Car Crash Collision Calculator

Analyze inelastic collisions between two objects based on conservation of momentum.

Enter the mass and velocity of two vehicles to calculate their final velocity after a collision and the total kinetic energy lost in the impact.

Vehicle 1

Vehicle 2

Practical Examples

Explore different collision scenarios to see how the physics plays out. Click on an example to load its data into the calculator.

Head-on Collision

Head-on Collision

Two cars of different masses moving towards each other.

Car 1: 1000 kg, 20 m/s

Car 2: 1200 kg, -15 m/s

Rear-end Collision

Rear-end Collision

A faster car hits a slower car from behind, both moving in the same direction.

Car 1: 1500 kg, 30 m/s

Car 2: 1000 kg, 10 m/s

Collision with Imperial Units

Different Units

A head-on collision scenario using pounds (lb) for mass and miles per hour (mph) for velocity.

Car 1: 3000 lb, 60 mph

Car 2: 2500 lb, -40 mph

Hitting a Stationary Car

Stationary Target

A moving car crashes into a stationary car of a different mass.

Car 1: 2000 kg, 25 m/s

Car 2: 1500 kg, 0 m/s

Other Titles
Understanding Car Crash Physics: A Comprehensive Guide
Delve into the principles of momentum and energy that govern collisions. This guide explains the what, why, and how of car crash physics, making complex concepts easy to understand.

What is the Car Crash Calculator?

  • Core Concepts
  • Calculator's Purpose
  • Inelastic Collisions
The Car Crash Calculator is a tool designed to analyze one-dimensional, perfectly inelastic collisions between two objects. In simple terms, it calculates what happens when two things crash and stick together. By inputting the mass and initial velocity of each object, you can determine their combined velocity after the collision and how much kinetic energy was lost during the impact.
The Principle of Conservation of Momentum
The calculator's core logic is built on one of the most fundamental laws of physics: the conservation of momentum. This law states that for any closed system (one without external forces like friction), the total momentum before a collision is equal to the total momentum after the collision. Momentum is the product of an object's mass and velocity (p = mv).
Focus on Inelastic Collisions
This calculator specifically models perfectly inelastic collisions. This is a type of collision where the maximum amount of kinetic energy is lost, and the objects stick together after impact, moving with a single, common final velocity. While real-world car crashes are more complex, this model provides a powerful and accurate first approximation for understanding the dynamics of such events.

Step-by-Step Guide to Using the Car Crash Calculator

  • Entering Vehicle Data
  • Understanding Units
  • Interpreting the Results
Using the calculator is straightforward. Here's how to get accurate results:
1. Input Data for Vehicle 1
Start by entering the mass and initial velocity for the first vehicle. You can choose units for both mass (kilograms or pounds) and velocity (meters per second, kilometers per hour, or miles per hour).
2. Input Data for Vehicle 2
Next, do the same for the second vehicle. A critical point here is the velocity's direction. The calculator assumes movement along a single axis (e.g., left-to-right). If Vehicle 2 is moving in the opposite direction (a head-on collision), you must enter its velocity as a negative number.
3. Calculate and Analyze
Once all data is entered, click the 'Calculate' button. The results will show the final, common velocity of the two-vehicle system, the total kinetic energy lost (converted mostly to heat, sound, and deformation), and the impulse experienced by each vehicle.
The sign of the final velocity indicates the direction of motion after the collision, following the same convention you used for the inputs.

Mathematical Derivation and Formulas

  • Conservation of Momentum
  • Kinetic Energy Calculation
  • Impulse Formula
The calculations are based on fundamental physics formulas. Understanding them can provide deeper insight into the results.
Conservation of Momentum
The core formula is for the conservation of momentum. Let m1 and v1 be the mass and initial velocity of the first car, and m2 and v2 be for the second car. After they collide and stick, their combined mass is (m1 + m2) and they move with a final velocity, v_final.
m1 v1 + m2 v2 = (m1 + m2) v_{final}
Solving for the final velocity gives:
v{final} = \frac{m1 v1 + m2 v2}{m1 + m_2}
Kinetic Energy Lost
Kinetic energy (KE) is the energy of motion, given by KE = 0.5 m v^2. In an inelastic collision, some of this energy is converted into other forms. The energy lost is the difference between the total initial KE and the total final KE.
KE{lost} = (\frac{1}{2}m1 v1^2 + \frac{1}{2}m2 v2^2) - \frac{1}{2}(m1 + m2)v{final}^2
Impulse (Change in Momentum)
Impulse is the change in momentum for an object. It measures the overall effect of a force acting over time. For each car, the impulse (J) is:
J1 = \Delta p1 = m1 v{final} - m1 v1
J2 = \Delta p2 = m2 v{final} - m2 v2
According to Newton's third law, the impulses on the two objects should be equal in magnitude and opposite in direction (J1 = -J2).

Real-World Applications of Collision Physics

  • Accident Reconstruction
  • Vehicle Safety Design
  • Educational Importance
The principles used in this calculator are not just academic exercises; they have critical real-world applications.
Accident Reconstruction
Forensic engineers use these same principles to reconstruct traffic accidents. By analyzing the final resting positions of vehicles, skid marks, and damage, they can work backward to estimate the initial speeds of the vehicles involved. This is crucial for determining fault in legal and insurance investigations.
Vehicle Safety Engineering
Understanding how energy is distributed and dissipated in a crash is fundamental to designing safer cars. Engineers design 'crumple zones'—parts of the car that are meant to deform and absorb kinetic energy during a collision. This extends the time of impact, which reduces the peak force felt by passengers, making the crash more survivable.
Setting Speed Limits
The relationship between speed and kinetic energy (KE = 0.5 m v^2) is quadratic. This means that doubling the speed of a car quadruples its kinetic energy. This is a key reason why speed limits are set, especially in residential areas. The higher the energy, the more devastating the consequences of a collision.

Common Misconceptions and Important Considerations

  • Elastic vs. Inelastic
  • External Forces
  • Rotational Motion
While this calculator is a powerful tool, it's based on a simplified model. It's important to understand its limitations.
Not All Collisions Are Perfectly Inelastic
Our model assumes the cars stick together perfectly. In reality, some bouncing (restitution) occurs. A perfectly elastic collision (where KE is conserved) is the opposite extreme. Most real-world crashes fall somewhere in between.
The Role of External Forces
The calculations assume a closed system, ignoring external forces like friction from the road and air resistance. Over the brief moment of a crash, this is a very good approximation. However, these forces are significant when analyzing what happens immediately before and after the impact.
One-Dimensional Motion
This calculator only handles collisions in one dimension (along a straight line). It does not account for angled impacts, which would involve vector components and potentially rotational motion (spinning) of the vehicles after the crash. Analyzing these two- or three-dimensional collisions requires more complex vector mathematics.