{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"cylinder"},"result":{"entity_type":"calculator","id":"cylinder","calculator_id":"cylinder","canonical_url":"https://tttkmbb.com/geometry/cylinder","name":"Cylinder Calculator","title":"Cylinder Calculator – Volume, Lateral Area and Total Surface Area from Radius and Height","category":"geometry","category_name":"Geometry","tool_name":"calculate_cylinder_properties","featured_mcp_tool":false,"description":"Computes the volume, base area, lateral (curved) surface area and total surface area of a right circular cylinder from its radius and height.","use_when":"You need the capacity or surface of a can, tank, pipe, pillar or any straight circular cylinder.","do_not_use_when":"The cylinder is hollow (compute outer minus inner), tilted (oblique), or tapers to a point (use cone).","inputs":[{"name":"radius","label":"Radius","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Radius of the circular base.","example":3},{"name":"height","label":"Height","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Distance between the two bases, measured perpendicular to them.","example":5}],"outputs":[{"name":"volume","label":"Volume","type":"number","unit":"units³","decimals":4,"description":"π × r² × h."},{"name":"base_area","label":"Base area","type":"number","unit":"units²","decimals":4,"description":"π × r², area of one circular end."},{"name":"lateral_area","label":"Lateral surface area","type":"number","unit":"units²","decimals":4,"description":"2 × π × r × h, the curved side only."},{"name":"total_surface_area","label":"Total surface area","type":"number","unit":"units²","decimals":4,"description":"2 × π × r × (r + h), both ends plus the side."}],"input_schema":{"type":"object","properties":{"radius":{"description":"Radius of the circular base. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[3],"x-unit":"units"},"height":{"description":"Distance between the two bases, measured perpendicular to them. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[5],"x-unit":"units"}},"additionalProperties":false,"required":["radius","height"]},"output_schema":{"type":"object","properties":{"volume":{"description":"π × r² × h. Unit: units³.","type":"number","x-unit":"units³"},"base_area":{"description":"π × r², area of one circular end. Unit: units².","type":"number","x-unit":"units²"},"lateral_area":{"description":"2 × π × r × h, the curved side only. Unit: units².","type":"number","x-unit":"units²"},"total_surface_area":{"description":"2 × π × r × (r + h), both ends plus the side. Unit: units².","type":"number","x-unit":"units²"}}},"formula":"volume = π · radius² · height; base_area = π · radius²; lateral_area = 2 · π · radius · height; total_surface_area = 2 · π · radius · (radius + height)","sources":[{"name":"Wikipedia – Cylinder","url":"https://en.wikipedia.org/wiki/Cylinder","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Cylinder","url":"https://mathworld.wolfram.com/Cylinder.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, height 5","inputs":{"radius":3,"height":5},"expected":{"volume":141.3717,"base_area":28.2743,"lateral_area":94.2478,"total_surface_area":150.7964},"url":"https://tttkmbb.com/api/v1/calculate/cylinder?radius=3&height=5"},{"name":"Radius 1, height 1","inputs":{"radius":1,"height":1},"expected":{"volume":3.1416,"lateral_area":6.2832,"total_surface_area":12.5664},"url":"https://tttkmbb.com/api/v1/calculate/cylinder?radius=1&height=1"}],"faq":[{"q":"How do I get litres from the volume?","a":"Use the cube of the input unit: 1 dm³ = 1 litre, 1 cm³ = 1 ml, 1 m³ = 1000 litres. Enter dimensions in dm to read the volume directly in litres."},{"q":"Is the top included in the surface area?","a":"total_surface_area includes both circular ends; lateral_area is the curved side only (e.g. a label wrapped around a can)."}],"tags":["cylinder","volume of a cylinder","surface area of a cylinder","tank volume","pipe"],"related":[{"calculator_id":"cone","reason":"Same base but tapering to a point (one third of the volume)."},{"calculator_id":"circle","reason":"Properties of the circular base."},{"calculator_id":"volume","reason":"Convert the volume to litres or gallons."}],"links":{"html":"https://tttkmbb.com/geometry/cylinder","markdown":"https://tttkmbb.com/geometry/cylinder.md","json":"https://tttkmbb.com/geometry/cylinder.json","api":"https://tttkmbb.com/api/v1/calculate/cylinder","schema":"https://tttkmbb.com/api/v1/calculators/cylinder","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:26:17Z","next_actions":[{"tool":"run_calculator","calculator_id":"cylinder","reason":"Run Cylinder Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/geometry/cylinder.md"}}