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Sphere Volume

V=43πr3V = \frac{4}{3} \pi r^{3}

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

Learning zone

The volume of a sphere is four-thirds π times the radius cubed. Archimedes considered this his finest result: a sphere fills exactly two-thirds of the smallest cylinder that contains it, and he asked that the figure be carved on his tombstone. Because volume scales with the cube of the radius, small changes in size have outsized effects — doubling a balloon's radius gives it eight times the volume of gas.

A worked example: a spherical propane tank with a radius of 1.5 m holds V = (4/3)π(1.5)³ ≈ 14.14 m³, or about 14,100 litres. Going the other way, solving for r takes a cube root, which is single-valued for real numbers — no sign ambiguity to worry about. The same cubic scaling explains why raindrops, planets, and bubbles are dominated by their largest members: most of the total volume lives in the biggest few.

Sphere Volume
V=43πr3V = \frac{4}{3} \pi r^{3}
Where
  • VV= Volume
  • rr= Radius
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