Free fall

Time · height · final velocity

Free fall — illustration
Fall time
2.019
s
Height
20
m
Final velocity
19.809
m/s

g = 9.81 m/s², initial velocity = 0. Formulas: v = g·t, h = ½·g·t², v² = 2·g·h. In a vacuum all bodies fall equally fast (regardless of mass).

Free fall is motion under gravity alone, with zero initial velocity. It is governed by the formulas (for g=9.81 ms2g=9.81\ \tfrac{\text{m}}{\text{s}^2}):

v=g th=12 g t2v2=2 g hv=g\,t\qquad h=\tfrac12\,g\,t^2\qquad v^2=2\,g\,h

Enter one known quantity — the fall time, the height or the final velocity — and the calculator works out the rest. In a vacuum all bodies fall equally fast, regardless of mass (as shown by the feather-and-hammer experiment on the Moon).

Examples

Fall from height h = 20 m
→ t ≈ 2.02 s, v ≈ 19.8 m/s
Falling for t = 3 s
→ h ≈ 44.1 m, v ≈ 29.4 m/s

Frequently asked questions

Does a heavier body fall faster?+

No — in a vacuum they all fall equally (the acceleration g does not depend on mass). Differences on Earth are due solely to air resistance.

How do you find the height from a known time?+

From h = ½·g·t². For example, after 2 seconds a body falls ½·9.81·4 ≈ 19.6 m.

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