# 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.

- Calculator id: `sphere` · Category: Geometry (`geometry`) · Tool name: `calculate_sphere_properties`
- Canonical page: https://tttkmbb.com/geometry/sphere · This document: https://tttkmbb.com/geometry/sphere.md · JSON definition: https://tttkmbb.com/geometry/sphere.json

## Purpose

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.

**Use when:** 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).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `radius` | number | units | required | Radius of the sphere (half the diameter). (> 0) |

## Output

| Field | 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. |

## Formula

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

## Data Sources

- Wikipedia – Sphere — https://en.wikipedia.org/wiki/Sphere (reference, retrieved 2026-09-23)
- Wolfram MathWorld – Sphere — https://mathworld.wolfram.com/Sphere.html (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/sphere?radius=…`
- `POST https://tttkmbb.com/api/v1/calculate/sphere` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/sphere · OpenAPI operationId `calculate_sphere_properties` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "sphere", "inputs": {…}}`

## Example

- Radius 2: inputs `{"radius":2}` → `{"volume":33.5103,"surface_area":50.2655,"diameter":4,"great_circle_circumference":12.5664}`
- Earth mean radius 6371 km: inputs `{"radius":6371}` → `{"volume":1083206916846,"surface_area":510064472,"great_circle_circumference":40030.1736}`

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

## Limitations

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). All values are computed from the formula above; no measurement or live data is involved.

## 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

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