Free Fall Calculator
Calculate the fall time, distance, and impact velocity of an object dropped from rest under gravity, from either the height or the fall time (ignoring air resistance).
How to use this calculator
- 1Choose whether you know the drop height or the fall time.
- 2Enter that value.
- 3Adjust gravity if the fall is on another planet (9.81 is Earth).
- 4Read the fall time or distance, and the impact velocity.
How it works
Free fall (from rest)
distance: h = ½ g t² time from height: t = √(2h ÷ g) velocity: v = g t = √(2gh) g ≈ 9.81 m/s² on Earth
Free fall describes the motion of an object dropped from rest under gravity alone, with no other forces such as air resistance. Because gravity produces a constant acceleration, the standard equations of motion for constant acceleration apply. The distance fallen grows with the square of the time — half the gravitational acceleration times the time squared — which is why a falling object covers far more ground in its second second than its first. The velocity grows linearly with time, equal to the gravitational acceleration times the elapsed time, so it can also be written as the square root of twice the gravity times the height fallen. From a known drop height, the fall time is found by rearranging the distance equation, and the impact velocity follows. The gravitational acceleration is about 9.81 metres per second squared on Earth, but the same equations work on other worlds by substituting the local gravity — 1.62 on the Moon, 3.71 on Mars — which is why objects fall in slow motion on the Moon.
Worked example
An object dropped from 45 metres, ignoring air resistance, falls for √(2 × 45 ÷ 9.81) ≈ 3.03 seconds and hits the ground at 9.81 × 3.03 ≈ 29.7 metres per second — about 107 km/h. In its first second it falls only about 4.9 metres, but in the third second it covers over 24, showing how the speed builds.
Free Fall Calculator: the complete guide
Why everything falls at the same rate
One of the most counterintuitive facts in physics, famously demonstrated by dropping objects from the Leaning Tower of Pisa and by an astronaut dropping a hammer and a feather on the airless Moon, is that in the absence of air resistance, all objects fall at the same rate regardless of their mass. A heavy stone and a light pebble, released together in a vacuum, hit the ground at the same instant. This is because although gravity pulls harder on the heavier object, that object also has more inertia resisting acceleration, and the two effects cancel exactly, leaving the same acceleration for everything.
This is why the free-fall equations contain no mass term at all — the fall time and impact velocity depend only on the height and the gravitational acceleration, not on what is falling. The everyday impression that heavier things fall faster comes entirely from air resistance, which affects light, spread-out objects like feathers far more than dense, compact ones. Remove the air, and the feather and the hammer fall identically. This universality of free fall is a deep principle, later generalised by Einstein into the equivalence principle at the heart of general relativity.
The square relationship with time
A defining feature of free fall is that distance grows with the square of time, not in proportion to it. This means a falling object accelerates in a very specific way: in the first second it falls about 5 metres, but by the end of the second second it has fallen 20 metres total, and by the third, 45. Each successive second adds more distance than the last, because the object is moving faster and faster. The velocity, by contrast, grows steadily — the same amount each second — but the distance, being the accumulation of an ever-increasing speed, curves upward.
This squared relationship has practical and sometimes sobering consequences. It means fall distances and impact speeds escalate quickly with height. Doubling the drop height does not double the impact speed but multiplies it by the square root of two, while the fall time also stretches. It explains why falls from even modest heights can be dangerous — the impact velocity builds fast — and why the difference between falling from the second storey and the fourth is far more than double in terms of the energy involved. The kinetic energy at impact grows with the height directly, so a fall from twice the height delivers twice the energy, which the calculator shows as energy per kilogram.
Where air resistance changes the story
The clean free-fall equations describe an idealised world without air, and knowing when that idealisation breaks down is important. For dense, compact objects falling modest distances — a dropped tool, a stone off a bridge — air resistance is negligible and the equations are accurate. But as an object falls faster, air resistance grows, pushing back against gravity, until at some speed the two balance and the object stops accelerating. This is terminal velocity, and beyond it the free-fall equations no longer apply because the fall is no longer accelerating.
Terminal velocity depends heavily on the object's size, shape, and mass relative to its area. A skydiver in a spread belly-down position reaches a terminal velocity of around 55 metres per second, while the same skydiver head-down and streamlined can exceed 90. A feather or a sheet of paper has such high air resistance relative to its weight that it reaches terminal velocity almost immediately and drifts down slowly. This is precisely why light objects seem to fall slower in everyday life. The calculator computes true free fall, so it is accurate for the compact, short-fall cases where air resistance can be ignored, and it deliberately notes the terminal-velocity limit as the boundary beyond which real falls diverge from the ideal.
Frequently asked questions
How do I calculate the time to fall from a height?
Use t = √(2h ÷ g), where h is the height and g is 9.81 m/s² on Earth. An object dropped from 45 metres falls for √(2 × 45 ÷ 9.81) ≈ 3.03 seconds, ignoring air resistance. The impact velocity is then g × t.
Do heavier objects fall faster?
No — in the absence of air resistance, all objects fall at the same rate regardless of mass, because gravity's greater pull on a heavier object is exactly offset by its greater inertia. The free-fall equations contain no mass term. Air resistance is what makes light, spread-out objects fall slower in everyday life.
How fast is something going when it lands?
The impact velocity is v = g × t, or equivalently √(2gh). From 45 metres that's about 29.7 m/s (107 km/h). Impact speed grows with the square root of the height, so it escalates quickly — which is why falls from height are so dangerous.
Does this account for air resistance?
No — it assumes free fall in a vacuum. That's accurate for dense, compact objects over modest distances. Over longer falls, air resistance caps the speed at a terminal velocity (about 55 m/s for a belly-down skydiver), beyond which the object stops accelerating and the equations no longer apply.