Free Fall Calculator

What the free fall calculator does

Drop something from a height and you want to know two things: how long until it lands, and how fast it is going when it does. This calculator answers both. You give it the height, the strength of gravity, and an initial speed if the object is thrown downward rather than simply released, and it returns the time of fall and the impact velocity.

Because gravity is a value you can set, it works just as happily for a drop on the Moon or Mars as on Earth. Below is the physics of a falling object, the equations behind it, and a worked example.

How to use it

1. Set gravity. It starts at 9.80665 m/s², the standard value for Earth. You can enter it in g or in feet per second squared, or change it for another world.
2. Enter the initial velocity. Leave it at 0 for an object dropped from rest, or enter a downward speed if it is thrown down.
3. Enter the height it falls through, in whatever length unit suits you.
4. Press Calculate for the fall time and impact speed, or Reset to clear it.

The physics of falling

An object is in free fall when gravity is the only thing acting on it, with nothing else pushing or dragging. Under that condition gravity gives every falling object the same steady acceleration, about 9.81 metres per second squared near Earth's surface, so its speed grows by that much every second it falls.

Here is the part that surprised people for two thousand years. That acceleration does not depend on how heavy the object is. A cannonball and a pebble, released together, fall side by side and land together. Galileo argued it, and the reason is clean: gravity pulls harder on more massive things, but more massive things are exactly that much harder to get moving, and the two effects cancel. A feather only loses the race because of the air, and in a vacuum the feather and the cannonball truly land at the same instant.

The equations it uses

Free fall is constant-acceleration motion with the acceleration set to gravity, g. With h for the height, v₀ for any initial downward speed, t for time, and v for the impact speed, the calculator first finds the time to fall by asking when the object has dropped the full height:

t = ( −v₀ + √( v₀² + 2 g h ) ) ÷ g

Then the impact speed is the starting speed plus everything gravity added over that time:

v = v₀ + g t

For the common case of a straight drop from rest, v₀ is zero and these tidy up to the forms you may recognise, the time to fall t = √(2h ÷ g) and the impact speed v = √(2 g h). Notice that mass appears nowhere in any of them, which is the falling-together result written in symbols.

Units, gravity, and precision

The calculator works in SI units, with gravity in metres per second squared, height converted to metres, and the results in seconds and metres per second, which you can then read in other units. Its default gravity is 9.80665 m/s², the formally defined standard value, slightly more exact than the everyday 9.81. The true local figure shifts a little with where you stand, from roughly 9.78 near the equator to about 9.83 near the poles, and it weakens with altitude, which is why the value is yours to change.

Results are carried to several significant figures, more than the precision of any real drop, so the rounding is only in the display. The honest limit on the answer is the assumption underneath the model, which the next section covers.

A worked example: a drop from 45 m

A rock is dropped from a 45 metre cliff, from rest, with gravity at 9.81 m/s².

The time to fall is t = √(2 × 45 ÷ 9.81) = √9.17 = 3.03 s. The speed at impact is v = √(2 × 9.81 × 45) = √883 = 29.7 m/s, which is about 107 km/h. So in just over three seconds the rock builds up to highway speed, a good reminder of how quickly a fall becomes dangerous.

Where the model holds: air and terminal velocity

This calculator uses pure free fall, gravity alone with no air resistance. For a dense, compact object over a moderate drop, a stone, a wrench, a steel ball, that is very close to reality, often within a percent or two. It is the right tool for those cases.

Air changes the picture for light or large objects, and for very long falls. As something falls faster, the air pushes back harder, until that push balances gravity and the object stops speeding up. From then on it falls at a steady pace called the terminal velocity, around 55 metres per second for a skydiver in a spread position. This model does not include that, so for a feather, a parachute, or a fall of hundreds of metres, treat its answer as the no-air ideal, the speed the object would reach if the air were not in the way.

Questions people ask

Do heavier objects fall faster?

Not from gravity alone. In free fall, every object accelerates at the same rate regardless of mass, so they fall together. Heavier objects only seem to win in air because they push through it more easily.

How long does it take to fall a given height?

For a drop from rest, the time is the square root of twice the height divided by gravity. From 45 metres on Earth that is about 3 seconds.

What is terminal velocity?

It is the steady speed a falling object reaches in air, once air resistance balances gravity and it stops accelerating. This calculator ignores air, so it does not cap the speed at a terminal value.

Can I use it for the Moon or other planets?

Yes. Set gravity to the value for that world, such as 1.62 m/s² for the Moon, and the fall time and impact speed update for the weaker or stronger pull.

What if the object is thrown down instead of dropped?

Enter its starting speed as the initial velocity. The object reaches the ground sooner and hits harder than a object simply released from the same height.

References

A quick note on where the physics comes from. Free fall as constant-acceleration motion under gravity, and the result that all objects fall at the same rate regardless of mass, are standard kinematics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The value of standard gravity, 9.80665 m/s², and the SI units throughout follow the US National Institute of Standards and Technology.

1. OpenStax, University Physics Volume 1, Section 3.5, Free Fall. https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall
2. HyperPhysics, Georgia State University, Description of Motion. http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811