Sphere Volume Calculator

Calculate the volume and surface area of a sphere from its radius. Instant results with step-by-step formulas.

Enter the radius of the sphere

Sphere Formulas

Volume = (4/3) × π × r³
Surface Area = 4 × π × r²
Example: A sphere with radius 6
Volume = (4/3) × π × 216 = 288π ≈ 904.7787 cubic units
Surface Area = 4 × π × 36 = 144π ≈ 452.3893 square units

Understanding the Sphere

A sphere is a perfectly round 3D shape where every point on its surface is equidistant from the center. Common real-world examples include balls, planets, and bubbles.

Volume vs Surface Area

PropertyFormulaMeasures
Volume(4/3)πr³Space inside the sphere (cubic units)
Surface Area4πr²Total outer surface (square units)

Frequently Asked Questions

How do I find the volume if I know the diameter?

Divide the diameter by 2 to get the radius, then apply V = (4/3)πr³. Alternatively, V = (π/6) × d³.

Why is the factor 4/3 in the volume formula?

The factor 4/3 comes from integrating circular cross-sections along the diameter. It relates to how a sphere's volume compares to the cylinder that encloses it (the sphere is exactly 2/3 of the enclosing cylinder's volume).

How does doubling the radius affect volume?

Doubling the radius increases the volume by a factor of 8 (since 2³ = 8). Volume scales with the cube of the radius.

Last updated: 2026-08-08