An object falling under gravity alone, starting from rest, follows a fixed set of equations. This works out velocity, time and distance from whichever one you know, using the internationally fixed value of standard gravity.
How it works
Motion under gravity, from rest
v = g t · h = ½ g t² · v = √(2 g h)
g = 9.80665 m/s², the same standard gravity constant the potential-energy and force calculators use — an internationally fixed value, not a locally measured one.
Why “ignoring air resistance” is not a small caveat for everything
These equations are exact for a dense, compact object falling a modest height — a dropped tool, a diver leaving a board. They become badly wrong for anything where air resistance matters at the speeds involved, which is why a feather does not fall at the rate these equations predict, but a hammer very nearly does. The famous 1971 Apollo 15 demonstration dropped a feather and a hammer together on the Moon’s airless surface specifically to show them landing at the same instant — with no air resistance at all to separate the two, exactly matching what these equations predict for any object regardless of its shape or mass.
How to use this calculator
- Choose whether you know the time fallen or the height fallen.
- Enter that value.
- Read the velocity, and the other of time or height, computed from it.
Frequently asked questions
Does mass affect how fast something falls?
Not in this model — every object accelerates at the same rate under gravity alone, regardless of mass, which is the whole point of the Apollo 15 hammer-and-feather demonstration. Mass only appears to matter in everyday life because air resistance affects light or spread-out objects (like feathers) far more than dense, compact ones.
Why doesn’t this calculator ask for the object’s shape or mass?
Because in free fall under gravity alone, neither one changes the outcome — the equations here describe an idealised fall with no air resistance, where every falling object behaves identically regardless of what it is.
How fast does something fall after 10 seconds?
Using v = gt: about 98.07 m/s, or roughly 353 km/h — a reminder of how quickly free-fall speed builds, and part of why terminal velocity (where air resistance finally balances gravity) matters in practice for anything falling that long.
What is terminal velocity, and why isn’t it in this calculator?
Terminal velocity is the speed at which air resistance grows to match gravity’s pull, so the object stops accelerating. It depends on shape, mass and air density — details this simplified, air-resistance-free model does not include, and it is why real long falls (like a skydive) eventually stop matching these equations.
Is g really the same everywhere on Earth?
Not quite — real gravitational acceleration varies slightly with latitude and altitude, roughly 9.78 to 9.83 m/s². The 9.80665 m/s² value used here is the internationally fixed standard reference, not a measurement of any one specific location.
