Free Fall Calculator

What is a free fall?

A free fall is any motion where the only force acting upon an object is gravity. Despite the name, an object doesn’t necessarily have to be falling to be in a free fall. It only needs to be subject to gravity. As a result, the Moon is technically in free fall around the Earth. However, its orbital speed keeps it very far from the Earth’s surface.

In a gravitational field that is almost uniform, gravitation acts on each part of an object equally. This is possible because of the absence of all other forces. If the gravitational force is also weak, there will be a sense of weightlessness. This will happen if the object is far from any sources of gravity. A feeling of weightlessness will also occur when there is no normal force between the object and it’s surrounding objects.

Generally, we use the term “free fall” more loosely. For example, falling through an atmosphere with a deployed parachute is considered a free fall. However, in these cases, there is no sense of weightlessness. Instead of this, skydivers have a feeling of their weight being supported on a cushion of air. This happens when they reach terminal velocity.

Free fall speed

An object during a free fall in a vacuum, gains speed (accelerates), at a rate of 9.81 m/s² or 32.1850394 ft/s². When not in a vacuum, however, we have to account for the force of drag as well. As we said, in a vacuum, all objects have equal acceleration during a free fall. In reality, the mass of the object is very important. This is why, when you drop a piece of paper, it just gets carried by the wind, but when you drop a ball, it falls straight to the ground. But even a heavy ball wouldn’t keep accelerating until it hit the ground, because eventually it would reach terminal velocity.

Terminal velocity

Terminal velocity is the maximum velocity an object can reach during a free fall. This can be in any fluid, not just air, although air is the most common example. In other words, an object has reached terminal velocity if its speed is constant, or if the gravitational acceleration is 0. The acceleration is 0 because of the restraining forces of the fluid it’s falling through. The restraining forces are the drag force, or air resistance (F_d) and buoyancy. When their sum equals the downward force of gravity (F_G), the object will stop accelerating. For more about acceleration, check out our Acceleration Calculator!

It was calculated that the terminal velocity of a skydiver during a free fall is about 195 km/h, 120 mph or 54 m/s. This is in a belly-to-earth skydiving position. It will take about 15 seconds to achieve 99% of the terminal velocity. Higher speeds can be achieved during a skydive, by changing the skydiving position, which lowers the air resistance. For example, if the skydiver pulls their limbs, they take the freeflying position. When in this position, the terminal velocity jumps to 320 km/h, 200 mph, or 90 m/s. The height most skydivers jump from is 4.2 km or 2.6 miles (14 000 feet).

Essentially, after terminal velocity has been reached, the time the object continues falling for does not matter, as the air resistance and buoyancy will are going to prevent further acceleration.

Speed skydivers compete to achieve the highest terminal velocity during a free fall. They can reach speeds up to 530 km/h, 330 mph or 150 m/s. The current world for the highest terminal velocity is around 1,357 km/h, 840 mph or 380 m/s. For reference, that is 1.25 faster than the speed of sound (Mach 1.25). This incredible record is held by Felix Baugmartner since 14 October 2012. He achieved this by jumping to Earth from a helium balloon from the stratosphere. Keep in mind, this was from a height of 39km, or 24 miles. He was also the first person to break the sound barrier in a free fall.

How to calculate free fall velocity with no drag – formulas

The easiest way to calculate it is to, of course, use our calculator. However, if you want to calculate it by yourself, we’ll go over that too.

For this first section we will assume a free fall in a vacuum, with no drag. With this in mind, the formula for calculating the velocity of the object at a given point will be:

v= v_{0} + g*t

v is the velocity at that point, and v₀ is the initial velocity. If the object started falling from a standstill, the initial velocity will be 0. In that case, we can remove it from the equation. g is the gravitational acceleration, and it is equal to 9.80665 m/s² or 32.17405 ft/s². t is the time the object has been falling (measured in seconds).

If you want to calculate how long an object has been falling using its velocity, you can use the following formula:

t= \frac {v-v_{0}}{g}

If you want to calculate the distance an object has traveled in a free fall, the formula you need is:

h=v_0 + \frac {g \cdot t^2}{2}

This can either be the height the object started falling from, or just the distance it traveled. That depends on t, which is the time the object has been falling for.

From this, we can also get another formula for t:

t^2=\frac {2 \cdot h}{g} - 2 \cdot v_0

As an example, let’s assume an object has started falling in a vacuum from a standstill. Its velocity after 10 seconds of falling will be:

v= 0+9.80665 \frac {m}{s^{2}} * 10s = 98.0665 \frac {m}{s}

And, after 10 seconds, the distance it will have passed is:

h = \frac {9.80664 /frac {m}{s^2} \cdot (10s)^2}{2} \\ h= \frac {9.80664 \frac {m}{s^2} \ cdot 100s^2}{2} \\ h = \frac {980.664 m}{2} \\ h= 490.332 m

However, this is not very useful for calculating actual free falls. For those calculations, we need to consider the drag force.

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