# How long and how fast is the free fall?

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.

- Page: https://www.acalculator.org/physics/free-fall-calculator
- JSON spec: https://www.acalculator.org/physics/free-fall-calculator.json
- Version: 836b66956d82

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| h | Fall height | How far the object falls, from where it is let go to where it lands. |
| t | Fall time | How long the fall takes, from release to landing. |
| v | Impact speed | The speed at the end of the fall, just before it lands. |
| g | Gravity (m/s²) | The acceleration of gravity in meters per second squared: 9.80665 on Earth, about 1.62 on the Moon. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| height | Fall height | h = ½gt². |
| time | Fall time | t = √(2h ÷ g), in seconds. |
| velocity | Impact speed | v = gt = √(2gh), in meters per second. |
| g | Gravity (m/s²) | The acceleration of gravity in meters per second squared: 9.80665 on Earth, about 1.62 on the Moon. |
| mph | Impact speed (mph) | The impact speed in miles per hour: v ÷ 0.44704. |
| kmh | Impact speed (km/h) | The impact speed in kilometers per hour: v × 3.6. |
| feet | Fall height (ft) | The fall height in feet: h ÷ 0.3048. |
| average | Average speed (m/s) | The height ÷ the time, which is half the impact speed. |

## Method

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

## Assumptions

- 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.

## Worked examples

1. h = 98, g = 9.8 gives t = 4.472136, v = 43.826932. 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. t = 3, g = 9.80665 gives h = 44.129925, v = 29.41995, 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. v = 20, g = 9.80665 gives h = 20.394324, t = 2.039432. 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. h = 30.48, g = 9.80665 gives t = 2.493229, v = 24.450223. 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).

## FAQ

### 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.

## Sources

- OpenStax, University Physics Volume 1, §3.5 Free Fall (kinematic equations with a = −g; worked examples), CC BY 4.0. https://openstax.org/books/university-physics-volume-1/pages/3-5-free-fall (retrieved 2026-10-02)
- NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8 (standard acceleration of gravity 9.80665 m/s²; 1 ft = 0.3048 m and 1 mi = 1,609.344 m exactly). https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)