Sphere Volume Calculator ($V = \frac{4}{3} \pi r^3$)

Calculate the volume ($V$), surface area ($A$), and circumference ($C$) of a sphere. Enter either the **Radius ($r$)** or the **Diameter ($d$)** below, and the tool will solve for all other properties.

Formulas for Sphere Volume and Area

The volume and surface area formulas for a sphere, first rigorously derived by Archimedes, demonstrate a simple and elegant relationship with the radius, $r$.

1. Volume ($V$)

The volume of the sphere is determined by cubing the radius:

Historically, Archimedes showed that the volume of a sphere is two-thirds the volume of the smallest cylinder that can enclose it.

2. Surface Area ($A$)

The surface area formula is exactly four times the area of the sphere's great circle ($\pi r^2$, the cross-section passing through the center):

Key Sphere Terminology

• **Radius ($r$):** The distance from the center to any point on the surface.
• **Diameter ($d$):** The distance across the sphere passing through the center ($d = 2r$).
• **Great Circle:** The largest circle that can be drawn on the surface of the sphere. Its circumference is $C = 2\pi r$.

Frequently Asked Questions (FAQ)

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V = \frac{4}{3} \pi r^3

A = 4 \pi r^2

C = 2 \pi r

$V = \frac{4}{3} \pi r^3$