Quick answer
In free fall t = √(2h ÷ g), v = √(2gh) and h = ½gt². Dropping from 45 m takes 3.0294 s and hits at 29.71 m/s (about 107 km/h).
Choose whether you know the height or the time. The calculator returns the fall time, impact speed or height.
Related tools: Acceleration Calculator: Average acceleration from change in velocity over time. SUVAT Calculator: Solve constant-acceleration motion for the missing quantities. Projectile Motion Calculator: Range, flight time and peak height of a projectile without air resistance.
How to use the Free Fall Calculator
- Choose i know the: From a height and From a fall time.
- Enter height (m) or time (s) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| I know the | Choose one: From a height; From a fall time | Starts at From a height |
| Height (m) or time (s) | A number | > 0 |
Formula and method
Formula
t = √(2h ÷ g); v = √(2gh); h = ½gt²
IEEE-754 double precision; shown to the decimals indicated.
No air resistance; g = 9.80665 m/s².
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: I know the = From a height; Height (m) or time (s) = 45.
| Result | Value |
|---|---|
| Fall time | 3.0294 s |
| Impact speed | 29.7086 m/s |
Example 2
Inputs: I know the = From a fall time; Height (m) or time (s) = 3.
| Result | Value |
|---|---|
| Fall height | 44.1299 m |
| Impact speed | 29.42 m/s |
Example 3
Inputs: I know the = From a height; Height (m) or time (s) = 100.
| Result | Value |
|---|---|
| Fall time | 4.516 s |
| Impact speed | 44.2869 m/s |
The first line is the headline result (fall time). Below it the free Fall Calculator lists impact speed, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Worked example
t = √(90 ÷ 9.80665) = 3.029 s; v = g × t = 9.80665 × 3.029 = 29.71 m/s. A fall of 20 m takes 2.02 s.
Air resistance
The model ignores air resistance, which matters for long falls: a skydiver reaches terminal velocity around 55 m/s. Light, flat objects fall far slower than the formula says. g is taken as 9.80665 m/s².
How the result changes with height or time
Holding every other input at the first worked example, this table changes only height or time. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Height or time | Fall time | Impact speed |
|---|---|---|
| 22.5 | 2.1421 s | 21.0071 m/s |
| 45 | 3.0294 s | 29.7086 m/s |
| 90 | 4.2843 s | 42.0142 m/s |
| 180 | 6.0589 s | 59.4171 m/s |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Height (m) or time (s): entering "0" shows "Height (m) or time (s) must be greater than 0." beside that field and no result.
Choosing between the Free Fall Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Acceleration Calculator](/science/acceleration-calculator/) | initial velocity, final velocity and time | Acceleration |
| [SUVAT Calculator](/science/suvat/) | you know and initial velocity u | Final velocity v |
| [Projectile Motion Calculator](/science/projectile-motion-calculator/) | launch speed and launch angle | Range |
| [Magnitude of Acceleration Calculator](/science/magnitude-of-acceleration-calculator/) | x component and y component | Magnitude |
| [Terminal Velocity Calculator](/science/terminal-velocity-calculator/) | mass, frontal area and drag coefficient | Terminal velocity |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Air resistance matters for long falls
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for height (m) or time (s) to confirm this.
Frequently asked questions
How far does an object fall in 1 second?
In 1 second a dropped object falls ½ × 9.80665 × 1² ≈ 4.9 m.
Does mass affect fall time?
Not in a vacuum: a feather and a hammer fall together because acceleration is g for every mass; air resistance causes the difference on Earth.
What is terminal velocity?
The speed where drag equals weight.
What does the Free Fall Calculator calculate?
Fall time, height and impact speed in free fall from rest. It returns Fall time and Impact speed.
What formula does the Free Fall Calculator use?
t = √(2h ÷ g); v = √(2gh); h = ½gt². No air resistance; g = 9.80665 m/s².
What do I need to enter in the free Fall Calculator?
You enter I know the and Height (m) or time (s).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Air resistance matters for long falls.
What does the “I know the” option change?
It sets how the free Fall is worked out. The choices are From a height and From a fall time.
What is an example of a free Fall result?
With i know the From a height and height (m) or time (s) 45, the fall time is 3.0294 s.
Related calculators
- Acceleration Calculator — Average acceleration from change in velocity over time.
- SUVAT Calculator — Solve constant-acceleration motion for the missing quantities.
- Projectile Motion Calculator — Range, flight time and peak height of a projectile without air resistance.
- Magnitude of Acceleration Calculator — Magnitude of an acceleration vector from its components.
- Terminal Velocity Calculator — Terminal speed of a falling object from mass, area and drag coefficient.
- Days Until Fall — Days until the astronomical start of fall.
Sources
- CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.