{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"sphere"},"result":{"entity_type":"calculator","id":"sphere","calculator_id":"sphere","canonical_url":"https://tttkmbb.com/geometry/sphere","name":"Sphere Calculator","title":"Sphere Calculator – Volume, Surface Area and Diameter from Radius","category":"geometry","category_name":"Geometry","tool_name":"calculate_sphere_properties","featured_mcp_tool":false,"description":"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).","inputs":[{"name":"radius","label":"Radius","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Radius of the sphere (half the diameter).","example":2}],"outputs":[{"name":"volume","label":"Volume","type":"number","unit":"units³","decimals":4,"description":"4/3 × π × r³."},{"name":"surface_area","label":"Surface area","type":"number","unit":"units²","decimals":4,"description":"4 × π × r²."},{"name":"diameter","label":"Diameter","type":"number","unit":"units","decimals":4,"description":"2 × r."},{"name":"great_circle_circumference","label":"Great-circle circumference","type":"number","unit":"units","decimals":4,"description":"2 × π × r, the length of the equator of the sphere."}],"input_schema":{"type":"object","properties":{"radius":{"description":"Radius of the sphere (half the diameter). Unit: units.","type":"number","exclusiveMinimum":0,"examples":[2],"x-unit":"units"}},"additionalProperties":false,"required":["radius"]},"output_schema":{"type":"object","properties":{"volume":{"description":"4/3 × π × r³. Unit: units³.","type":"number","x-unit":"units³"},"surface_area":{"description":"4 × π × r². Unit: units².","type":"number","x-unit":"units²"},"diameter":{"description":"2 × r. Unit: units.","type":"number","x-unit":"units"},"great_circle_circumference":{"description":"2 × π × r, the length of the equator of the sphere. Unit: units.","type":"number","x-unit":"units"}}},"formula":"volume = 4/3 · π · radius³; surface_area = 4 · π · radius²; diameter = 2 · radius; great_circle_circumference = 2 · π · radius","sources":[{"name":"Wikipedia – Sphere","url":"https://en.wikipedia.org/wiki/Sphere","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Sphere","url":"https://mathworld.wolfram.com/Sphere.html","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Radius 2","inputs":{"radius":2},"expected":{"volume":33.5103,"surface_area":50.2655,"diameter":4,"great_circle_circumference":12.5664},"url":"https://tttkmbb.com/api/v1/calculate/sphere?radius=2"},{"name":"Earth mean radius 6371 km","inputs":{"radius":6371},"expected":{"volume":1083206916846,"surface_area":510064472,"great_circle_circumference":40030.1736},"url":"https://tttkmbb.com/api/v1/calculate/sphere?radius=6371"}],"faq":[{"q":"I know the diameter, not the radius.","a":"Enter half the diameter. Doubling the radius multiplies the surface area by 4 and the volume by 8."},{"q":"How do I find the radius from a volume?","a":"r = (3 × volume / (4π))^(1/3). Enter that radius to get the other properties."}],"tags":["sphere","volume of a sphere","surface area of a sphere","ball","radius"],"related":[{"calculator_id":"circle","reason":"The great circle (cross-section through the centre) of the same radius."},{"calculator_id":"cylinder","reason":"Compare with a cylinder of the same radius and height 2r (Archimedes' 2:3 ratio)."},{"calculator_id":"volume","reason":"Convert the volume to litres, gallons or other units."}],"links":{"html":"https://tttkmbb.com/geometry/sphere","markdown":"https://tttkmbb.com/geometry/sphere.md","json":"https://tttkmbb.com/geometry/sphere.json","api":"https://tttkmbb.com/api/v1/calculate/sphere","schema":"https://tttkmbb.com/api/v1/calculators/sphere","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:24:43Z","next_actions":[{"tool":"run_calculator","calculator_id":"sphere","reason":"Run Sphere Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/geometry/sphere.md"}}