Free Fall Calculator
Dropped from rest: the time to the ground and the speed at the bottom, with Galileo's odd-number ladder computed and the mass question settled where the hammer and the feather tie.
Free Fall Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- From rest — any launch speed belongs to the projectile page
- Vacuum; terminal velocity exists but is not modelled
In short: Drop something from 20 m under standard gravity: it lands after t = √(2h/g) = 2.019620 s, at v = √(2gh) = 19.805706 m/s — and the check is one multiplication: g × t gives the same speed, because falling from rest is just g accumulating on a stopwatch. The ladder card shows Galileo's odd numbers live: 4.903325 m falls in the first second, 19.613300 by two, 44.129925 by three — each second's fall 1, 3, 5 times the first. Mass appears nowhere: on the Moon the same 20 m takes 4.969040 s and lands at 8.049845 m/s, and the hammer lands WITH the feather. What the page does not model is air — the reason real feathers lose.
Formula
t = √(2h/g) · v = √(2gh) = g·t · d(t) = ½g·t² · 1 : 3 : 5 (the odd numbers)
Free fall from rest is the ½gt² law with nothing up its sleeve: no launch speed, no mass, no air. The speed identity v = √(2gh) = g·t is worth internalising — it says the landing speed is just gravity's steady accrual over the fall time, which is why the two cards must always agree.
Worked Example
- Enter the drop height and pick the gravity.
- Read the fall time and the landing speed — and check the identity by hand once: g times t.
- Read the ladder to see the odd-number growth that makes falling distances accelerate.
- Switch gravity to the Moon to settle the mass question with numbers.
Defaults: 2.019620 s and 19.805706 m/s from 20 m. On the Moon: 4.969040 s, landing at 8.049845 m/s. First-second falls: 4.903325 m (Earth), 0.810000 m (Moon).
Strengths & Limits Of This Model
Where this engine is strong
- The g·t = √(2gh) identity visible on the card
- Odd-number ladder computed, not asserted
Where it stops
- No drag or terminal-velocity model
- One surface — no layered fluids or bounce
Practical Use Cases
Safety
drop heights to impact speeds
Rigging & climbing
what a dropped tool arrives doing
Teaching
Galileo's ladder without the lecture
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Free Fall Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does mass not matter?
Because gravity accelerates every mass identically — double the mass, double the force, but also double the inertia to move, and the two cancel exactly. The Moon astronauts dropped a hammer and a feather in vacuum and they landed together: no air, no debate. This page is always that vacuum.
What is the odd-number ladder?
Distances fallen in successive equal times grow as 1, 3, 5 — so cumulative distance runs 1, 4, 9 (the squares). It falls straight out of ½gt² and it is the oldest lab-verified law in the book: Galileo timed it with water clocks and inclined ramps because he could not stopwatch a fall directly.
How fast is the object falling after one second?
Exactly g seconds worth: 9.80665 m/s on Earth after 1 s, having fallen 4.903325 m. The speed grows by the same g every second — that LINEAR growth is why the DISTANCE grows quadratically, and why the last metre of a fall takes far less time than the first.
Where does air enter?
Only in the refusal to model it. Drag grows with speed until it balances weight — terminal velocity — after which the fall stops accelerating. A real feather never reaches the speed on this card; a dense ball barely notices. The page is the shared vacuum both objects would enjoy.
Is the landing speed the same regardless of drop height units?
The PHYSICS is per-metre: double the height, and the speed grows by √2 — the square-root law. Quadruple the height doubles the speed. That diminishing return is why 100 m is only twice the impact of 25 m, not four times.
Why is a = g here but not on other pages?
Free fall is the special case where gravity is the ONLY force, so the acceleration IS g. Throw air resistance in and the net acceleration drops; stand on the ground and the normal force cancels it. This page owns the clean case; the acceleration page prices the general push.
What does 'from rest' rule out?
An initial push. Any v₀ makes it the projectile page's problem (thrown down is an angle of 90° with a head start there). Keeping rest strict keeps the ladder honest — the odd numbers assume nothing was moving at t = 0.
Can the page price a fall into water or onto a net?
The FALL, yes; the LANDING, no. Impact forces are the impulse page's contract — they depend on the stopping distance and time, not on the fall alone. This page hands off at the surface, at the speed printed, and refuses to guess what happens next.