Rule of thumb · PhysicsNº 87 / 167

Falling: 5 metres in the first second

A dropped object falls ~5 m in the first second and gains ~10 m/s of speed every second.

Why it works

d = ½gt² with g ≈ 9.8 m/s². Two seconds ≈ 20 m — a quick way to depth-sound a well or cliff with a stone.

When it fails

Only while drag is negligible, which for a human body is about the first two seconds. After that you approach terminal velocity, around 55 m/s skydiving flat, and the 10 m/s per second stops entirely. For a sheet of paper the rule is wrong from the first instant.

How wrong is it?

At 1 s the rule says 5 m and the exact answer is 4.903 m — 2% high. It stays inside 5% across the whole range shown.

+5%0−5%0.52.755Time falling (s)

A flat 2% over-estimate at every time, because 5 is a rounded-up 4.9 - the error never grows, it just never goes away.

The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open Galileo Drop Experiment →

More in Physics

← PreviousPendulum period: √length, not mass Next →Braking distance goes as speed squared

How far does something fall in one second?

A dropped object falls ~5 m in the first second and gains ~10 m/s of speed every second. d = ½gt² with g ≈ 9.8 m/s².

Browse all 167 rules of thumb →