sphere volume calculator

Sphere Volume Calculator

V = (4/3) × π × r³. Surface area: S = 4 × π × r². A sphere has the smallest surface for a given volume.

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Derivation of sphere volume

Archimedes proved that the sphere volume is (2/3) of the circumscribed cylinder. The formula V = (4/3)πr³ is confirmed by integration in spherical coordinates.

Examples

r = 3 cm

Input: r = 3
Expected output: V ≈ 113.1 cm³, S ≈ 113.1 cm²

V = (4/3)π×27 ≈ 113.1.

Safe use

Input: context + tool result
Expected output: interpreted with limits and next steps

Use the result as technical or educational support, keeping the tool limits explicit in the workflow.

Full tool FAQ

What unit should I use?

Use any unit you prefer (cm, m, inches…). The area/volume will be in the corresponding squared/cubed unit. For example, if you enter cm, area will be in cm².

Why does the triangle perimeter show '—'?

Does the cone formula use the slant height?

What is the formula for circle area?

How do I calculate sphere volume?

What is a rectangular box?

Can I use this for physics problems?

How precise are the results?

Frequently asked questions

Can the volume and surface area have the same value?

For r=3, V ≈ S ≈ 113 (in cm³ and cm²). It is a numerical coincidence with no physical meaning — the units differ.

Does this page replace official or professional review?

No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.