Free Fall Calculator
Calculate free fall time, impact velocity, and distance fallen from height, time, or final speed. Enter any one known quantity, initial velocity, and gravity to get instant results.
Find Fall Time, Impact Speed and Distance Fallen
Free Fall Formula
Where:
- \(h\) — fall height, the vertical distance travelled (m)
- \(t\) — fall time, from release to impact (s)
- \(v_0\) — initial velocity (m/s); 0 for a simple drop
- \(v\) — impact velocity (m/s)
- \(g\) — gravitational acceleration (m/s²); 9.81 on Earth
These are the standard equations of uniformly accelerated motion, with the downward direction taken as positive. Knowing any one of \(h\), \(t\), or \(v\) is enough to solve for the other two.
Free Fall – Calculation Example
Example: an object is dropped from a height of 20 m with no initial velocity, under Earth gravity \(g = 9.81\ \text{m/s}^2\).
\[ t = \frac{-v_0 + \sqrt{v_0^2 + 2gh}}{g} = \frac{\sqrt{2 \cdot 9.81 \cdot 20}}{9.81} = \frac{19.809}{9.81} \approx 2.019\ \text{s} \]
\[ v = v_0 + g\,t = 9.81 \cdot 2.019 \approx 19.81\ \text{m/s} \]
Result: the object falls for about 2.019 s and hits the ground at 19.81 m/s (≈ 71.3 km/h or 44.3 mph), after falling 20 m.
How to use the calculator
- In the Solve using dropdown, choose which quantity you know: Fall height (h), Fall time (t), or Impact velocity (v). Only the matching input box is shown; the other two are calculated.
- Enter the known value and pick its unit — metres or feet for height; m/s, km/h, ft/s, or mph for velocity.
- Set the Initial velocity (v₀). Enter 0 for an object that is simply dropped, a positive value if it is thrown downward, or a negative value if it is thrown upward first.
- Adjust Gravity (g) if needed. The default 9.81 m/s² applies to Earth; use 1.62 m/s² for the Moon or 3.72 m/s² for Mars.
- Read the results: fall time, impact velocity in four units, and distance fallen in metres and feet, plus the exact equations used with your numbers substituted in.
What is free fall?
An object is in free fall when gravity is the only force acting on it. Because gravity accelerates every object at the same rate regardless of its mass, a hammer and a feather dropped in a vacuum hit the ground at the same time. The fall time, impact velocity, and distance depend only on the height, the initial velocity, and the strength of the gravitational field.
Note what the equations do not contain: mass. A 1 kg stone and a 10 kg stone dropped from 20 m both land after about 2.02 s at about 19.8 m/s. Mass would only matter if air resistance played a role — more on that below.
The motion is symmetric in a useful way. An object thrown upward with speed \(v_0\) comes back down past its starting point with the same speed \(v_0\) (in the opposite direction), and the total flight time up-and-down is \(2v_0/g\). That is why this calculator also works for problems like "a ball is thrown up at 15 m/s from a cliff" — enter the downward height to the ground below and a negative initial velocity.
The impact velocity is often the most practically important result, since it determines the kinetic energy at landing — the quantity that matters for damage in a crash or for a safe landing speed. You can convert the impact velocity into landing energy with our Kinetic Energy calculator, or explore the underlying physics with the Conservation of Energy calculator: in free fall, potential energy \(mgh\) converts entirely into kinetic energy \(\tfrac{1}{2}mv^2\).
Assumptions and limitations
- No air resistance. The equations assume a vacuum. For compact, heavy objects falling a few tens of metres, the error is small (a few percent). For light or large objects (paper, parachutes, hailstones) or falls from hundreds of metres, real speeds and times are noticeably lower because air drag grows with speed.
- Constant gravity. \(g\) is treated as constant over the fall. This is accurate for everyday heights; \(g\) decreases only about 0.3% per 10 km of altitude.
- Flat ground, vertical motion. The object must fall straight down onto a level surface. Falls down slopes are better handled with the Inclined Plane calculator.
- Sign convention: downward is positive. An initial velocity thrown upward must be entered as a negative number, and the impact velocity must be at least as large as the initial velocity.
- Terminal velocity on Earth (about 55 m/s for a skydiver in a spread position, ~200 km/h) never appears in these equations — the calculator will happily report speeds above it because it ignores drag.
Quick reference: fall from rest on Earth (g = 9.81 m/s²)
| Height | Fall time | Impact velocity |
|---|---|---|
| 1 m | 0.452 s | 4.43 m/s (16 km/h) |
| 5 m | 1.010 s | 9.90 m/s (36 km/h) |
| 10 m | 1.428 s | 14.0 m/s (50 km/h) |
| 20 m | 2.019 s | 19.8 m/s (71 km/h) |
| 50 m | 3.193 s | 31.3 m/s (113 km/h) |
| 100 m | 4.515 s | 44.3 m/s (159 km/h) |
A useful rule of thumb: in a vacuum, an object falling from rest travels about 5 m in the first second, 20 m in two seconds, and 45 m in three seconds, because distance grows with the square of time. For other motion problems, the Kinematic Equations solver handles the general case with arbitrary acceleration.
Frequently Asked Questions
How do I calculate free fall time by hand?
For an object dropped from rest, use \( t = \sqrt{2h/g} \). For example, from 45 m on Earth: \( t = \sqrt{2 \cdot 45 / 9.81} \approx 3.03 \) s. If the object is thrown downward with speed \(v_0\), use \( t = (-v_0 + \sqrt{v_0^2 + 2gh}) / g \). Always keep units consistent: height in metres, velocity in m/s, and \(g\) in m/s².
How do I find the impact velocity if I only know the height?
Use the time-independent formula \( v = \sqrt{v_0^2 + 2gh} \). For a drop from rest, it simplifies to \( v = \sqrt{2gh} \). From 30 m on Earth: \( v = \sqrt{2 \cdot 9.81 \cdot 30} \approx 24.3 \) m/s, which is about 87 km/h. To convert, divide m/s by 3.6 for km/h or multiply by 2.237 for mph.
How do I handle an object that is thrown upward first?
Enter the initial velocity as a negative number, because this calculator treats downward as the positive direction. The height should be the vertical drop from the release point down to where the object lands. For example, a ball thrown up at 10 m/s from a 25 m cliff needs \(v_0 = -10\) and \(h = 25\). The upward part of the flight is included automatically in the fall time.
How far does an object fall in a given number of seconds?
Choose "Fall time" in the solver and enter \(t\). For a drop from rest, distance equals \( h = \tfrac{1}{2}gt^2 \), so distance grows with the square of time: roughly 4.9 m after 1 s, 19.6 m after 2 s, 44 m after 3 s on Earth. Note that doubling the time quadruples the distance, not doubles it.
When does ignoring air resistance give wrong answers?
The error stays within a few percent for dense, compact objects (stones, steel balls, coins) falling up to a few dozen metres. Results become unreliable for light or flat objects (paper, feathers, parachutes), hailstones, or falls from hundreds of metres, because drag grows with the square of speed. A skydiver never exceeds about 55 m/s, so any calculator result above that in air is unrealistic.
Can I use this calculator for the Moon, Mars, or other planets?
Yes — just change the Gravity field. The Moon has \( g \approx 1.62 \) m/s² and Mars about 3.72 m/s², so the same 20 m drop takes roughly 5 s on the Moon and 3.3 s on Mars. You can also enter gravity in ft/s² (e.g. 32.17 ft/s² for Earth) if you are working in imperial units; the calculator converts it automatically.
From what height is a fall dangerous for a person?
There is no safe threshold — even falls from 1–2 m can cause serious injury depending on how you land, your age, and health. Stunt doubles and safety engineers treat anything above roughly 3–6 m as high-risk. This calculator gives impact speed only; it cannot predict injury. For fall-protection planning, workplace safety rules, or after any fall, consult qualified safety professionals or medical advice.