{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"cake-pan-conversion"},"result":{"entity_type":"calculator","id":"cake-pan-conversion","calculator_id":"cake-pan-conversion","canonical_url":"https://tttkmbb.com/food/cake-pan-conversion","name":"Cake Pan Conversion Calculator","title":"Cake Pan Conversion Calculator – Pan Area, Volume and Recipe Scaling Factor Between Round, Square and Rectangular Pans","category":"food","category_name":"Food & Cooking","tool_name":"convert_cake_pan_size","featured_mcp_tool":false,"description":"Computes the surface area (and volume, if a depth is given) of two baking pans of round, square or rectangular shape and the factor by which a recipe must be scaled so the batter reaches the same depth in the new pan, with a baking-time note.","use_when":"A recipe is written for one pan size and you want to bake it in another, or you need the capacity of a pan in millilitres or US cups.","do_not_use_when":"You want to scale a recipe by servings rather than pan size (use recipe-scaler), or the pan is a bundt, tube or oddly shaped tin (measure its capacity with water instead).","inputs":[{"name":"from_shape","label":"Original pan shape","type":"enum","required":true,"values":[{"value":"round","label":"Round (diameter)","aliases":["circle","springform"]},{"value":"square","label":"Square (side)"},{"value":"rectangular","label":"Rectangular (length × width)","aliases":["rectangle","loaf","sheet"]}],"description":"Shape of the pan the recipe was written for.","example":"rectangular"},{"name":"from_size","label":"Original pan size","type":"number","required":true,"max":200,"exclusive_min":0,"description":"Diameter (round), side (square) or length (rectangular) of the original pan, in size_unit.","example":13},{"name":"from_width","label":"Original pan width","type":"number","required":false,"max":200,"exclusive_min":0,"description":"Width of the original pan; only for rectangular pans.","example":9},{"name":"to_shape","label":"New pan shape","type":"enum","required":true,"values":[{"value":"round","label":"Round (diameter)","aliases":["circle","springform"]},{"value":"square","label":"Square (side)"},{"value":"rectangular","label":"Rectangular (length × width)","aliases":["rectangle","loaf","sheet"]}],"description":"Shape of the pan you want to use.","example":"round"},{"name":"to_size","label":"New pan size","type":"number","required":true,"max":200,"exclusive_min":0,"description":"Diameter, side or length of the new pan, in size_unit.","example":9},{"name":"to_width","label":"New pan width","type":"number","required":false,"max":200,"exclusive_min":0,"description":"Width of the new pan; only for rectangular pans."},{"name":"size_unit","label":"Size unit","type":"enum","required":false,"default":"cm","values":[{"value":"cm","label":"Centimetres","aliases":["centimetre","centimeter","centimetres","centimeters"]},{"value":"in","label":"Inches","aliases":["inch","inches"]}],"description":"Unit of all pan dimensions.","example":"in"},{"name":"depth","label":"Pan depth (optional)","type":"number","required":false,"max":50,"exclusive_min":0,"description":"Depth of the pans in size_unit; when given, pan volumes are reported (the same depth is assumed for both pans).","example":2}],"outputs":[{"name":"scale_factor","label":"Recipe scale factor","type":"number","decimals":3,"description":"to_area / from_area: multiply every ingredient by this to get the same batter depth in the new pan."},{"name":"scale_percent","label":"Recipe scale","type":"number","unit":"%","decimals":1,"description":"Scale factor as a percentage of the original recipe."},{"name":"from_area_cm2","label":"Original pan area","type":"number","unit":"cm²","decimals":1,"description":"Bottom area of the original pan."},{"name":"to_area_cm2","label":"New pan area","type":"number","unit":"cm²","decimals":1,"description":"Bottom area of the new pan."},{"name":"from_area_in2","label":"Original pan area","type":"number","unit":"in²","decimals":1,"description":"Same in square inches."},{"name":"to_area_in2","label":"New pan area","type":"number","unit":"in²","decimals":1,"description":"Same in square inches."},{"name":"from_volume_ml","label":"Original pan volume","type":"number","unit":"ml","decimals":0,"description":"area × depth (only when depth is given)."},{"name":"to_volume_ml","label":"New pan volume","type":"number","unit":"ml","decimals":0,"description":"area × depth (only when depth is given)."},{"name":"from_volume_cups","label":"Original pan volume","type":"number","unit":"US cups","decimals":2,"description":"Volume in 236.6 ml US cups (only when depth is given)."},{"name":"to_volume_cups","label":"New pan volume","type":"number","unit":"US cups","decimals":2,"description":"Volume in US cups (only when depth is given)."},{"name":"unscaled_depth_ratio","label":"Batter depth if not scaled","type":"number","decimals":2,"description":"Relative batter depth in the new pan when the recipe is used unchanged (from_area / to_area)."},{"name":"baking_note","label":"Baking note","type":"string","decimals":4,"description":"How to scale the recipe and what to expect for baking time."}],"input_schema":{"type":"object","properties":{"from_shape":{"description":"Shape of the pan the recipe was written for.","type":"string","enum":["round","square","rectangular"],"examples":["rectangular"]},"from_size":{"description":"Diameter (round), side (square) or length (rectangular) of the original pan, in size_unit.","type":"number","maximum":200,"exclusiveMinimum":0,"examples":[13]},"from_width":{"description":"Width of the original pan; only for rectangular pans.","type":"number","maximum":200,"exclusiveMinimum":0,"examples":[9]},"to_shape":{"description":"Shape of the pan you want to use.","type":"string","enum":["round","square","rectangular"],"examples":["round"]},"to_size":{"description":"Diameter, side or length of the new pan, in size_unit.","type":"number","maximum":200,"exclusiveMinimum":0,"examples":[9]},"to_width":{"description":"Width of the new pan; only for rectangular pans.","type":"number","maximum":200,"exclusiveMinimum":0},"size_unit":{"description":"Unit of all pan dimensions.","type":"string","enum":["cm","in"],"default":"cm","examples":["in"]},"depth":{"description":"Depth of the pans in size_unit; when given, pan volumes are reported (the same depth is assumed for both pans).","type":"number","maximum":50,"exclusiveMinimum":0,"examples":[2]}},"additionalProperties":false,"required":["from_shape","from_size","to_shape","to_size"]},"output_schema":{"type":"object","properties":{"scale_factor":{"description":"to_area / from_area: multiply every ingredient by this to get the same batter depth in the new pan.","type":"number"},"scale_percent":{"description":"Scale factor as a percentage of the original recipe. Unit: %.","type":"number","x-unit":"%"},"from_area_cm2":{"description":"Bottom area of the original pan. Unit: cm².","type":"number","x-unit":"cm²"},"to_area_cm2":{"description":"Bottom area of the new pan. Unit: cm².","type":"number","x-unit":"cm²"},"from_area_in2":{"description":"Same in square inches. Unit: in².","type":"number","x-unit":"in²"},"to_area_in2":{"description":"Same in square inches. Unit: in².","type":"number","x-unit":"in²"},"from_volume_ml":{"description":"area × depth (only when depth is given). Unit: ml.","type":"number","x-unit":"ml"},"to_volume_ml":{"description":"area × depth (only when depth is given). Unit: ml.","type":"number","x-unit":"ml"},"from_volume_cups":{"description":"Volume in 236.6 ml US cups (only when depth is given). Unit: US cups.","type":"number","x-unit":"US cups"},"to_volume_cups":{"description":"Volume in US cups (only when depth is given). Unit: US cups.","type":"number","x-unit":"US cups"},"unscaled_depth_ratio":{"description":"Relative batter depth in the new pan when the recipe is used unchanged (from_area / to_area).","type":"number"},"baking_note":{"description":"How to scale the recipe and what to expect for baking time.","type":"string"}}},"formula":"area: round = π·(d/2)², square = s², rectangular = l × w; scale_factor = to_area / from_area; volume = area × depth (1 in² = 6.4516 cm², 1 in³ = 16.387 ml, 1 US cup = 236.588 ml)","method":"Scaling by bottom area keeps the batter depth, and therefore the baking time and crumb, the same; pans should be filled no more than about two-thirds. A 9-inch round (63.6 in²) and an 8-inch square (64 in²) are interchangeable.","sources":[{"name":"King Arthur Baking – The essential alternative baking pan sizes","url":"https://www.kingarthurbaking.com/blog/2019/04/23/the-essential-alternative-baking-pan-sizes","type":"reference","retrieved_at":"2026-09-24"},{"name":"NIST Special Publication 811 – Guide for the Use of the SI (Appendix B: US customary volume units in litres)","url":"https://www.nist.gov/pml/special-publication-811","type":"standard","retrieved_at":"2026-09-24"}],"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":"8 in round → 9 in round, 2 in deep","inputs":{"from_shape":"round","from_size":8,"to_shape":"round","to_size":9,"size_unit":"in","depth":2},"expected":{"scale_factor":1.266,"scale_percent":126.6,"from_area_in2":50.3,"to_area_in2":63.6,"from_area_cm2":324.3,"to_area_cm2":410.4,"from_volume_ml":1647,"to_volume_ml":2085,"from_volume_cups":6.96,"to_volume_cups":8.81,"unscaled_depth_ratio":0.79},"url":"https://tttkmbb.com/api/v1/calculate/cake-pan-conversion?from_shape=round&from_size=8&to_shape=round&to_size=9&size_unit=in&depth=2"},{"name":"20 cm round → 20 cm square","inputs":{"from_shape":"round","from_size":20,"to_shape":"square","to_size":20,"size_unit":"cm"},"expected":{"scale_factor":1.273,"from_area_cm2":314.2,"to_area_cm2":400,"to_area_in2":62},"url":"https://tttkmbb.com/api/v1/calculate/cake-pan-conversion?from_shape=round&from_size=20&to_shape=square&to_size=20&size_unit=cm"}],"faq":[{"q":"Do I have to scale the recipe?","a":"Not for differences under about 10 %. For larger pans the unscaled batter is thinner and bakes faster; for smaller pans it is deeper and needs longer, possibly at a slightly lower temperature, so it sets before the top over-browns."},{"q":"How do I convert to a bundt or tube pan?","a":"Measure the pan's capacity by filling it with water (1 US cup = 237 ml). A 10–12 cup bundt takes the batter of a 9 × 13 in pan and, per King Arthur Baking, bakes about 30 % longer because of the depth."},{"q":"Why are the volumes larger than the batter a recipe makes?","a":"Volumes are for the full pan; batter should fill only one-half to two-thirds of it to leave room for rising."}],"tags":["cake pan conversion","pan size substitution","round to square pan","cake pan area","baking pan volume"],"related":[{"calculator_id":"recipe-scaler","reason":"Apply the scale factor to every ingredient."},{"calculator_id":"oven-temperature","reason":"Convert oven settings between °C, °F, gas mark and fan ovens."},{"calculator_id":"circle","reason":"Area of round pans."}],"links":{"html":"https://tttkmbb.com/food/cake-pan-conversion","markdown":"https://tttkmbb.com/food/cake-pan-conversion.md","json":"https://tttkmbb.com/food/cake-pan-conversion.json","api":"https://tttkmbb.com/api/v1/calculate/cake-pan-conversion","schema":"https://tttkmbb.com/api/v1/calculators/cake-pan-conversion","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:48:18Z","next_actions":[{"tool":"run_calculator","calculator_id":"cake-pan-conversion","reason":"Run Cake Pan Conversion Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/food/cake-pan-conversion.md"}}