Free fall calculator

A free fall calculator works out the motion of something falling under gravity alone. Near the Earth's surface every object in free fall speeds up at g = 9.81 m/s², so a stone dropped from 45 m takes t = √(2h/g) = 3.03 s to land and hits the ground at v = √(2gh) = 29.7 m/s. Our SUVAT Calculator solves any free fall problem from three known values, with the working.

There is no separate free fall mode. To use the SUVAT Calculator for a fall, type 9.81 for the acceleration a, or choose g₀ as the acceleration unit and type 1, and fill in two more values.

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SUVAT Calculator

Solve any equation of motion from three known values

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How to use the free fall calculator

1. Choose a positive direction. For something falling, take down as positive, so a = 9.81 m/s². For something thrown up, take up as positive, so a = −9.81 m/s².
2. Under Known values, type a, then two more of s (displacement), u (starting velocity), v (final velocity) and t (time). Leave the other two empty.
3. For an object dropped from rest, u = 0. That is one of your three values.
4. Read the two answers. The calculator says which of the five equations it used for each, and why.
5. Check the velocity-time graph, where the shaded area is the displacement.

It opens on u = 0, a = 2 m/s² and t = 5 s, so change a to 9.81 first. Under Units you can pick km/h or mph for velocities and g₀ (standard gravity, 9.80665 m/s²) for acceleration; distances run from mm to km and miles, but not feet. Practice and help sets falling stone, thrown ball and car questions with worked solutions.

The free fall equations

Free fall is motion with constant acceleration g, so the SUVAT equations apply with a = g. For an object dropped from rest (u = 0) and falling a height h:

g is 9.80665 m/s² by definition of standard gravity, and 9.81 m/s² is the usual school value. Mass does not appear anywhere: without air resistance, a hammer and a feather fall together, as Apollo 15 astronaut David Scott showed on the Moon.

Worked examples you can check in the calculator

Example 1: dropped from a height

A stone is dropped from rest off a 45 m cliff. How long does it take to land, and how fast is it going? Down is positive: u = 0, a = 9.81, s = 45.

Type u = 0, a = 9.81 and s = 45. The calculator gives v = 29.7 m/s from the equation with no t, then t = 3.03 s from v = u + at. With 1 g₀ instead of 9.81, it gives 3.0294 s, the same to 3 significant figures.

Here x is the time in seconds and y is the velocity in m/s, taking down as positive. The gradient is g, and the area under the line, ½ × 3.03 × 29.7, is the 45 m fallen.

Example 2: how far in a given time

An object falls from rest for 2.5 s. How far does it fall?

Type u = 0, a = 9.81 and t = 2.5: the calculator gives s = 30.66 m and v = 24.5 m/s. The distance grows with t²: 4.9 m in the first second, 19.6 m after 2 s and 44.1 m after 3 s.

Choosing the right equation is the skill here. Try one in the course, then press Mark:

Example 3: thrown straight up

A ball is thrown straight up at 15 m/s. How high does it go? Now up is positive, so a = −9.81, and at the top v = 0:

Type u = 15, a = −9.81 and v = 0. The calculator gives s = 11.5 m and t = 1.53 s to reach the top.

Example 4: passing the same height twice

When is the ball from Example 3 at 10 m? Type u = 15, a = −9.81 and s = 10. The calculator gives both answers: t = 0.982 s on the way up, moving at 5.37 m/s, and t = 2.08 s on the way down, at −5.37 m/s. The minus sign means it is moving downwards.

Example 5: thrown up from a height

Someone standing on a 25 m high wall tosses a ball upwards at 8 m/s, and it lands on the ground below. With up as positive, the ground is 25 m below the start, so s = −25. Type u = 8, a = −9.81 and s = −25: the calculator gives t = 3.22 s and v = −23.5 m/s.

Free fall on other planets

Change a to the gravity of another world. On the Moon, g = 1.62 m/s², so the 45 m drop takes 7.45 s and lands at 12.1 m/s. On Mars, g = 3.71 m/s². These values come from NASA's planetary fact sheet.

What the calculator does not do

• No air resistance. SUVAT assumes constant acceleration, which is only true without drag. Real falling objects reach a terminal velocity. The Projectile Motion Simulator has air resistance: launch at 0° from a height to watch a drop with drag, and our projectile motion calculator guide shows how to find terminal velocity.
• No feet. Distances can be in mm, cm, m, km or miles. Convert feet first: 100 ft is 30.48 m.
• No changing gravity. g is taken as constant, which is fine for falls of a few kilometres at most.

Common mistakes

• Mixing signs. Pick a positive direction and stick to it. If up is positive, g is −9.81 and a point below the start has negative s.
• Forgetting u = 0. "Dropped" or "released from rest" means u = 0, one of your three values.
• Saying v = 0 at the bottom. The velocity is zero at the top of a throw, not when a falling object lands.
• Thinking heavy objects fall faster. Without air resistance, every mass falls with the same acceleration.
• Using g = 10. Some courses allow it; use the value the question gives, usually 9.81 or 9.8.

Practise motion in a short timed paper

Falling objects come up in AP Physics 1 and AP Physics C: Mechanics practice, and in A-level Physics: Year 1 and A-level Maths: Mechanics in the UK. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. For motion with any constant acceleration, see our acceleration calculator guide.

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