Free Fall with Air Resistance Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jul 20, 2022

This free fall with air resistance calculator is a variation of our free fall calculator that takes into consideration not only the influence of gravity but also the air drag force. With its help, you will be able to assess the time of fall, as well as the terminal and maximum velocity more accurately.

In the text below, we will explain how this tool works. Not only will we provide you with a detailed explanation of how to calculate air resistance, but also with a handy drag force equation that will make all computations a breeze!

Prefer watching rather than reading? Check out our deep dive into the concept of free fall here:

What is free fall?

In physics, free fall is a motion of the body where no forces, except for gravity, are acting upon it. It doesn't mean that the object must move downwards; for example, we can consider the Moon to be in free fall, as it is only subject to Earth's gravitational force.

In this calculator, however, we treat the term "free fall" a little less scientific and consider any object that moves towards the ground (without external acceleration or deceleration) as an object in free fall. For example, a skydiver or a parachute jumper who moves toward the ground will be in such a motion. Two forces are acting on him: one is gravity, and the other one (that causes deceleration) is called the air resistance.

Air resistance formula

Air resistance, or aerodynamic drag force, is a force that opposes the motion of a body in free fall. The faster you fall, the higher the force is. It can be expressed by the following drag force equation:

F = k × v²

where v is the instantaneous speed, and k is the air resistance coefficient, measured in kilograms per meter.

The air resistance coefficient is dependent on quite a few factors. The following air resistance formula can calculate it:

k = ρ × A × C / 2

where:

  • ρ – Density of the medium the body is traveling through. By default, our calculator assumes the density of air at the temperature of 15 °C is equal to 1.225 kg/m³. If you are trying to analyze the free fall in different conditions, feel free to open the advanced mode to change this value. You can also use the Stokes' law calculator to analyze a particle falling through a different medium, such as water or glycerine.
  • A – Cross-sectional area of the falling body.
  • C – Dimensionless drag coefficient associated with the shape of the falling body. For example, a falling cube will cause much higher air resistance than a tear-shaped object; this is why a cube has a much higher drag coefficient.

The default value of k = 0.24 kg/m corresponds to a person who is skydiving. Feel free to change this value as you'd like, or open the advanced mode to calculate it with the air resistance formula. Note that you will first need to delete the existing 0.24 figure to calculate a new value.

Maximum vs. terminal velocity

While falling, the object is steadily accelerating due to gravity. On the other hand, the air resistance force increases with velocity. At some point, the drag force will become large enough to oppose the gravitational force entirely. At this point, the body stops accelerating and reaches its terminal velocity.

It doesn't mean, though, that every object in free fall will reach its terminal velocity – after all, it may hit the ground before it reaches the terminal velocity. That's why our free fall with air resistance calculator will give you a different value: the maximum velocity that the body reaches before coming to a stop.

How to calculate air resistance

Let's analyze an example of a skydiver falling to the ground. Our goal is to calculate the time of fall, his maximum velocity, and terminal velocity, as well as the magnitude of the drag force when he reaches his maximum velocity.

  1. Find out what is the mass of the skydiver. Let's assume it is equal to 75 kg.

  2. Decide on the altitude the skydiver is falling from – let's say it is equal to 2000 m.

  3. Choose the air resistance coefficient (or open the advanced mode to calculate it – delete the default value first). In this example, we will stick to the default value of 0.24 kg/m.

  4. Input all these values into the free fall with air resistance calculator. You will automatically obtain the results: the time of fall equal to 40 seconds, a terminal velocity of 55.4 m/s, and a maximum velocity equal to 55.4 m/s. It seems that the skydiver has managed to reach his terminal velocity!

  5. Copy the value of 55.4 m/s to the last section of the calculator to find out what is the drag force acting on the skydiver. The calculator will perform the following computations:

    F = k × v²

    F = 0.24 × 55.4²

    F = 736.6 N

  6. Compare this result with the results from the free-fall calculator. Can you see the difference?

If you have read this far, here is a video of one of the most iconic free-fall experiments performed.

And here is our very own Alvaro explaining the difference between this calculator and the regular free fall calculator.

Bogna Szyk
Traveling object
Mass (m)
lb
Altitude (h)
ft
Gravitational acceleration (g)
ft/s²
Air resistance coefficient (k)
kg/m
Time and velocity
Time of fall (t)
sec
Maximum velocity (vmax)
m/s
Terminal velocity (vt)
m/s
Drag force
at velocity...
m/s
Drag force is
N
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