Car Crash Calculator

Step 1: Input Vehicle Mass

Enter the mass for Vehicle 1 and Vehicle 2. You can typically find a car's curb weight in the owner's manual or online. For simplicity, ensure your units are consistent (e.g., both in kilograms or pounds).

Step 2: Input Initial Velocities

Enter the speed of each vehicle before the collision. Pay close attention to direction! For a head-on collision, one velocity should be positive and the other negative (e.g., Car 1 is +60 mph, Car 2 is -50 mph). For a rear-end collision, both velocities would be positive, with the rear car having a higher velocity.

Step 3: Estimate Collision Time

This is a critical and often estimated value. It represents the duration of the impact itself—the time from first contact until the vehicles come to a relative rest or separate. For a modern car with crumple zones, this is typically in the range of 0.1 to 0.2 seconds (100-200 milliseconds). A more rigid collision would have a shorter time. This variable dramatically affects the calculated force.

Step 4: Calculate and Interpret

Click the "Calculate" button. The tool will provide outputs like the total force of impact, the change in momentum (impulse) for each vehicle, and the total kinetic energy involved. Use these results to see how changing one variable, like speed, exponentially impacts the outcome.

1. The Law of Conservation of Momentum (p = mv)

Momentum is often called "mass in motion." It is calculated by multiplying an object's mass (m) by its velocity (v). The law of conservation of momentum states that in a closed system (like a collision), the total momentum before the crash is equal to the total momentum after the crash. Momentum is a vector, meaning direction matters.

In a perfectly inelastic collision—the kind that best describes a car crash where the vehicles stick together—the two objects move with a single, shared final velocity. Our calculator uses this principle: (m₁v₁) + (m₂v₂) = (m₁ + m₂)v_final. This is why a heavy truck colliding with a small car causes a much more violent change in velocity for the small car. The truck's massive momentum dominates the system.

2. Kinetic Energy: The Capacity for Damage (KE = ½mv²)

If momentum is about the motion, kinetic energy is about the destructive capability. Notice the formula: energy is proportional to mass, but it is proportional to the square of the velocity. This is the single most important concept for any driver to understand.

Let's illustrate the terrifying power of "velocity squared":

• • Doubling your speed from 30 mph to 60 mph doesn't double your car's kinetic energy. It quadruples it (2² = 4).
• • Tripling your speed from 30 mph to 90 mph multiplies the energy by nine (3² = 9).

This energy doesn't just vanish in a crash. It is violently converted into other forms: the sound of the impact, heat, and, most significantly, the work of deforming metal—crushing bumpers, bending frames, and shattering glass. The more energy, the more destruction.

3. Impulse and Force: The Science of Survival (F = Δp / Δt)

Impulse (J) is simply the change in momentum (Δp). To change an object's momentum, you must apply a force (F) over a period of time (Δt). The formula is Impulse = FΔt. We can rearrange this to find the average impact force: F = Δp / Δt.

This simple equation holds the secret to modern car safety. In any given crash, the change in momentum (Δp) is fixed. Your car is going from a certain speed to zero. What engineers *can* change is the collision time (Δt). By making Δt larger, the average impact force (F) experienced by the occupants becomes smaller. This is the entire philosophy behind safety features.

Q: Why is a collision with a solid wall different from a head-on collision with an identical car at the same speed?

Physically, they are surprisingly similar for the occupants. In a head-on crash with an identical car moving at the same speed, the point of impact acts like an immovable plane of symmetry—much like a solid wall. Both cars come to a dead stop from their initial speed. Hitting a stationary, immovable object effectively mirrors this scenario. The situation changes dramatically if the masses or speeds are different.

Q: Does this calculator account for the angle of impact?

No. Our calculator simplifies the scenario to a one-dimensional, perfectly inelastic collision (e.g., a direct head-on or rear-end impact). Real-world angled collisions are far more complex, introducing rotational forces (spinning) and vector components that require much more advanced calculations.

Q: How can I use this knowledge to be a safer driver?

Two key takeaways: 1) Respect the power of v². The single biggest factor you control is your speed. Reducing your speed slightly has a massive effect on reducing the kinetic energy of a potential impact. 2) Maximize your personal "Δt" by increasing your following distance. This gives you more time to react and brake, extending the time over which you decelerate and reducing the forces involved.

Q: Is a heavier car always safer?

In a two-vehicle collision, the occupants of the heavier vehicle generally experience a smaller change in velocity and thus lower forces, due to the conservation of momentum. However, a heavier vehicle also carries more kinetic energy, which can make single-vehicle accidents (e.g., hitting a tree) more severe. Modern safety design is a balance, but all else being equal, mass is a significant advantage in a multi-car crash.