How this instrument works
Free fall distance answers a narrower question than plain acceleration: not how fast something is going, but how far it has actually travelled since release. The formula, d = ½gt², comes straight from integrating constant acceleration twice — speed builds as v = gt, and distance is the area under that speed-time line, a triangle of base t and height gt, which works out to half their product. Standard gravity, g = 9.80665 m/s², is fixed by international agreement rather than measured fresh each time, since local gravity varies by only about half a percent across the planet.
The squared term is the whole story. Because speed keeps climbing for as long as the object falls, each additional second adds more distance than the one before it — not a fixed amount, as constant-velocity motion would. Galileo demonstrated the same pattern with balls rolled down a ramp centuries before anyone could time a genuine free fall directly: distances covered in successive, equal time slices follow the ratio 1 : 3 : 5 : 7 ..., the odd numbers, rather than climbing in equal steps.
The formula assumes two things that a real drop rarely gives for free: release from rest, with no initial push, and no air pushing back. Add a downward launch speed and the correct relation becomes d = v₀t + ½gt² instead. Let the fall run long enough and drag starts eating into the acceleration — a skydiver stops gaining speed near terminal velocity, and ½gt² starts overshooting reality well before that point. For a dropped coin, tool, or test weight falling a few metres in open air, the error from ignoring drag is small enough to ignore in turn.
- Enter the Fall time — how long the object has been dropping since release, in seconds (switch to milliseconds for a short bench drop).
- Leave gravity alone; the instrument fixes it at standard gravity, 9.80665 m/s², since this formula only covers a start-from-rest drop near Earth's surface.
- Read Distance fallen in metres, or switch its unit menu to centimetres for a short test rig.
- Try doubling the Fall time and watch Distance fallen roughly quadruple, not double — that square-law jump is the whole point of the formula.
Worked example — 2 seconds after release
Drop something from rest — no throw, just let go — and let it fall for exactly 2 seconds. Distance fallen = ½ × 9.80665 × 2² = ½ × 9.80665 × 4 = 19.6133 m, a drop past roughly six storeys in about the time it takes to say two words aloud.
Split that same fall into its two one-second halves and the square law shows its teeth: the first second alone covers ½ × 9.80665 × 1² = 4.903325 m, but the second second covers 19.6133 − 4.903325 = 14.709975 m — exactly three times as far, because the object is no longer starting from rest for that second leg. Extend to a third second and the next slice covers close to five times the first, continuing Galileo's 1 : 3 : 5 pattern for equal time slices.
Questions
Does air resistance change this result?
For a dense object falling a few metres — a dropped wrench, a coin, a test weight — the difference is small enough to ignore, which is why d = ½gt² is trusted for short, everyday drops. It stops applying once drag becomes significant: a skydiver's speed levels off near terminal velocity, and beyond that point the formula overstates the actual distance covered.
Why does distance grow with the square of time instead of linearly?
Because speed itself is climbing the whole time it falls. Velocity grows as v = gt, a straight line through the origin, and distance is the area under that speed-time graph — a triangle, whose area scales with the square of its base. Constant speed would give a flat rectangle and a linear distance; constant acceleration gives a growing triangle instead.
Can I use this if the object was thrown downward rather than dropped?
No — this instrument assumes release from rest, with zero starting speed. A thrown-down object needs the extended relation d = v₀t + ½gt², adding the initial speed's own contribution to distance. Plug a launch speed into the plain ½gt² formula and the result comes out short of the real distance fallen.
What gravity value does the calculator use, and does real gravity vary?
It uses 9.80665 m/s², the standard gravity fixed by international agreement at the 1901 Conférence Générale des Poids et Mesures. Measured gravity actually ranges from about 9.78 m/s² at the equator to 9.83 m/s² near the poles, a spread of about half a percent — negligible for a dropped tool, but the reason precision gravimeters still report a location-specific figure.
Who actually needs a free-fall distance figure outside a classroom?
Packaging engineers running loaded-container drop tests convert a required drop height into the release timing their test rig needs. Fall-protection engineers use the same relation to estimate the free-fall portion of a work-at-height arrest system before a lanyard begins absorbing the load, ahead of the fuller clearance calculation a harness system demands.
How far does something fall in the very first tenth of a second?
Only about 4.9 centimetres — ½ × 9.80665 × 0.1², under two inches. That slow start is easy to underestimate: a fall needs roughly 0.45 seconds to cover the first metre, but only another 0.19 seconds to cover the second metre, because speed has already built up by then.