{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"rectangular-prism"},"result":{"entity_type":"calculator","id":"rectangular-prism","calculator_id":"rectangular-prism","canonical_url":"https://tttkmbb.com/geometry/rectangular-prism","name":"Rectangular Prism Calculator","title":"Rectangular Prism (Box) Calculator – Volume, Surface Area and Space Diagonal","category":"geometry","category_name":"Geometry","tool_name":"calculate_rectangular_prism_properties","featured_mcp_tool":false,"description":"Computes the volume, total surface area, space diagonal and total edge length of a rectangular prism (cuboid or box) from its length, width and height.","use_when":"You need the capacity, surface or longest internal dimension of a box, room, aquarium, container or any cuboid.","do_not_use_when":"The base is not a rectangle (use cylinder or pyramid) or you only need the floor area (use rectangle).","inputs":[{"name":"length","label":"Length","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Length of the base.","example":3},{"name":"width","label":"Width","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Width of the base.","example":4},{"name":"height","label":"Height","type":"number","unit":"units","required":true,"exclusive_min":0,"description":"Height of the prism.","example":12}],"outputs":[{"name":"volume","label":"Volume","type":"number","unit":"units³","decimals":4,"description":"length × width × height."},{"name":"surface_area","label":"Surface area","type":"number","unit":"units²","decimals":4,"description":"2 × (length×width + length×height + width×height)."},{"name":"space_diagonal","label":"Space diagonal","type":"number","unit":"units","decimals":4,"description":"√(length² + width² + height²), the longest straight line inside the box."},{"name":"total_edge_length","label":"Total edge length","type":"number","unit":"units","decimals":4,"description":"4 × (length + width + height)."}],"input_schema":{"type":"object","properties":{"length":{"description":"Length of the base. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[3],"x-unit":"units"},"width":{"description":"Width of the base. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[4],"x-unit":"units"},"height":{"description":"Height of the prism. Unit: units.","type":"number","exclusiveMinimum":0,"examples":[12],"x-unit":"units"}},"additionalProperties":false,"required":["length","width","height"]},"output_schema":{"type":"object","properties":{"volume":{"description":"length × width × height. Unit: units³.","type":"number","x-unit":"units³"},"surface_area":{"description":"2 × (length×width + length×height + width×height). Unit: units².","type":"number","x-unit":"units²"},"space_diagonal":{"description":"√(length² + width² + height²), the longest straight line inside the box. Unit: units.","type":"number","x-unit":"units"},"total_edge_length":{"description":"4 × (length + width + height). Unit: units.","type":"number","x-unit":"units"}}},"formula":"volume = length · width · height; surface_area = 2 · (length·width + length·height + width·height); space_diagonal = √(length² + width² + height²); total_edge_length = 4 · (length + width + height)","sources":[{"name":"Wikipedia – Cuboid","url":"https://en.wikipedia.org/wiki/Cuboid","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Cuboid","url":"https://mathworld.wolfram.com/Cuboid.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":"3 × 4 × 12","inputs":{"length":3,"width":4,"height":12},"expected":{"volume":144,"surface_area":192,"space_diagonal":13,"total_edge_length":76},"url":"https://tttkmbb.com/api/v1/calculate/rectangular-prism?length=3&width=4&height=12"},{"name":"2 × 3 × 4","inputs":{"length":2,"width":3,"height":4},"expected":{"volume":24,"surface_area":52,"space_diagonal":5.3852,"total_edge_length":36},"url":"https://tttkmbb.com/api/v1/calculate/rectangular-prism?length=2&width=3&height=4"}],"faq":[{"q":"How do I use it for a cube?","a":"Enter the same value for all three sides: volume = side³, surface area = 6 × side², space diagonal = side × √3."},{"q":"Will a rod of a given length fit in the box?","a":"Only if it is no longer than the space diagonal (ignoring the rod's thickness)."}],"tags":["rectangular prism","cuboid","box volume","surface area of a box","space diagonal"],"related":[{"calculator_id":"rectangle","reason":"Area and diagonal of one face."},{"calculator_id":"volume","reason":"Convert the volume to litres, gallons or cubic feet."},{"calculator_id":"concrete-slab","reason":"Concrete needed for a rectangular slab of these dimensions."}],"links":{"html":"https://tttkmbb.com/geometry/rectangular-prism","markdown":"https://tttkmbb.com/geometry/rectangular-prism.md","json":"https://tttkmbb.com/geometry/rectangular-prism.json","api":"https://tttkmbb.com/api/v1/calculate/rectangular-prism","schema":"https://tttkmbb.com/api/v1/calculators/rectangular-prism","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:23:04Z"}