Geometry GlanceSources

Sphere calculator

cm

Centre to the circular edge.

Advanced

Changing a measurement unit keeps its number: 3 cm becomes 3 m. Unit for all measurements applies to every input and the result. Result unit converts only the answers.

A complete sphere, without a shell or separate base.

Number format

Use a decimal point or comma, without thousands separators. Up to 15 significant digits and 64 characters; no fractions or expressions.

Sphere schematic. A complete sphere, without a shell or separate base.Ord

Not to scale

Enter your measurements to see the results.

No personal result is available. These are the sphere formulas and conditions.

Formulas and conditions

Sphere

A complete sphere with center O, radius r from O to its surface, and diameter d through O. The dashed rear equator is a guide, not an extra surface or base.Ord
Radius / diameter
d=2r
Volume
V=4πr33
Surface area
SA=4πr2

r radius · d diameter · O center · V volume · SA surface area

Complete sphere; r > 0. No hemisphere or shell.

Surface area uses square units; volume uses cubic units.

Diagrams are schematic, not to scale.

Radius measures from the center to the sphere’s surface. A diameter passes through the center and is twice the radius.

These formulas describe a complete sphere. The equator drawn as a guide is not an extra base to add. A shell or hemisphere needs a different model.

Use the same length unit throughout a formula. Convert mixed measurements first. Length and perimeter use units such as cm; area uses cm²; volume uses cm³. Decimal examples below are rounded to at most six significant figures, with ≈ marking an approximation.

Worked example: A sphere with radius 3 cm

  1. V = 4π × 3³ ÷ 3 = 36π cm³ ≈ 113.097 cm³.
  2. SA = 4π × 3² = 36π cm² ≈ 113.097 cm².

The numerical coefficients happen to agree, but volume uses cm³ and area uses cm². Doubling the radius would multiply volume by eight and area by four.

Formula sources

Formulas are checked against these references. The explanation, diagrams and worked calculations here are authored for Geometry Glance.