# Car Crash Calculator

Table of contents

Force of impact definition – impact force equationHow to calculate impact force? G-force in car crashesHow can seat belts and airbags protect you?At what speed can you die in a car crash?FAQsOur car crash calculator is a tool that you can use to estimate **what g-force acts on you** in a car crash. Everybody knows that automobile collisions are very dangerous, but what is the physics behind them? Can we predict the consequences of a car crash? The answer is yes and no. The damages to health in an accident can be severe, and they depend on many factors, e.g.:

**Car speed**– the higher the speed, the more energy you have;**Seat belt**– we will show that seat belts can save your life;**Airbag**– another thing that can protect your life;**Car type**– you are more likely to survive a car crash if you're in a bigger car; and**Obstacle**– the situation is different when we hit a bush or a tree.

We can't precisely calculate whether you will survive or not, but we can make some estimations to be aware of crash consequences. What happens if you drive at a speed of $20\ \mathrm{mph}$ and you suddenly stop? **Just imagine that a 7-tonne block lies on your chest**. Yes, it's almost the same. Recently, the **NHTSA** (National Highway Traffic Safety Administration) performed many crash tests with dummies. Based on these tests, we can make some approximations at what speed you can die in a car crash.

In this car crash calculator, we explain **how to calculate the impact force** in car crashes and how seat belts and airbags can protect you. You'll find out that they can drastically increase your chances of surviving. You can learn about the force of impact definition and impact force equation in the following text.

You do not need to be the driver to know that **you can't stop the car immediately**. The total stopping distance depends on the perception time of a driver and the braking distance. The same energy estimated with the kinetic energy calculator will be dispersed much faster on a tree than in water. Thus, hitting trees almost always results in dangerous car crashes.

## Force of impact definition – impact force equation

Force of impact is the total force exerted on an object during a collision. To derive the impact force equation, you can consider the law of conservation of energy. In the beginning, a moving object possesses kinetic energy that **reduces to zero** after the collision (object stops). To fulfill the conservation law, the change of kinetic energy must be compensated by the work done by the impact force. We express it with the below impact force equation

where:

- $F$ – Average impact force;
- $m$ – Mass of an object;
- $v$ – Initial speed of an object; and
- $d$ – Distance traveled during a collision.

*Check the work calculator or work and power calculator to get familiar with work in physics and how it is related to energy.*

What may surprise you is that extending the distance moved during the collision reduces the average impact force. It should be easier to understand if we rewrite the above impact force formula in the alternative version using the time of collision $t$ instead of the distance $d$:

This is a special case of the formula for momentum, described in the impulse and momentum calculator. Now, you can see that extending the time of the collision will decrease the average impact force.

Let's consider two situations where you jump from a specific height. In the first case, you jump to the ground, and in the second, on a trampoline. Because the surface of a trampoline is more stretchy, it extends the time of the collision. You can feel your legs are subjected to a lesser average impact force.

This case is analogical to car crashes. **Cars are made to collapse upon impact** extending the time of the collision and lessening the impact force. That's why they can't be too durable.

## How to calculate impact force? G-force in car crashes

The impact force formulas we used above describe an ideal collision between two objects. In the actual situation of a car crash, **the profile of force during the accident can be more extensive** – e.g., you should take into account that the car collapses and that a human is not a point mass but a complex body. However, you can still make some estimations of impact force during a car crash.

Take a look at the picture below. At first, the driver sits in the car in constant motion with speed $v$. Then, a car hits the tree and immediately stops. **The driver flies forward due to the inertial force** until suddenly stopped by the impact on the steering column or windshield. The stopping distance is very short because none of the colliding objects (including the body and, e.g., the windshield) are contractible enough. These are usually dense objects; you can find the density of the most common materials with the density calculator for a comparison. We can estimate the stopping distance to be approximately $4\ \mathrm{cm}$ in our case (you can change it in the "Additional variables" section of this impact force calculator).

How to calculate the impact force acting on a driver with a mass of $70\ \mathrm{kg}$? Let's use our car crash calculator! If the initial car speed is $30\ \mathrm{km/h}$ and the collision distance is $4\ \mathrm{cm}$, then the impact force is about $60\ \mathrm{kN}$. **It is an equivalence of 6 tons!** It is just as if someone put a large stone block on your chest. On the other hand, the stopping time is only $9.6\ \mathrm{ms}$ which means that to reduce the driver's velocity from $30\ \mathrm{km/h}$ to zero, the driver has to decelerate almost **89 times faster than Earth's standard gravity g**.

## How can seat belts and airbags protect you?

The primary task of seat belts and airbags is the same. They both **extend the distance of the collision**. Assume that we've got the same situation as before. The $70\ \mathrm{kg}$ driver drives a car with a speed of 30 km/h, but this time, he is firmly held in a seat belt harness. The seat belt will stretch slightly when the impact force is applied. We can say that it can expand by about $20\ \mathrm{cm}$ (you can change it in the "Additional variables" section of this impact force calculator).

Again, after using the car crash calculator, you can obtain the average impact force of about $2.5\ \mathrm{kN}$, which is almost 25 times smaller than without the seat belt. It corresponds to a weight of $1.24\ \mathrm{t}$. The stopping time lengthens to $48\ \mathrm{ms}$, and now, the driver decelerates "only" 18 times faster than with Earth's standard gravity g.

To sum up, the seat belt is designed to stop your body from hitting hard things in the car and **reduce the impact force you experience by spreading it out over time**. The seat belt could occasionally contribute to severe internal injury or even death if the impact force is too big. However, nowadays, seat belts have a mechanism that breaks them at a predefined level of stress. Usually, there are still airbags placed in front of the driver in order to increase their safety.

We have made an example with the driver, but **any person** in the vehicle is subjected to these dangers. If you crash with a heavy truck, it doesn't matter whether you sit behind the wheel or at the back seat of the car.

Even in low-speed collisions, **the impact force which stops your body is in the range of tonnes**. You simply won't be able to hold on and prevent injury without fastened seat belts. Moreover, if you sit at the back of the car and you aren't constrained by a seat belt, you will fly straight ahead like a boulder of several tonnes. **You will not only hurt yourself but also your friend in front of you!**

## At what speed can you die in a car crash?

This is one of those questions that **doesn't have one unambiguous answer**. The heavier the car is, the harder it is to stop it, and the impact force is smaller. On the other hand, the vehicle will immediately stop if it hits a wall of a house, but the situation will be different if it hits another car that participates in traffic. Therefore, we must take into account many different factors.

In general, **high speed doesn't produce harmful injuries**. What is dangerous for a human is the high acceleration or deceleration given at a specific amount of time. The National Highway Traffic Safety Administration (NHTSA) is an agency that conducts traffic safety research around the world. It describes its mission as *Save lives, prevent injuries, reduce vehicle-related crashes*. The NHTSA states that "the maximum chest acceleration **shall not exceed 60 g for time periods longer than 3 milliseconds**" (source: ).

With our car crash calculator, you have learned that the accelerations during car crashes can be a lot higher than 60 g without fastened seat belts. **So use them and save your life!** NHTSA states that seat belts reduce death rates by 45% and reduce the risk of injury by 50%.

### How do I calculate the forces in a car crash?

To calculate the impact force in a car crash, follow these simple steps:

- Measure the velocity at the moment of the impact,
`v`

. - Measure the mass of the subject of the collision,
`m`

. - Either use:
- The
**stopping distance**`d`

in the formula:`F = mv²/2d`

; or - The
**stopping time**`t`

in:`F = mv/t`

- The
- If you want to measure the g-forces, divide the result by
`mg`

, where`g = 9.81 m/s²`

.

### What is the impact force in a crash at 160 km/h?

Assuming the weight of the driver is `70 kg`

, we can calculate the impact forces in two situations:

- Without the seatbelt, the stopping distance would be
`4 cm`

, and the impact force is:

`F = 70 kg × (44.44 m/s)²/(2 × 0.04 m) = 1728 kN`

- With the seatbelt on, the stopping distance increases to
`20 cm`

. The force becomes:

`F = 70 kg × (44.44 m/s)²/(2 × 0.2 m) = 346 kN`

Divide `F`

by `m × g = 686.7 m/s²`

to find the deceleration in terms of `g`

. It’s `2517 g`

without a seatbelt and `504 g`

with.

### Why does wearing a seatbelt increase your safety?

A seatbelt **extends** the time your body slows down from the speed before the crash to 0. In a car crash, speed is not the only factor that can be dangerous: the **stopping time and distance** have an even more critical role. A seatbelt keeps you in your seat, only partially expanding, thus **distributing the deceleration** over a safer time. However, they are not a guarantee: drive safely, always!

### How do I find the stopping time in a car crash?

We can find the **stopping time** from the **impact force** using the following formula:

`t = m × v/F`

where:

`t`

— The**stopping time**;`m`

— The**weight of the victim**;`v`

— The speed of the vehicle; and`F`

— The**impact force**.

You can find the stopping distance with the simple relationship between time and space:

`d = t × v/2`