Example 1
They fell for 0.45 s: from what height?
Free Fall Calculator
Enter fall time. The calculator computes distance h = ½ g t² from rest. 1 s is 4.9 m, 2 s is 19.6 m: doubling time multiplies distance by four, not by two.
You have a vertical v₀: vertical throw. Off an edge with horizontal v₀: horizontal throw.
Result
Fall time (s) and g (m/s², default 9.81). Drop distance shows up here.
How it works
Free fall starts at v₀ = 0. Distance h = ½ g t². After 1 s: 4.9 m. After 2 s: 19.6 m. After 3 s: 44.1 m. Twice the time is four times the distance, not two. After 0.45 s you get about 1.0 m. After 0.8 s about 3.1 m. After 1.4 s about 9.6 m.
Field t is in seconds. Empty g = 9.81 m/s². Result h in meters. No air drag, no v₀. A comma and a period are the same time: 1,5 and 1.5. A minute is 60 s, not 1.
t must be a number. Typed 0 s gives h = 0. This calculator goes from t to h and does not compute t from height. Time from h is t = √(2h/g), by hand or on horizontal throw, where t comes from h with a horizontal v₀.
A throw up or down with v₀ is on the neighbouring page. Off an edge with horizontal v₀, fall time from 8 m is the same, about 1.28 s, but there you also get Z. Here only h from t.
Type 2, leave g empty, click Calculate, and match 19.6 m. Then 1 and 3: 4.9 m and 44.1 m. The header symbol does not drop a stone off a bridge.
The model is classroom vacuum and constant g. In air, after a few seconds drag starts to matter and distance grows slower than t². At 1 s and 2 s, school stays with ½gt².
How to use
- Type fall time in seconds, for example 2. That is time from release, not height. 0.45 s and 0.8 s sit on the example cards.
- Leave g blank for Earth, or type 9.81. Another planet needs another g; do not guess 10 if the problem gives 9.81.
- Click Calculate. 2 s give 19.6 m. 1 s gives 4.9 m. 3 s give 44.1 m. 0.8 s gives about 3.1 m.
- Typed 0 s gives 0 m. t must be a number. This calculator does not invert the formula: t from h is t = √(2h/g), by hand or on horizontal throw.
- With a vertical v₀, open vertical throw. Off an edge with horizontal v₀, open horizontal throw. Here start from rest and only h from t.
Formula
h = ½ · g · t2
t is the fall time in seconds and g is the gravitational acceleration in m/s² (9.81 on Earth). The result h is the distance fallen in meters, air resistance not included.
h, g, and t in a drop from rest
Free fall in this calculator starts at v₀ = 0. Distance is h = ½ g t², no air drag. Time from the field, blank g = 9.81.
- h
- Drop distance in meters. At t = 2 s and g = 9.81 you get about 19.6 m. That is not H_max of an upward throw.
- t
- Fall time in seconds, first field. Zero seconds gives h = 0. Horizontal v₀ lives on the horizontal-throw page.
- g
- Gravitational acceleration. Default 9.81 m/s². It enters linearly in h = ½ g t².
- v₀
- Start from rest here, so v₀ = 0. A nonzero downward v₀ is on the vertical-throw page, not this card.
Real-life examples
Example 2
You hear the splash 2 s after letting go.
Example 3
A full 3 s of falling (this is why decks have nets).
Example 4
From the eaves to the windowsill in 0.8 s.
Example 5
About 1.4 s between takeoff and hitting the water.
Example 6
It slid out and fell 0.4 s, mercifully onto grass.
Example 7
A classroom classic: 0.7 s from branch to ground.
Example 8
Apollo 15, 1971: Scott’s hammer fell for 1.4 s at the lunar g = 1.62 m/s².
Example 9
A rover knocks a pebble loose; it falls 2 s at the Martian g = 3.71 m/s².
Example 10
A kid drops a ball; it falls for 1.1 s.
Example 11
One full second of flight from a high branch.
Frequently asked questions
How many meters after 2 s?
h = 0.5 × 9.81 × 4 = 19.62 m, 19.6 m on the page. After 1 s: 4.9 m. After 3 s: 44.1 m. After 0.8 s: about 3.1 m.
Do I type height or time?
Time t. The result is h. This calculator does not compute t from h. The inverse is t = √(2h/g).
Which units do I type?
t in seconds, g in m/s². Result in meters. Empty g = 9.81. A minute is 60 s.
What if t = 0?
h = 0. Nothing has fallen. t must be a number before 19.6 m can appear.
Is there a v₀?
No. Start from rest. With v₀ up or down, open vertical throw. There H_max = v₀²/(2g).
Why is 2 s not twice 1 s in meters?
Because t is squared. Twice the time is four times h: 4.9 m versus 19.6 m, not 9.8 m.
Is there air drag?
No. Classroom model. After a few seconds in air, distance grows slower than t². Here it stays ½gt².
Where is t from height?
This calculator goes from t to h. Time from h is t = √(2h/g) by hand, or use horizontal throw, where t comes from h.
How much after 0.45 s?
About 1.0 m. After 1.4 s about 9.6 m. Both instants sit on the example cards.
Does a comma in 1.5 s work?
Yes. 1,5 and 1.5 are the same time. The calculator does not require a period.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.