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Cake Pan Conversion Calculator

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.

When to use

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).

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)

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.

Inputs

Parameter	Type	Required	Description
`from_shape`	enum: round \| square \| rectangular	yes	Shape of the pan the recipe was written for.
`from_size`	number	yes	Diameter (round), side (square) or length (rectangular) of the original pan, in size_unit. Range: > 0, ≤ 200
`from_width`	number	no	Width of the original pan; only for rectangular pans. Range: > 0, ≤ 200
`to_shape`	enum: round \| square \| rectangular	yes	Shape of the pan you want to use.
`to_size`	number	yes	Diameter, side or length of the new pan, in size_unit. Range: > 0, ≤ 200
`to_width`	number	no	Width of the new pan; only for rectangular pans. Range: > 0, ≤ 200
`size_unit`	enum: cm \| in	default cm	Unit of all pan dimensions.
`depth`	number	no	Depth of the pans in size_unit; when given, pan volumes are reported (the same depth is assumed for both pans). Range: > 0, ≤ 50

Outputs

Output	Type	Unit	Description
`scale_factor`	number		to_area / from_area: multiply every ingredient by this to get the same batter depth in the new pan.
`scale_percent`	number	%	Scale factor as a percentage of the original recipe.
`from_area_cm2`	number	cm²	Bottom area of the original pan.
`to_area_cm2`	number	cm²	Bottom area of the new pan.
`from_area_in2`	number	in²	Same in square inches.
`to_area_in2`	number	in²	Same in square inches.
`from_volume_ml`	number	ml	area × depth (only when depth is given).
`to_volume_ml`	number	ml	area × depth (only when depth is given).
`from_volume_cups`	number	US cups	Volume in 236.6 ml US cups (only when depth is given).
`to_volume_cups`	number	US cups	Volume in US cups (only when depth is given).
`unscaled_depth_ratio`	number		Relative batter depth in the new pan when the recipe is used unchanged (from_area / to_area).
`baking_note`	string		How to scale the recipe and what to expect for baking time.

Example

8 in round → 9 in round, 2 in deep: {"from_shape":"round","from_size":8,"to_shape":"round","to_size":9,"size_unit":"in","depth":2} → {"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}

20 cm round → 20 cm square: {"from_shape":"round","from_size":20,"to_shape":"square","to_size":20,"size_unit":"cm"} → {"scale_factor":1.273,"from_area_cm2":314.2,"to_area_cm2":400,"to_area_in2":62}

GET 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

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/cake-pan-conversion (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/cake-pan-conversion · Markdown: https://tttkmbb.com/food/cake-pan-conversion.md · JSON definition: https://tttkmbb.com/food/cake-pan-conversion.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="cake-pan-conversion"
OpenAPI operationId: convert_cake_pan_size
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

FAQ

Do I have to scale the recipe?

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.

How do I convert to a bundt or tube pan?

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.

Why are the volumes larger than the batter a recipe makes?

Volumes are for the full pan; batter should fill only one-half to two-thirds of it to leave room for rising.

Related calculators

Recipe Scaler — Apply the scale factor to every ingredient.
Oven Temperature Converter — Convert oven settings between °C, °F, gas mark and fan ovens.
Circle Calculator — Area of round pans.