Key takeaways
- Free fall distance is d = ½ × g × t², using g = 9.81 m/s² on Earth.
- Doubling the fall time doesn't double the distance — it roughly quadruples it.
- Every falling object speeds up at the same rate, regardless of its mass.
- This formula ignores air resistance, so it's most accurate for dense, compact objects.
In this guide
What is free fall?
Free fall describes an object falling under gravity alone, with no other forces like air resistance slowing it down. On Earth, every falling object speeds up at the same steady rate, no matter how heavy it is.
Why does free fall matter?
Free fall is the simplest possible motion problem, and it shows up constantly, from estimating how long a dropped object takes to hit the ground to understanding early skydiving before a parachute opens.
Galileo is said to have shown that a heavy and a light object dropped together hit the ground at the same time. Without air resistance, that's exactly what free fall predicts, no matter the mass.
The formula
| Symbol | What it means | Example |
|---|---|---|
| d | The distance fallen, in metres (m) | 19.62 m |
| g | Gravity's pull, taken as 9.81 m/s² | 9.81 m/s² |
| t | The time spent falling, in seconds (s) | 2 s |
How to calculate free fall distance step by step
- 1Note the falling time. Measure it in seconds.
- 2Square the time. Multiply it by itself, for example
2 × 2 = 4. - 3Multiply by gravity. Use 9.81 m/s².
- 4Multiply by ½. This gives the distance fallen in metres.
Try the calculator below with your own falling time to see every step worked out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Ignoring air resistance in real life. This formula assumes no air resistance, so it's most accurate for dense objects like a stone rather than a feather or a sheet of paper.
- Mixing up distance and speed. This formula gives the distance fallen, not the velocity at that moment.
- Using the wrong g. 9.81 m/s² is for Earth — other planets and the Moon have very different values.
Tips and tricks
- To estimate quickly, remember the rule of thumb:
4.9 × t²gives a close approximation of the distance in metres. - Working backwards from distance to time? Divide by 4.905, then take the square root:
t = √(d ÷ 4.905). - Free fall distance connects directly to gravitational potential energy, which converts into speed as the object falls.
Where you'll use it in real life
- Safety engineering: estimating how long it takes an object to hit the ground when dropped from a height.
- Sport science: understanding the physics behind skydiving before a parachute opens.
- Construction sites: predicting fall times helps assess risks from dropped tools or materials.
- Physics education: free fall is often the first real-world example used to teach motion under constant acceleration.
Quick summary
To find free fall distance, square the falling time, multiply by gravity (9.81 m/s²), then multiply by ½. Because time is squared, small increases in falling time add up to much bigger increases in distance. Use the calculator above to check your own numbers.
Worked example
A ball is dropped from a tall building and falls freely for 2 seconds before you check on it. How far has it fallen?
- 01d = ½gt² (g = 9.81 m/s²)
- 02d = ½ × 9.81 × 2²
- 03d = 4.905 × 4
- 04d = 19.62 m
- 05Impact speed = 19.62 m/s
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate free fall distance?
Square the falling time in seconds, multiply by gravity (9.81 m/s²), then multiply by ½: d = ½gt². The result is in metres.
Why do heavy and light objects fall at the same rate?
In true free fall, with no air resistance, gravity accelerates every object at the same rate, 9.81 m/s², regardless of its mass.
Does air resistance affect this formula?
Yes. This formula assumes no air resistance, so it's very accurate for a dropped stone but less accurate for something light and wide like a piece of paper.
How fast is an object falling after a few seconds?
Its speed equals g × t. After 2 seconds of free fall, an object is moving at about 19.62 m/s, or roughly 70 km/h.
