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Sphere Calculator

Computes the volume, surface area, diameter and great-circle circumference of a sphere from its radius. The volume is in the cube and the surface area in the square of the input unit.

When to use

You need the volume or surface area of a ball, globe, bubble or planet from its radius.

Do not use when: The object is a hemisphere or spherical cap (halve or use the cap formula), an ellipsoid, or you only need a flat circle (use circle).

Formula

volume = 4/3 · π · radius³; surface_area = 4 · π · radius²; diameter = 2 · radius; great_circle_circumference = 2 · π · radius

Inputs

Parameter	Type	Unit	Required	Description
`radius`	number	units	yes	Radius of the sphere (half the diameter). Range: > 0

Outputs

Output	Type	Unit	Description
`volume`	number	units³	4/3 × π × r³.
`surface_area`	number	units²	4 × π × r².
`diameter`	number	units	2 × r.
`great_circle_circumference`	number	units	2 × π × r, the length of the equator of the sphere.

Example

Radius 2: {"radius":2} → {"volume":33.5103,"surface_area":50.2655,"diameter":4,"great_circle_circumference":12.5664}

Earth mean radius 6371 km: {"radius":6371} → {"volume":1083206916846,"surface_area":510064472,"great_circle_circumference":40030.1736}

GET https://tttkmbb.com/api/v1/calculate/sphere?radius=2

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/sphere (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/sphere · Markdown: https://tttkmbb.com/geometry/sphere.md · JSON definition: https://tttkmbb.com/geometry/sphere.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="sphere"
OpenAPI operationId: calculate_sphere_properties
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Sphere (reference)
Wolfram MathWorld – Sphere (reference)

FAQ

I know the diameter, not the radius.

Enter half the diameter. Doubling the radius multiplies the surface area by 4 and the volume by 8.

How do I find the radius from a volume?

r = (3 × volume / (4π))^(1/3). Enter that radius to get the other properties.

Related calculators

Circle Calculator — The great circle (cross-section through the centre) of the same radius.
Cylinder Calculator — Compare with a cylinder of the same radius and height 2r (Archimedes' 2:3 ratio).
Volume Converter — Convert the volume to litres, gallons or other units.