Free Fall Calculator
Free fall is the motion of an object under gravity alone with no air resistance. This calculator computes the velocity reached, distance fallen, and time of fall given any one of the three variables.
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Formula
v = g × t, d = ½gt²
For an object starting from rest in free fall: velocity v = g × t (gravity times time). Distance fallen d = ½ × g × t². On Earth, g = 9.81 m/s². Every second of free fall adds 9.81 m/s to the velocity. Air resistance is ignored — real objects reach terminal velocity.
How to use the Free Fall Calculator
- 1
Enter your fall time
Value should be in s.
- 2
Enter your gravity
Value should be in m/s².
- 3
Read your results instantly
Results update in real time as you type.
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Free fall and terminal velocity
In a vacuum, all objects fall at the same rate regardless of mass — the famous result Galileo demonstrated (or popularized) at the Leaning Tower of Pisa. Near Earth's surface, gravitational acceleration is 9.81 m/s², meaning every second adds about 9.81 m/s (35 km/h) to the falling speed.
In reality, air resistance limits maximum speed. Terminal velocity — when drag force equals gravitational force — depends on mass, size, and shape. A skydiver in a belly-to-earth position reaches terminal velocity of about 55 m/s (200 km/h) after about 12 seconds. In a head-down 'bullet' position, terminal velocity can exceed 90 m/s. A raindrop reaches terminal velocity of only about 9 m/s.
Galileo's experiment and the equivalence principle
Aristotle believed heavier objects fall faster — an intuitive but wrong idea that persisted for nearly 2,000 years. Galileo showed through experiments (and likely thought experiments) that all objects fall at the same rate. The reason: gravitational force is proportional to mass, but so is inertia (Newton's F = ma). The mass cancels, leaving a = g for all objects.
Einstein's equivalence principle — the cornerstone of General Relativity — takes this further: being in a gravitational field is physically indistinguishable from accelerating at g. An astronaut in a uniformly accelerating rocket experiences the same physics as standing on Earth.
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Impact force from free fall
The velocity at impact determines the force of landing. Using v = √(2gh) and the impulse-momentum theorem, impact force depends heavily on how long the stop takes. A person falling 1 meter reaches about 4.4 m/s. Stopping in 0.01 s (concrete) requires about 4,400× their weight. Stopping in 0.5 s (foam pad) requires only 88× their weight — still significant but survivable.
Survival falls from extreme heights are rare but documented. In 1944, RAF Sergeant Nicholas Alkemade survived a 5,500 m fall (terminal velocity ~55 m/s) when snow and pine branches cushioned his landing over several meters — extending the stopping time enough to survive.
Tips & Insights
g varies slightly by location
g = 9.81 m/s² is the standard value. It ranges from 9.78 at the equator to 9.83 at the poles. For most calculations, 9.81 is accurate enough.
Distance scales as time squared
In the first second, an object falls 4.9 m. In 2 seconds: 19.6 m. In 3 seconds: 44.1 m. Distance increases as t² — each additional second adds much more distance.
Moon and Mars gravity
Moon: g ≈ 1.62 m/s². Mars: g ≈ 3.72 m/s². You can change the gravity input to explore free fall on other bodies.
Worked Examples
Dropping from a building
After 4 seconds: velocity = 39.2 m/s (141 km/h). Distance fallen = 78.5 m (about 26 stories).
Free fall on the Moon
After 4 seconds on the Moon: velocity = 6.48 m/s. Distance = 12.96 m — much slower than Earth.
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Frequently Asked Questions
Do heavier objects fall faster?
No — in a vacuum, all objects fall at the same rate regardless of mass. Air resistance causes differences in everyday life.
What is terminal velocity?
Terminal velocity is the maximum speed reached when air drag equals gravitational force. For a human skydiver it's about 55 m/s (200 km/h).
What is g?
g is the gravitational acceleration at Earth's surface: 9.81 m/s². It means velocity increases by 9.81 m/s every second of free fall.
How far does an object fall in 1 second?
d = ½ × 9.81 × 1² = 4.9 m in the first second. After 2 s: 19.6 m total. After 3 s: 44.1 m total.
What is the free fall formula?
v = gt (velocity) and d = ½gt² (distance), where g = 9.81 m/s² and t is time in seconds.
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