{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"circle"},"result":{"entity_type":"calculator","id":"circle","calculator_id":"circle","canonical_url":"https://tttkmbb.com/geometry/circle","name":"Circle Calculator","title":"Circle Calculator – Area, Circumference and Diameter from Radius or Diameter","category":"geometry","category_name":"Geometry","tool_name":"calculate_circle_properties","featured_mcp_tool":true,"description":"Computes the area, circumference, diameter and radius of a circle from either its radius or its diameter. Lengths are unit-agnostic: the area is in the square of the input unit.","use_when":"You know a circle's radius or diameter and need its area, circumference or the other dimension.","do_not_use_when":"The shape is an ellipse (use ellipse), a solid ball (use sphere) or a disc with thickness (use cylinder).","inputs":[{"name":"radius","label":"Radius","type":"number","unit":"units","required":false,"exclusive_min":0,"description":"Radius of the circle. Give either radius or diameter.","example":3},{"name":"diameter","label":"Diameter","type":"number","unit":"units","required":false,"exclusive_min":0,"description":"Diameter of the circle (2 × radius). Used when radius is not given.","example":6}],"outputs":[{"name":"radius","label":"Radius","type":"number","unit":"units","decimals":4,"description":"Radius r (as given, or diameter / 2)."},{"name":"diameter","label":"Diameter","type":"number","unit":"units","decimals":4,"description":"2·r."},{"name":"circumference","label":"Circumference","type":"number","unit":"units","decimals":4,"description":"2·π·r."},{"name":"area","label":"Area","type":"number","unit":"units²","decimals":4,"description":"π·r², in the square of the input unit."}],"input_schema":{"type":"object","properties":{"radius":{"description":"Radius of the circle. Give either radius or diameter. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[3],"x-unit":"units"},"diameter":{"description":"Diameter of the circle (2 × radius). Used when radius is not given. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[6],"x-unit":"units"}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"radius":{"description":"Radius r (as given, or diameter / 2). Unit: units.","type":"number","x-unit":"units"},"diameter":{"description":"2·r. Unit: units.","type":"number","x-unit":"units"},"circumference":{"description":"2·π·r. Unit: units.","type":"number","x-unit":"units"},"area":{"description":"π·r², in the square of the input unit. Unit: units².","type":"number","x-unit":"units²"}}},"formula":"r = radius (or diameter / 2); diameter = 2·r; circumference = 2·π·r; area = π·r²","sources":[{"name":"Wikipedia – Circle","url":"https://en.wikipedia.org/wiki/Circle","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Circle","url":"https://mathworld.wolfram.com/Circle.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 3","inputs":{"radius":3},"expected":{"radius":3,"diameter":6,"circumference":18.8496,"area":28.2743},"url":"https://tttkmbb.com/api/v1/calculate/circle?radius=3"},{"name":"Diameter 10","inputs":{"diameter":10},"expected":{"radius":5,"circumference":31.4159,"area":78.5398},"url":"https://tttkmbb.com/api/v1/calculate/circle?diameter=10"}],"faq":[{"q":"What units are the results in?","a":"The same unit as the input for lengths and its square for the area: a radius in cm gives a circumference in cm and an area in cm²."},{"q":"What if I give both radius and diameter?","a":"They must agree (diameter = 2 × radius); otherwise the calculator returns an INVALID_PARAMETER error rather than guessing which one is right."},{"q":"How do I get the radius from the area?","a":"r = √(area / π). Enter that radius here to get the remaining properties."}],"tags":["circle","area of a circle","circumference","radius","diameter","pi"],"related":[{"calculator_id":"sphere","reason":"Volume and surface area of a ball with the same radius."},{"calculator_id":"cylinder","reason":"Volume of a circular disc or tube with this cross-section."},{"calculator_id":"ellipse","reason":"Area and perimeter when the two axes differ."}],"links":{"html":"https://tttkmbb.com/geometry/circle","markdown":"https://tttkmbb.com/geometry/circle.md","json":"https://tttkmbb.com/geometry/circle.json","api":"https://tttkmbb.com/api/v1/calculate/circle","schema":"https://tttkmbb.com/api/v1/calculators/circle","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:23:58Z","next_actions":[{"tool":"calculate_circle_properties","calculator_id":"circle","reason":"Run Circle Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/geometry/circle.md"}}