Sphere Volume Calculator
Calculate the volume and surface area of a sphere from its radius or diameter.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
Choose radius or diameter. Switching preserves the same circle or sphere.
Worked example
calculated with the default values below
Measurement Radius · Radius 5 cm · Diameter 0 Volume 523.5988 cm³ · Surface area 314.1593 cm² · Radius 5 cm · Volume 0.523599 L
Method and assumptions
Formula basis and scope
V = 4πr³/3; surface area = 4πr².
Ideal Euclidean shapes; use consistent length units. A diameter is twice the radius.
Data sources
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
r = D ÷ 2; V = 4÷3 × π × r³; A = 4πr²
- D
- Diameter
- r
- Radius
- V
- Volume
- A
- Surface area
If diameter is 0 or less, the radius input is used directly. V÷1000 gives litres when r is entered in cm.
Frequently asked questions
Why does doubling the radius multiply the sphere volume by eight?
Volume is four-thirds pi times the radius cubed, so the radius enters as a cube, not a square. A sphere of radius 5 cm holds about 524 cm cubed, but radius 10 cm holds roughly 4,189 cm cubed, eight times as much for double the size. This is why small changes in radius, such as a 1 cm thicker shell, add disproportionately more volume than the same change near a tiny sphere, and why the litre output scales just as steeply.