Free Fall Distance Calculator
Drop a rock off a cliff and time its fall, and you can work out how far it dropped without ever measuring the cliff. That is the whole idea behind free fall: with gravity as the only force acting, distance depends on time, gravity, and any initial downward speed. Enter the fall time below and this calculator returns the distance fallen, the impact velocity, and the math behind the answer, with gravity presets for the Moon, Mars, and beyond, plus a meters-or-feet toggle.
The values below are a verified worked example: an object dropped from rest falling for 3.5 seconds on Earth. Press Calculate to see it run.
Free Fall Distance Calculator
Distance fallen and impact velocity from fall time, gravity, and initial speed
Distance fallen
Idealized free fall only: gravity is treated as constant and air resistance is ignored. For long falls of light objects, or for a human body past the first seconds, real distances and speeds run lower than these figures.
Quick Answer
An object dropped from rest falling for 3.5 seconds on Earth covers 60.09 meters and hits 34.34 m/s, about 123.6 km/h. In feet, that is 197.13 ft fallen at 112.65 ft/s. The distance grows with the square of time, so doubling the fall time quadruples the distance.
Key takeaways
- Distance fallen is d equals v0 times t plus one half times g times t squared. Dropped from rest, that simplifies to d equals one half times g times t squared.
- Impact velocity is v equals v0 plus g times t. After 3.5 seconds on Earth from rest, that is 34.34 m/s.
- Mass never enters the formula. In free fall without air resistance, a bowling ball and a feather accelerate identically.
- Air resistance is the model's limit. For dense objects over short drops it barely matters; for light, wide objects it dominates from the start.
- Quick Answer
- How to use the free fall distance calculator
- The formula, and why time is squared
- Worked example, checked against the tool
- Fall time to distance reference table (Earth, g = 9.81 m/s²)
- Gravity across the solar system
- Where other free fall calculators fall short
- When air resistance breaks the model
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the free fall distance calculator
Enter the time of fall in seconds. This is the only required input: how long the object has been falling. Pick a gravity preset or enter your own: Earth at 9.81 m/s² is the default, with the Moon, Mars, Venus, and Jupiter on the list, or Custom for any other body. Enter an initial downward velocity if there was one, and leave it at 0 for an object simply dropped. Choose meters or feet for the output, then press Calculate. The results show the distance fallen, the velocity at impact, and the full math.
The worked example above is the natural first check: t equals 3.5 with the Earth preset and zero initial velocity. If your numbers do not match 60.09 meters and 34.34 m/s, check that the gravity field still reads 9.81: switching to a preset and back is the usual fix when a stray Custom value is sitting in the field.
The formula, and why time is squared
Free fall is motion with constant acceleration, so it uses the kinematic equations directly. The distance formula is d equals v0t plus one half gt², where d is the distance fallen, v0 is the initial downward velocity, g is gravity, and t is time. For an object dropped from rest, v0 equals 0 and the formula simplifies to the classic d equals one half gt², which is exactly what this calculator's default inputs compute. The impact velocity comes from v equals v0 plus gt.
The squared time is what surprises people. Because velocity itself grows with time, the distance covered in each passing second also grows, so total distance grows with the square. That is why the table below jumps by ever larger steps: the second second of a fall covers three times the distance of the first, and the tenth second covers nineteen times the first. Three assumptions sit behind the formula: the fall starts from the stated initial velocity with no push afterward, gravity stays constant, and air resistance is ignored. Over everyday drop heights on Earth these are excellent approximations.
The bars are the Earth table below, drawn to scale against the 10-second fall. The 1-second bar is barely visible next to it, which is the whole point: ten seconds of free fall covers over 490 meters, taller than most skyscrapers, while one second covers about 4.91 meters, roughly a storey and a half.
Worked example, checked against the tool
An object is dropped from rest and falls for 3.5 seconds on Earth. Enter t equals 3.5 with the Earth preset in the calculator and you will get exactly these numbers:
- Distance: d equals 0 times 3.5 plus 0.5 times 9.81 times 3.5², which is 0.5 times 9.81 times 12.25, which is 60.09 meters.
- Impact velocity: v equals 0 plus 9.81 times 3.5, which is 34.34 m/s, about 123.6 km/h.
- In feet, the tool converts the unrounded values: 60.08625 m times 3.28084 is 197.13 ft, and 34.335 m/s times 3.28084 is 112.65 ft/s.
- With a downward throw instead: thrown at 5 m/s with a 2-second fall, d equals 5 times 2 plus 0.5 times 9.81 times 4, which is 29.62 m.
Fall time to distance reference table (Earth, g = 9.81 m/s²)
Every row below is what the calculator itself returns for a drop from rest at Earth gravity. Use it as a sanity check, or as a quick lookup when you know the time and want the distance without touching the tool.
| Fall time (s) | Distance (m) | Distance (ft) | Impact velocity (m/s) |
|---|---|---|---|
| 1 | 4.91 | 16.09 | 9.81 |
| 2 | 19.62 | 64.37 | 19.62 |
| 3 | 44.14 | 144.83 | 29.43 |
| 4 | 78.48 | 257.48 | 39.24 |
| 5 | 122.63 | 402.31 | 49.05 |
| 6 | 176.58 | 579.33 | 58.86 |
| 7 | 240.34 | 788.53 | 68.67 |
| 8 | 313.92 | 1,029.92 | 78.48 |
| 9 | 397.31 | 1,303.49 | 88.29 |
| 10 | 490.50 | 1,609.25 | 98.10 |
Gravity across the solar system
Switch the preset in the calculator to use any of these standard approximate values. The last column is a 3-second drop from rest on each body, computed with the same formula, so the comparison is apples to apples. Note that the preset values are rounded approximations, not survey-grade measurements: NASA's own fact sheet rounds these to one decimal, while the calculator carries two, which is why the Moon shows 1.62 here against 1.6 there.
| Body | Gravity (m/s²) | 3-second drop distance |
|---|---|---|
| Earth | 9.81 | 44.14 m |
| Moon | 1.62 | 7.29 m |
| Mars | 3.71 | 16.70 m |
| Venus | 8.87 | 39.91 m |
| Jupiter | 24.79 | 111.56 m |
The Moon row explains Apollo footage: a 3-second drop there covers only 7.29 meters, so everything looks like slow motion. The Jupiter row is a thought experiment more than a practical one, since Jupiter has no solid surface to drop things onto, but the preset is useful for physics problems set on other worlds. For any body not listed, choose Custom and type its surface gravity.
Where other free fall calculators fall short
Every rival page covers the basic formula, but each leaves something out. The best-known physics calculator converts units well and solves from time, velocity, or height, yet it has no gravity presets for other worlds. The reference-table style calculators give a handy height-to-time chart but stop at Earth gravity and dropped-from-rest cases. The forward-model calculators that accept an initial height and velocity rarely show the worked math line, so students cannot check their homework against it. None of them combine planet presets, initial velocity, impact velocity, a meters-or-feet toggle, and a visible math line the way this calculator does.
This page also keeps the model's limits in plain sight instead of burying them. The formula assumes constant gravity and no air resistance, and the article says so wherever the numbers could mislead, from skydiving to light objects. That honesty is part of the tool: a calculator that silently overstates a 30-second human fall by kilometers is worse than no calculator at all.
When air resistance breaks the model
For dense objects over short drops, air resistance barely matters, and the formula is a fine approximation. For light objects with large surface areas, like a sheet of paper or a badminton shuttlecock, air resistance dominates from the start and this formula does not apply at all. In between sits the case people actually ask about: a human body. A skydiver stops accelerating once drag balances weight, reaching a steady falling speed, and from that point on distance grows linearly with time, not with its square. Beyond roughly the first 10 to 12 seconds, this calculator's distances run too large for a human body, and the gap only widens.
Two links help here. The acceleration calculator covers the general relationship between force, mass, and acceleration that sits behind both free fall and drag. The terminal velocity calculator models the steady speed where drag and weight balance, which is the right tool once a fall stops accelerating. Use this page for the idealized fall, and switch to terminal velocity when drag takes over.
Frequently asked questions
No. In free fall without air resistance, a bowling ball and a feather accelerate identically. Galileo demonstrated this centuries ago, and it falls straight out of the formula: mass appears nowhere in d equals one half gt².
Only for the first few seconds. Real skydivers quickly reach terminal velocity, where air resistance balances gravity and the fall stops accelerating. This calculator ignores air resistance, so beyond roughly 10 to 12 seconds its distances run too large for a human body.
Enter the throw speed as the initial downward velocity. The calculator uses the full d equals v0t plus one half gt² form. For example, throwing downward at 5 m/s with a 2-second fall gives 5 times 2 plus 0.5 times 9.81 times 4, which is 29.62 m.
This tool models downward motion only. An upward throw needs the projectile-motion equations, where gravity first slows the object to a stop before it starts falling. Do not enter a negative velocity here; the calculator rejects it.
That is the standard average acceleration due to gravity near Earth's surface. It varies slightly with latitude and altitude, from about 9.78 at the equator to 9.83 at the poles, but 9.81 is the accepted average value for calculations. The exact defined standard value is 9.80665 m/s².
4.91 meters, or 16.09 feet. It is a handy mental anchor: after one second of free fall from rest on Earth, an object has dropped about 4.91 meters, roughly a storey and a half.
For dense objects over short drops, barely. For light objects with large surface areas, like a sheet of paper or a badminton shuttlecock, air resistance dominates from the start and this formula does not apply.
Yes. Select the Moon (1.62 m/s²) or Mars (3.71 m/s²) preset, or choose Custom for any other body. A 3-second drop on the Moon covers only 7.29 meters, which is why Apollo footage looks like slow motion.
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References
- OpenStax, University Physics Volume 1. 3.5 Free Fall. Accessed October 25, 2026.
- OpenStax, University Physics Volume 1. 13.2 Gravitation Near Earth's Surface. Accessed October 25, 2026.
- OpenStax, College Physics for AP Courses. 2.7 Falling Objects. Accessed October 25, 2026.
- OpenStax, University Physics Volume 1. Chapter 3 Summary: Motion Along a Straight Line. Accessed October 25, 2026.
- The Physics Classroom. 1-D Kinematics Lesson 5: Introduction. Accessed October 25, 2026.
- NASA National Space Science Data Center. Planetary Fact Sheet. Accessed October 25, 2026.