Case 1
- Time falling
- 1s
4.903m
Open with these valuesFree Fall Distance Calculator
44.130m
Result: 44.130 mA dropped object covers ½ × g × t², so after three seconds it has fallen 44.13 m. The distance grows with the square of the time: the third second alone accounts for more than the first two together. Air resistance is ignored, so this is the vacuum value and an upper bound.
Worked examples
Case 2
- Time falling
- 3s
44.130m
Open with these valuesCase 3
- Time falling
- 5s
122.583m
Open with these valuesHow it's calculated
d = ½ × g × t²
- StepEnter how long the object has been falling, in seconds.
- StepRead the distance fallen in metres, measured from the release point.
- ResultThe speed at that moment is g × t — the middle column shows it.
What this number means
The third second beats the first two together
After one second the drop is 4.903 m and after two it is 19.613 m, but after three it is 44.130 m. The third second alone therefore adds 24.517 m, more than the first two put together.
g = 9.80665 m/s² is fixed, not measured
Standard gravity is a conventional value listed as exact by NIST, which is why one second of falling gives exactly half of it: 4.903325 m. Local gravity varies slightly with latitude and altitude, and on the Moon it is only about 1.62 m/s².
In a vacuum a feather falls like a bullet
The formula contains no shape and no density, only time, so a feather and a lead ball both reach 44.130 m after three seconds. In real air the feather is left behind almost immediately.
Terminal velocity is where this stops working
A belly-down skydiver stops accelerating at roughly 55 m/s, which v = g × t reaches after about 5.6 seconds. Beyond that the calculator keeps speeding the fall up while the real one no longer does, so long drops through air come out far too deep.
Commonly misread
Heavier objects fall faster, so a bowling ball beats a tennis ball.
With air resistance ignored the mass drops out of the formula entirely and both cover 44.130 m in three seconds. Drag separates them in real air, not weight.
Three times the falling time means three times the distance.
It means nine times the distance, because the time is squared: 4.903 m after one second becomes 44.130 m after three.
Reading 44.130 as the speed reached after three seconds.
That is the distance in metres, measured from the release point. The speed at that moment is g × t = 29.42 m/s, about 106 km/h.
Reference table
| Time (s) | Speed reached (m/s) | Distance fallen (m) |
|---|---|---|
| 0 | 0.00 | 0.000 |
| 1 | 9.81 | 4.903 |
| 2 | 19.61 | 19.613 |
| 3 | 29.42 | 44.130 |
| 5 | 49.03 | 122.583 |
| 10 | 98.07 | 490.332 |
Questions
What is free fall and how is the distance calculated?
Free fall is motion under gravity alone, with air resistance ignored. The distance an object drops after a time t is d = ½ × g × t², where g is the acceleration due to gravity. With g = 9.80665 m/s², an object falling for 3 seconds covers 44.129925 m.
Why does the formula use g = 9.80665 m/s²?
That is standard gravity, the conventional value fixed by international agreement and listed as exact by NIST. It means a falling object gains about 9.81 m/s of speed every second. Local gravity varies slightly with latitude and altitude, and on the Moon g is only about 1.62 m/s².
How fast is the object moving at that point?
The speed is not the output here, but it follows from the same g: v = g × t. After 3 seconds that is 29.41995 m/s, about 106 km/h. Distance grows with the square of time while speed grows in a straight line.
Does this calculator account for air resistance?
No — it computes idealised free fall in a vacuum. In real air, drag grows with speed until it balances gravity and the object stops accelerating at its terminal velocity, roughly 55 m/s for a belly-down skydiver. For short drops or dense objects the difference is small.
Where is the free fall formula used?
It predicts how long a dropped object takes to reach the ground and how fast it arrives, which is the basis of drop-tower rides, construction safety rules, and ballistics. Turned around, it also gives the height of a cliff or a well from the time a stone takes to fall.
Sources and last check
Information, not professional advice.