Sphere: volume and surface area

Volume of a sphere from its radius.

V = \frac{4}{3} π r^{3}, S = 4 π r^{2}

r is the radius, half the diameter. Volume is in cubic units and surface area in square units.

The volume of a sphere grows with the cube of its radius: double the radius and the volume is eight times larger.

Calculator

Solve for

VVolumeComputed

cm³

rRadius

0.550

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Volume (cm³) current value 523.6 cm³

rRadiusKey driver

0.524524,000

Volume goes as r³ and surface area as r², so large spheres have less surface per unit volume.
Use the radius, not the diameter.

Chart data as tables

Variable	Typical range	Lowest result	Highest result	Swing (cm³)	Local step	Change in result
r Radius	0.5 to 50 cm	0.5236	523,600	523,600	+10%	+33.1 %

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Volume (cm³)Hover, touch, or use the arrow keys on the chart

Result · cm³

What the equation gives you. Everything else feeds it.

cm · typical 0.5 to 50

Distance from the centre to the surface. Cubed: +10% radius gives +33% volume.

The cube amplifies errors by three: δV/V = 3δr/r. A 1% error in diameter gives a 3% error in volume.