Sphere Calculator — Radius, Surface Area, Volume

Enter any value. Private by design — runs locally in your browser.

Diagram & Inputs

Tip: Enter any one value (r, d, S, or V). The calculator checks consistency if you provide multiple values.

Results

How the Sphere Calculator Works

A sphere is fully determined by its radius r (or diameter d = 2r). From r you can compute the surface area S = 4πr² and the volume V = (4/3)πr³. This tool infers r from whatever you provide and derives the rest, checking consistency if multiple values are entered.

  • From S: r = √(S/(4π))
  • From V: r = ³√(3V/(4π))
  • Then: d = 2r, S = 4πr², V = (4/3)πr³

Units: r and d use length units (e.g., cm); S uses squared units (e.g., cm²); V uses cubed units (e.g., cm³). You can set decimal places and choose a π approximation for classroom alignment.

Formulas & Relationships

  • Diameter: d = 2r
  • Surface area: S = 4πr²
  • Volume: V = (4/3)πr³
  • Solve for r: r = √(S/(4π)) = ³√(3V/(4π))

Common pitfalls: mixing units between inputs, entering negative values, or rounding too early. If you see an inconsistency warning, double-check your unit labels and π choice.

5 Fun Facts about Spheres

Area to volume dance

Double the radius and S grows by 4× while V jumps by 8×. Radius changes dominate volume because of the r³ term.

Scaling intuition

Shortest path = great circle

Airplanes fly “curved” great-circle routes because those are the shortest paths on a sphere—straight on a globe, bendy on a flat map.

Navigation secret

Map distortions are inevitable

You can’t flatten a sphere without stretching or cutting (Gauss’s Theorema Egregium). Every world map picks what to distort—area, shape, or distance.

Cartography twist

Shell theorem magic

Outside a uniform sphere, gravity acts as if all mass is at its center. That’s why planet-sized bodies pull like perfect point masses in orbital math.

Physics neatness

Earth is almost—but not quite

Earth’s equatorial radius is ~21 km larger than its polar radius. The “oblate spheroid” bulge comes from rotation; perfect spheres are rare in nature.

Reality check

Sphere Calculator: FAQs

Which inputs are valid to solve a sphere?

Any one of radius (r), diameter (d), surface area (S), or volume (V). Two or more values are also fine.

What formulas are used?

d = 2r, S = 4πr², V = (4/3)πr³.

Does the calculator keep my data private?

Yes. Computation is entirely client-side; nothing is uploaded.

Can I change units, decimal places, or π?

Yes. Choose a length unit for r and d. Surface area is labeled with the squared unit; volume with the cubed unit. You can also choose decimal places and π precision.

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