acalculator

How long and how fast is the free fall?

Type how far an object falls to get the fall time and the impact speed, from h = ½gt² and v = gt. Or type the time or the impact speed to get the height. The free fall calculator uses standard Earth gravity, 9.80665 m/s², unless you type another value.

Your numbers

Units
Fall time
2.49323 s

The fall takes 2.49323 s and ends at 54.6936 mph.

Impact speed
54.6936 mph
Impact speed (mph)
54.6936
Impact speed (km/h)
88.0208
Fall height (ft)
100
Average speed (m/s)
12.2251

Fall time: 2.49323 s. The fall takes 2.49323 s and ends at 54.6936 mph.

How to calculate

Works out how long an object takes to fall a height from rest and how fast it hits the ground, h = ½gt² and v = gt, or the height from the time or the speed, with no air resistance.

Example with the default inputs (Fall height 100 ft, Gravity (m/s²) 9.80665): The fall takes 2.49323 s and ends at 54.6936 mph.

Formula: h = ½gt², v = gt, v² = 2gh; t = √(2h ÷ g), v = √(2gh), h = v² ÷ 2g.

  • The object starts from rest and falls straight down.
  • There is no air resistance, so the speed keeps growing; a real object in air reaches a terminal speed.
  • Gravity is the same over the whole fall. On Earth the standard value is 9.80665 m/s².

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Fall height 98 m, Gravity (m/s²) 9.8 gives Fall time 4.47214 s, Impact speed 43.8269 m/s.Source: OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02): y = −½gt² with y = −98 m gives t = √(2 × 98 ÷ 9.8) = √20 s
  2. Fall time 3 s, Gravity (m/s²) 9.80665 gives Fall height 44.1299 m, Impact speed 29.42 m/s, Impact speed (mph) 65.810554.Source: NIST Special Publication 811, Guide for the Use of the International System of Units, B.8 (standard acceleration of gravity gₙ = 9.80665 m/s² exactly; 1 ft = 0.3048 m), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02); OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)
  3. Impact speed 20 m/s, Gravity (m/s²) 9.80665 gives Fall height 20.3943 m, Fall time 2.03943 s.Source: OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)
  4. Fall height 30.48 m, Gravity (m/s²) 9.80665 gives Fall time 2.49323 s, Impact speed 24.4502 m/s.Source: NIST Special Publication 811, Guide for the Use of the International System of Units, B.8 (standard acceleration of gravity gₙ = 9.80665 m/s² exactly; 1 ft = 0.3048 m), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02); OpenStax, University Physics Volume 1, §3.5 Free Fall (v = v₀ − gt, y = y₀ + v₀t − ½gt², v² = v₀² − 2g(y − y₀); g = 9.81 m/s²), https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)

How it works

An object let go from rest falls with constant acceleration g (OpenStax's equations with v₀ = 0, measured downward):

  • h = ½gt², so the fall time is t = √(2h ÷ g)
  • v = gt, the impact speed
  • v² = 2gh, so v = √(2gh) and h = v² ÷ (2g)

Type the gravity g in m/s² and any one of the fall height, the fall time and the impact speed; the other two follow. Heights are converted to meters (1 ft = 0.3048 m, 1 in = 0.0254 m, 1 yd = 0.9144 m, 1 mi = 1,609.344 m), times to seconds, and speeds to meters per second (1 mph = 0.44704 m/s, 1 km/h = 1 ÷ 3.6 m/s, 1 ft/s = 0.3048 m/s). Then:

  • impact speed in mph = v ÷ 0.44704 and in km/h = v × 3.6
  • fall height in feet = h ÷ 0.3048
  • average speed = h ÷ t, which is v ÷ 2

Rules

  • Gravity is from 0.001 to 1,000 m/s². The height is more than 0 and at most 10¹⁵ m, the time more than 0 and at most 10⁶ s, and the speed more than 0 and at most 10¹⁰ m/s. A value worked out beyond its range gives no answer.
  • h = t × (gt ÷ 2) and h = v × (v ÷ 2g) are formed that way, so a tiny time or speed does not round to a height of 0.
  • If you type two of the height, time and speed, they must agree with the gravity, or the page says they do not fit.

Output format. Every value to 6 significant figures.

Worked examples by hand

Dropped from 98 m with g = 9.8 m/s² (OpenStax's building height). t = √(2 × 98 ÷ 9.8) = √20 = 4.472136 s, v = √(2 × 9.8 × 98) = 43.82693 m/s.

A 3 second fall on Earth. h = ½ × 9.80665 × 9 = 44.129925 m, v = 9.80665 × 3 = 29.41995 m/s = 29.41995 ÷ 0.44704 = 65.81055 mph.

Landing at 20 m/s. h = 400 ÷ (2 × 9.80665) = 20.39432 m, t = 20 ÷ 9.80665 = 2.039432 s.

The default, 100 ft. 100 ft = 30.48 m; t = √(60.96 ÷ 9.80665) = 2.493229 s, v = √(2 × 9.80665 × 30.48) = 24.45022 m/s.

Other questions people ask

How long does it take to fall a given height?

From rest with no air resistance, t = √(2h ÷ g). A 100 ft (30.48 m) drop on Earth takes √(60.96 ÷ 9.80665) ≈ 2.49 seconds, and the object lands at about 24.45 m/s (54.7 mph).

How fast is an object going when it hits the ground?

The speed after falling a height h is v = √(2gh), or v = gt after a time t. Speed grows by 9.80665 m/s (about 21.9 mph) every second of the fall, so after 3 seconds it is 29.42 m/s.

Does a heavier object fall faster?

Not without air resistance. Every object falls with the same acceleration g, whatever its mass, so a hammer and a feather dropped together on the Moon land together. In air, drag slows light, broad objects more.

What value of g should I use?

The standard acceleration of gravity is 9.80665 m/s² (32.174 ft/s²), the value NIST defines. Real gravity varies a little with latitude and height, about 9.78 to 9.83 m/s². OpenStax uses 9.8 m/s² in its examples. On the Moon g is about 1.62 m/s².

Why does the calculator ignore air resistance?

Free fall means only gravity acts. That is a good model for short drops of dense objects. For a long fall in air, drag grows with speed until it balances the weight, and the object stops speeding up at its terminal velocity, so real falls take longer than the free fall time.