2 times delta-v2. The lighter vehicle therefore has the larger velocity change. For 1000 kg against 2000 kg the delta-v ratio is 2 to 1.
What is the average deceleration in a barrier crash?
If the vehicle stops uniformly over a crush distance d, the average deceleration is a = v^2 / (2 d). At 50 km/h with 0.6 m of crush it is 160.8 m/s2, about 16.4 g. The actual peak is higher than this average.
Can this calculator be used for accident reconstruction or legal cases?
No. It is an educational physics tool for a simplified one-dimensional collision. It does not model crush stiffness, angles, rotation, tyre friction or post-impact motion, so it must not be used for accident reconstruction, insurance or legal purposes.
What happens in an elastic collision between two equal masses?
With e = 1 and equal masses the vehicles swap velocities. A moving bumper car at 4 m/s that hits an identical stationary one stops, and the second car moves away at 4 m/s. Kinetic energy is unchanged.