Free Fall Calculator

This free fall calculator will help you to find the velocity and distance traveled by a falling object. Enter one known value and this tool will calculate the other two. The tool also shows the energy and momentum of impact as well as how it would be on the moon, mars or other celestial bodies.

What is free fall?

A free fall is a movement where an object is only affected by gravity. With no engines or cables and ideally no air resistance, the object will continually accelerate downwards.

This acceleration is about 9.81 meters per second squared near the Earth's surface and is denoted by "g". A spring and cannonball have the same acceleration. If you put them both in a vacuum and let go of them, they will land at the same time. Galileo Galilei proposed this idea four centuries ago, disproving the prevailing notion that "heavier objects fall faster." Later Apollo astronauts performed a famous demonstration on the airless moon using a hammer and a feather to prove it.

How to use this calculator:

Select the known value. If you know the time of fall, enter it to find the impact velocity and distance fallen. If you know the height, enter it to calculate the time of fall and impact velocity. If you know the final velocity, enter it to determine the time and distance.

If the object is dropped from rest, then initial velocity will be zero. If the object is thrown down initially, then enter that value. Select a celestial body in the Gravity menu or select Custom to enter any value. By enabling the energy option and entering mass, you can check the kinetic energy, potential energy, and momentum of the object at the time of impact.

Formulas for free fall:

Three formulas relate the initial velocity v0 to time, velocity and distance traveled by a falling object that is accelerating under the influence of gravity g. The final velocity increases at a constant rate over time.

The distance fallen is proportional to the square of time. So an object falling for a long time will travel much further during the last second than it did during the first second.

Combining these two formulas eliminates time and creates a direct relationship between final velocity and height. This form is most useful when you know the height from which an object fell.

In this case, v0 is the initial velocity, v is the final velocity, t is time, h is the distance fallen and g is the acceleration due to gravity. For an object falling from rest, the term with v0 disappears leaving only the familiar formulas v = gt and h = (1/2)gt².

Example calculation:

A stone falls off a bridge that is 20 meters above the water surface. We calculate the impact speed using a formula for height.

We then determine the time with the formula v = g * t. So the time t is equal to the value of 19.8 divided by 9.81, which is approximately 2.0 seconds. The stone hits the water surface after about two seconds at a speed of approximately 19.8 meters per second, or 71 kilometers per hour.

Free fall and air resistance:

Since a real case takes place in the air and not in vacuum, the situation changes due to air resistance when an object's speed increases. The resistance increases as the speed is higher and rises until it balances out gravity. After that, the object does not accelerate any more and falls with a constant final velocity.

The terminal velocity of a skydiver in the belly-down position is about 53 meters per second, which is approximately 190 kilometers per hour. With a parachute deployed, the speed reduces to safe values of a few meters per second. This calculator simulates an ideal state without air resistance, so the calculated speeds are maximum values. For light objects, wide objects or very long fall times, the actual impact velocity can be lower than those shown here.

Free fall on moons and other celestial bodies

Gravity is weak on small objects in space and strong on large ones. So the effects of free fall vary from place to place in our solar system. On the moon, gravity is about one-sixth as strong as it is here on Earth. That means falling takes longer and feels gentler. This explains why Apollo astronauts could jump so high on the moon.

If you switch the "Gravity" menu or open the "Solar System Comparison", you can determine the time and impact speed for a drop from the same height on the Moon, Mars, Venus, Jupiter and even the surface of the Sun. The airless moon is the only place where these vacuum data are almost perfectly in line with reality.

Energy and momentum at impact

When an object falls, potential energy is converted into kinetic energy due to gravity. For a fall from height h the potential energy released is m g h. If there is no air resistance then all of this energy will be converted into kinetic energy at the bottom.

The momentum of the impact is mass times velocity, so mv. To bring an object to a stop, the surface must absorb that momentum. If you turn on energy and enter in a mass, then you can get three data points for this case.

The meaning of each result:

In addition to impact velocity, this calculator also displays the following values.

Examples of free fall applications:

Free fall is relevant to various everyday and scientific problems. Skydivers and base jumpers plan the altitude required to reach a desired speed and when to open their parachutes. Engineers use drop tests to determine the size of packaging materials, protective padding, and crush zones based on impact velocity.

Students studying physics use free fall to learn about uniformly accelerated motion while astronomers combine the same formula with different values for Earth's acceleration (g) to explain the motions of objects on other planets and moons. Even throwing a coin into a well allows for a quick measurement of its depth, by recording the time until the sound of impact is heard, the height can be determined using the corresponding formula.

Tips for accurate results:

Please use consistent units and leave the conversion to the calculator tool. Avoid manually mixing units such as feet and seconds. As this is an ideal vacuum result, treat it as an upper limit for objects falling very far or encountering a lot of air mass. Adjust gravity to your location. Use preset values for Moon or Mars outside Earth, and use "Custom" for high altitudes or specific latitudes. In that case g changes by less than one hundredth.