Free Fall Calculator
How long does a fall take and how fast does it hit? Solve from height, time or speed, in vacuum or with air drag and terminal velocity, and compare the two.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Free Fall Calculator?
This free fall calculator tells you how long an object takes to fall a given height and how fast it is going when it lands. You can also start from the fall time (to estimate the depth of a well from how long the splash takes) or from the impact speed. An initial downward speed is optional, for something thrown rather than dropped.
Switch on air resistance to make the answer realistic. Enter the mass, choose a shape for the drag coefficient (sphere, cube, cylinder, flat plate, skydiver or your own Cd), give the diameter or frontal area, and the calculator uses the exact solution for quadratic drag. It shows the terminal velocity, how long it takes to reach 95% of it, and the same fall in vacuum for comparison.
A speed-against-time chart shows the vacuum line climbing straight up while the drag curve bends over towards terminal velocity. All the maths runs in your browser.
- Solve from height, fall time or impact speed
- Exact quadratic-drag solution with terminal velocity
- Shape presets for the drag coefficient, or your own Cd
- Vacuum comparison and speed-time chart
- Initial downward speed, planet gravity, metric and US units
How to use the Free Fall Calculator
- Choose what you know: Height, Fall time or Impact speed, and enter it with its unit.
- Leave the initial downward speed at 0 for a drop from rest, or enter a speed for a throw.
- Pick the gravity: Earth by default, or the Moon, Mars, another planet or a custom value.
- For a realistic answer, select With air resistance and enter the mass, shape, diameter or area, and the air density.
- Read the fall time, impact speed, distance, terminal velocity and vacuum comparison, and look at the speed chart.
Worked examples
Dropped from 100 m, no air
Input
Height 100 m, from rest
Output
4.516 s, 44.29 m/s (159.4 km/h)
t = √(2h/g) = √(200/9.80665). The average speed is half the final speed.
A baseball from 100 m
Input
With drag: 0.145 kg, sphere Cd 0.47, diameter 7.4 cm, air 1.225 kg/m³
Output
5.18 s, 30.66 m/s; terminal velocity 33.89 m/s
Drag costs 0.66 s and a third of the impact speed. The ball is at 90% of its terminal velocity by the time it lands.
Ping-pong ball versus steel ball from 10 m
Input
2.7 g and 268 g spheres, both 40 mm across
Output
Ping-pong: 1.76 s at 8.26 m/s. Steel: 1.431 s at 13.91 m/s
Same size, same drag force at a given speed, but the light ball reaches its 8.56 m/s terminal velocity almost at once. In vacuum both would take 1.428 s.
How deep is the well?
Input
Fall time 2.5 s, no air
Output
30.65 m
This ignores the time sound takes to come back up (about 0.09 s for 30 m), so the true depth is a little less.
Skydiver
Input
Fall time 12 s; 80 kg, Cd 1.0, area 0.7 m²
Output
384.7 m fallen at 42.4 m/s; terminal 42.8 m/s (154 km/h)
A belly-to-earth skydiver reaches 95% of terminal speed in about 8 s. Real terminal speeds run around 50 to 55 m/s because body area and posture vary.
Background and insight
In a vacuum, every object falls with the same constant acceleration g, so distance grows with the square of time: h = ½ g t², and v = g t = √(2 g h). From 100 m that is 4.52 s and 44.3 m/s on Earth, whatever the mass. Galileo argued this from inclined-plane experiments, and Apollo 15 astronaut David Scott showed it on the Moon in 1971 by dropping a hammer and a feather together.
In air, a drag force ½ ρ Cd A v² grows with the square of speed until it balances the weight. That balance gives the terminal velocity vt = √(2 m g ÷ (ρ Cd A)). Solving m dv/dt = m g − ½ ρ Cd A v² gives closed forms: from rest, v = vt tanh(g t ÷ vt) and the distance is (vt² ÷ g) ln cosh(g t ÷ vt). The calculator also handles a starting speed above or below vt, using the energy form v² = vt² + (v0² − vt²) e^(−2 g h ÷ vt²).
The drag coefficient depends on shape and, more weakly, on the Reynolds number. Typical values at everyday Reynolds numbers (roughly 10⁴ to 10⁵), such as 0.47 for a sphere and 1.05 for a cube face-on, are tabulated from wind-tunnel data in fluid mechanics references such as White's Fluid Mechanics and Hoerner's Fluid-Dynamic Drag; NASA Glenn Research Center quotes 1.28 for a flat plate. Sea-level air in the ICAO standard atmosphere is 1.225 kg/m³; it falls to about 0.74 kg/m³ at 5,000 m, which raises terminal velocity by roughly 29%.
Common use cases
Physics labs and homework
Check free fall answers with or without drag and see how far apart the two models are.
Estimating heights and depths
Time a dropped stone to estimate the depth of a well, a shaft or a cliff.
Drop testing
Find the impact speed and energy of a product dropped from a given height for packaging and drop tests.
Skydiving and parachutes
Explore how mass, area and air density set terminal velocity and how long it takes to reach it.
Tips and limitations
- Without drag the mass does not matter. With drag it does: double the mass at the same size and terminal velocity rises by √2.
- For a falling object timed by sound, subtract the sound travel time (distance ÷ 343 m/s) from your stopwatch reading first.
- Drag coefficients are approximate and depend on speed and surface. Use the vacuum and drag answers as a bracket rather than an exact prediction.
- Air density falls with altitude and rises in cold weather. Use about 1.29 kg/m³ at 0 °C, 1.20 at 20 °C and 0.9 to 1.0 at 2,000 to 3,000 m.
- Over long distances g itself changes slightly, and for objects entering from space the air density varies hugely; this calculator assumes both are constant.
Frequently asked questions
How long does it take to fall 100 metres?
In a vacuum on Earth, 4.52 seconds, landing at 44.3 m/s (159 km/h). With air resistance it takes longer: a baseball needs about 5.2 s and lands at about 31 m/s.
What is the formula for free fall?
From rest: h = ½ g t², v = g t and v = √(2 g h), with g = 9.80665 m/s². With an initial downward speed v0, h = v0 t + ½ g t² and v = v0 + g t.
How is terminal velocity calculated?
It is the speed where drag equals weight: vt = √(2 m g ÷ (ρ Cd A)), with air density ρ, drag coefficient Cd and frontal area A. A 145 g baseball comes out at about 34 m/s.
Do heavier objects fall faster?
In a vacuum, no: everything falls at the same rate. In air, a heavier object of the same size and shape falls faster because drag is a smaller share of its weight, which raises its terminal velocity.
How long does it take to reach terminal velocity?
Speed approaches vt gradually. From rest it reaches 95% of terminal velocity after (vt ÷ g) × 1.83 seconds, about 6.3 s for a baseball and 8 s for a skydiver with a 43 m/s terminal speed.
Can I use this to measure the depth of a well?
Yes. Choose Fall time, enter the seconds until you hear the splash, and read the height. For accuracy, subtract the sound travel time (depth ÷ 343 m/s) and recalculate, or switch on drag for a light stone.
What drag coefficient should I use?
Use the shape presets: 0.47 for a sphere, 0.82 for a long cylinder end on, 1.05 for a cube face on, about 1.0 for a person falling flat and 1.28 for a flat plate. Teardrop-shaped bodies can be as low as 0.04.
Is there an in-depth guide to the Free Fall Calculator?
Yes. “Free Fall With and Without Air Resistance: Fall Time and Terminal Velocity” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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