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Free fall calculator

Find the time, speed and height for an object falling or thrown upward under gravity. Pick Earth, the Moon or any g, enter the values you know, and see the working and the graphs.

Units: metres, seconds, m/s and m/s². Free to use, with no sign-up, no adverts and no personal tracking. A learning and checking tool: check the signs and your exam board’s value of g.

Start from an example

Fill in any three boxes and leave the other two empty. Pick a direction as positive and keep to it: a value in the opposite direction is negative.

Displacement s (m)Initial velocity u (m/s)Final velocity v (m/s)Acceleration a (m/s²)Time t (s)

Gravity g Significant figures

Result

45.0 mDisplacement s (given)0 m/sInitial velocity u (given)29.7 m/sFinal velocity v (found)9.81 m/s²Acceleration a (given)3.03 sTime t (found)

Rejected: t = −3.03 s. This time is negative, so it describes a moment before the motion started. It is rejected.

The gradient of the velocity graph is the acceleration, and the area under it is the displacement. The acceleration is constant, so the velocity graph is a straight line and the displacement graph is a parabola.

Working

Known values
Displacement s = 45 m
Initial velocity u = 0 m/s
Acceleration a = 9.81 m/s²
Unknown: v and t.
Find the final velocity
Use v² = u² + 2as.
v² = u² + 2as = 0² + 2 × 9.81 × 45 = 883
v = ±√883 = ±29.7, so v = 29.7 m/s (positive root)
Find the time
Use v = u + at.
t = (v − u) / a = (29.7136 − 0) / 9.81 = 3.03 s

Practise free fall questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

How the free fall calculator works

Free fall is constant-acceleration motion with a = g, so the SUVAT equations apply directly. Take up or down as positive and keep to it. To solve a problem:

Write down the three quantities you know, with signs.
Name the quantity you want.
Choose the equation that contains those four and leaves out the fifth.
Substitute, solve and check the sign and size of the answer.

Sign convention

You choose the positive direction. For a ball thrown upward, take up as positive so that a = −9.81 m/s². For a dropped stone, take down as positive so that a = +9.81 m/s². A quantity in the opposite direction is negative.

Worked example

A ball is thrown vertically upward at 20 m/s. Take up as positive and g = 9.81 m/s². Find when the ball is 15 m above the launch point.

Known values
Displacement s = 15 m
Initial velocity u = 20 m/s
Acceleration a = −9.81 m/s²
Unknown: v and t.
Find the final velocity
Use v² = u² + 2as.
v² = u² + 2as = 20² + 2 × (−9.81) × 15 = 106
v = ±√106 = ±10.3, so v = 10.3 m/s (positive root)
Find the time
Use v = u + at.
t = (v − u) / a = (10.2811 − 20) / (−9.81) = 0.991 s

The first answer is t = 0.991 s, on the way up. Because the quadratic has two positive roots, there is a second answer: v = −10.3 m/s gives t = 3.09 s, when the ball is at the same height on the way back down. Both are correct.

Falling from rest on different worlds

Time and speed for an object dropped from rest through the stated height, with no air resistance. The Moon column shows why a hammer and a feather land together there.

Drop	Time to fall	Speed at the bottom
Earth, 5 m	1.01 s	9.9 m/s
Earth, 20 m	2.02 s	19.8 m/s
Earth, 45 m	3.03 s	29.7 m/s
Earth, 80 m	4.04 s	39.6 m/s
Moon, 20 m	4.97 s	8.05 m/s
Mars, 20 m	3.28 s	12.2 m/s
Jupiter, 20 m	1.27 s	31.5 m/s

Which formulas does this use?

Constant-acceleration displacement, Mean acceleration, Braking distance, Total stopping distance with reaction time, Gravitational field and orbit.

Related calculators

SUVAT calculator, Equations of motion calculator, Projectile motion calculator, and the A-level physics equation calculator for the rest of the A-level equations.

Common questions

What is free fall?

Free fall is motion under gravity alone, with no air resistance. Near the Earth’s surface the acceleration is about 9.81 m/s² downward, whatever the mass of the object.

How do I find the time to fall from a height?

For an object dropped from rest, s = ½gt², so t = √(2s / g). A drop of 45 m takes about 3.03 s. Enter s, u = 0 and a = 9.81 with down as positive and the calculator does it for you.

How do I treat an object thrown upward?

Take up as positive, so a = −9.81 m/s². At the highest point v = 0. Use u, v = 0 and a to get the maximum height, or u and a with s to find the times when the object is at a given height.

How fast is an object moving when it hits the ground?

Use v² = u² + 2as. Dropped from rest through 20 m, v = √(2 × 9.81 × 20), about 19.8 m/s. The speed does not depend on mass when air resistance is ignored.

Is the calculator free, and does it keep my numbers?

It is free to use, with no sign-up, no adverts and no personal tracking. The numbers you type stay in your browser.

What do I assume about air resistance and g?

Air resistance is ignored, so these are the idealised answers used in GCSE, A-level and first-year university mechanics. Use g = 9.81 m/s² unless your exam board says 9.8 or 10. You can change g to compare other values or other worlds.