Free Fall Calculator
Find how long an object takes to fall and how fast it hits the ground from any height, or work back from the fall time or impact speed. Includes an initial throw, planet gravity, a chart and a per-second table, all calculated in your browser.
0 = dropped. Positive = thrown down, negative = thrown up.
Step-by-step solution
Distance and speed over time
Fall table
How to use the Free Fall Calculator
- Choose what you know: Height, Time or Impact velocity.
- Enter the value and pick its unit, e.g. 30 m, 3 s or 100 km/h.
- Set the initial velocity: leave 0 for a dropped object, a positive value for a downward throw or a negative one for an upward throw.
- Pick the gravity preset (Earth by default) or type your own value.
- Read the results, check the chart and the fall table, and copy or download them.
Free fall equations
An object in free fall accelerates downward at a constant rate g (9.80665 m/s² standard on Earth). Measuring downward as positive, with initial velocity v₀:
- Distance fallen: h = v₀t + ½gt² (from rest: h = ½gt²)
- Velocity: v = v₀ + gt
- Velocity from height: v = √(v₀² + 2gh) (from rest: v = √(2gh))
- Time from height: t = (√(v₀² + 2gh) − v₀) / g (from rest: t = √(2h / g))
Free fall table on Earth (from rest, no air resistance)
| Time | Distance fallen | Speed |
|---|---|---|
| 1 s | 4.90 m (16.1 ft) | 9.81 m/s (35.3 km/h, 21.9 mph) |
| 2 s | 19.6 m (64.4 ft) | 19.6 m/s (70.6 km/h, 43.9 mph) |
| 3 s | 44.1 m (144.8 ft) | 29.4 m/s (105.9 km/h, 65.8 mph) |
| 4 s | 78.5 m (257.4 ft) | 39.2 m/s (141.2 km/h, 87.7 mph) |
| 5 s | 122.6 m (402.2 ft) | 49.0 m/s (176.5 km/h, 109.7 mph) |
Worked example: a stone dropped into a well hits the water after 2.5 s. The depth is ½ × 9.80665 × 2.5² = 30.6 m (ignoring the time the sound takes to come back up, about 0.09 s), and it hits the water at 24.5 m/s.
Air resistance and real falls
The calculator assumes a vacuum, which is very accurate for dense objects over a few metres and on airless bodies like the Moon. In air, drag increases with speed. A human skydiver reaches a terminal velocity of about 54 m/s (195 km/h, 120 mph) in a belly-down position after roughly 12 seconds, so beyond about 150 m of fall the vacuum results overestimate the real speed. Light objects such as paper, feathers or raindrops reach terminal velocity within moments: a large raindrop falls at only about 9 m/s.
To solve h = v₀t + ½gt² for t yourself, use the quadratic equation solver; for trips at a constant speed, the speed distance time calculator gives travel time and arrival.
Frequently asked questions
How long does it take to fall from a height?
Without air resistance and starting from rest, t = √(2h / g). From 30 m on Earth that is √(60 / 9.80665) ≈ 2.47 s; from 100 m about 4.52 s. Doubling the height multiplies the time by only √2 ≈ 1.41.
How fast does a falling object hit the ground?
The impact velocity is v = √(2gh) when dropped from rest, or v = √(v₀² + 2gh) with an initial speed. A 30 m drop gives about 24.3 m/s (87.3 km/h, 54.3 mph).
Do heavier objects fall faster?
Not in a vacuum: all objects fall with the same acceleration g regardless of mass, as Apollo 15 showed by dropping a hammer and a feather on the Moon. In air, light and broad objects fall slower because drag is larger relative to their weight.
What is terminal velocity?
In air, drag grows with speed until it balances weight, and the object stops accelerating. A skydiver in a belly-down position reaches roughly 54 m/s (about 195 km/h or 120 mph). This calculator ignores drag, so for long falls the real speed is lower than shown.
How far does an object fall in each second?
From rest on Earth it falls about 4.9 m in the first second, 19.6 m after two seconds, 44.1 m after three and 78.5 m after four, because distance grows with the square of time (h = ½gt²).
What value of g should I use?
Standard gravity is 9.80665 m/s² (often rounded to 9.81 or 9.8). Real gravity varies slightly, from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. On the Moon it is 1.62 m/s² and on Mars 3.71 m/s².