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Hemisphere Volume

Also known as volume of a half sphere · dome volume half sphere

V=23πr3V = \frac{2}{3}\pi r^3

Worked example: Hemisphere r = 3 m → 18 pi m3, half the 36 pi sphere — press Try an example to run it live, then adjust anything.

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Constant used — built into this formula, no need to enter
π=3.141592653589793\pi = 3.141592653589793Pi · exact
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Hemisphere Volume explained

rV

Half a sphere holds half a sphere's worth, so V=23πr3V = \tfrac{2}{3}\pi r^3. What makes it more than a trivial halving is the fact Archimedes proved and asked to have engraved on his tombstone: a sphere occupies exactly two thirds of the cylinder that just contains it. Cut everything in half and the hemisphere occupies two thirds of its enclosing cylinder too, which is where the 23\tfrac{2}{3} in front of πr3\pi r^3 literally comes from.

Practically it is the bowl formula and the dome formula. A mixing bowl 30 cm across holds 23π(0.15)3≈7.07\tfrac{2}{3}\pi(0.15)^3 \approx 7.07 litres brim full, which is why a "10 litre" bowl is larger than most people expect. It is also the capacity of a hemispherical tank head, the displacement of a dome-topped piston crown, and the earth volume in a hemispherical excavation.

Hemisphere Volume formula

V=23πr3V = \frac{2}{3}\pi r^3
Where
  • VV= Volume (L)
  • rr= Radius (m)

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