Cake Pan Conversion Calculator

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Original pan shape:

Original {{ dimensionName('original') }}:

Original width:

Original pan count:

Target pan shape:

Target {{ dimensionName('target') }}:

Target width:

Target pan count:

Scaling basis:

Keep the original batter depth, or fill the target capacity using the wall heights and fill levels in Advanced.

Equal depth Target capacity

Original inner wall depth:

Measure the inner wall height; the 5 cm default is an example.

Original batter fill:{{ original_fill }}%

Original recipe batter level as a percentage of wall height; 60% is an example.

Target inner wall depth:

Measure the replacement pan’s inner wall height.

Target fill limit:{{ target_fill }}%

Maximum intended batter level. Follow recipe guidance for room to rise; 60% is an example.

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Straight-sided pans only. Tapered, Bundt, tube and irregular pans need measured usable volume. Keep the recipe’s temperature and check its doneness cues; changes in depth, material and shape can change baking time. No time multiplier is implied.

Geometry and substitution guidance: King Arthur Baking.

Calculation method

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Replacing a round cake pan with a square pan of the same stated size changes how much batter it takes to reach the same depth. An 8-inch square has more base area than an 8-inch round, so an unchanged batch spreads more thinly. Cake pan conversion compares the space available for batter to work out how much of the original recipe to make.

The useful measurements are taken across the inside base, not the outside rim. For straight-sided pans, that base area stays the same all the way up the walls. A larger base needs more batter to maintain the original depth, while taller walls alone do not require a larger batch.

Inner wall height: The distance from the inside base to the rim. It describes the pan, not the height of the finished cake.
Batter depth and fill percentage: Batter depth is the height of the unbaked batter. A fill percentage expresses that height as a proportion of the inner wall height.
Brim capacity and usable capacity: Brim capacity is the volume right up to the rim. Usable capacity is the volume up to a chosen batter level, leaving space above it. That chosen level needs to suit the recipe and pan.

Cross-section of a straight-sided pan with a 5 cm inner wall, 3 cm of unbaked batter and 2 cm of space to the rim. — A 60% fill in a 5 cm pan gives 3 cm of unbaked batter. This is an illustrative level, not a universal filling recommendation.

A shallower replacement can rule out preserving that depth. With a 4 cm wall and the same chosen 60% fill limit, the intended batter level is only 2.4 cm. Keeping 3 cm of batter would exceed that limit, even if the replacement has a wider base. Reducing the batch to that capacity means using a shallower batter depth.

Pan count also changes the comparison. A recipe written for two pans represents the batter for both pans together. To keep the same batter depth in three replacement pans, the comparison uses the combined original and target areas, then divides the scaled batch among the replacements. The ingredient multiplier applies once to the complete original recipe.

These proportions describe unbaked batter, not the cake's rise or doneness. Pan material, shape and batter depth can change baking behavior. The ingredient multiplier is not a baking-time or temperature multiplier, and matching the starting depth does not guarantee the same finished height. Follow the recipe's temperature and doneness guidance rather than scaling its baking minutes.

How to Use This Tool:

Describe the pans used by the complete original recipe and the replacement pans you plan to fill. Results update as you change the measurements.

Choose the original and target pan shapes, then enter the inside base dimensions. Use diameter for a round pan, one side for a square, and length plus width for a rectangle or oval. Each measurement accepts cm or in; changing its unit converts the existing number.
Enter Original pan count and Target pan count. Each group must contain pans with the same shape and dimensions. The original count is the number filled by the recipe as written.
Open Advanced and enter both inner wall heights, Original batter fill and Target fill limit. Replace the illustrative 5 cm wall heights and 60% fills with measurements and recipe-appropriate levels. These values affect the depth and capacity comparison even when you choose area-based scaling.
Choose Equal depth to preserve the original unbaked batter depth, or Target capacity to make enough batter to reach the replacement pans' chosen fill limit. The latter may change the batter depth.
Check the Recipe multiplier and fill-limit message before applying the factor to your ingredients. In Conversion plan, compare Scaled target batter depth with the intended level and use Batter per target pan to divide the batch.
If Check pan inputs replaces the multiplier, correct the first reported field. The wall heights and fill percentages in Advanced must also be valid, even when that section is closed.

Interpreting Results:

Selected recipe multiplier describes the whole batch. A value above 1 means more of the original recipe, a value below 1 means less, and 1 means unchanged ingredient quantities. The calculator supplies that factor rather than editing an ingredient list. Its millilitre values estimate batter volume from the entered pan dimensions and fill level; they are not measurements of the recipe's actual yield.

Scaled target batter depth is the depth after applying the multiplier. Target depth without scaling instead spreads the unchanged original batch across the target pans. Neither number describes the finished cake.

Space below target fill limit is a signed volume measured against your chosen usable capacity, not against the rim. A positive value leaves spare volume below that level; a negative value means the batch exceeds it. Zero can still leave physical space above the batter, as in a pan filled to 60% of its wall height. At fill limit is the expected outcome of Target capacity scaling, not independent confirmation that the chosen fill percentage suits the recipe.

For Above fill limit, use deeper pans, reduce the actual batch, or select Target capacity to calculate a batch for the chosen level. Do not raise the fill percentage just to clear the warning. Adding more identical target pans while retaining Equal depth also increases the calculated batch, so it does not lower the planned depth in each pan.

Technical Details:

A straight-sided pan has a constant horizontal cross-section. Its volume therefore follows base area multiplied by depth. Using total base area makes the same calculation work for one pan or several identical pans, without assuming that the whole pan should be filled.

Pan area, batter depth and recipe scaling

First calculate the inside base area a of one pan. The oval model is an ellipse, with length and width measured across the full shape rather than from its centre.

Base-area formulas for the four supported pan shapes.
Shape	Area of one pan	Measurements
Round	$a = \frac{π d^{2}}{4}$	`d` is the inside diameter.
Square	$a = s^{2}$	`s` is one inside side length.
Rectangle	$a = L \times W$	`L` and `W` are inside length and width.
Oval	$a = \frac{π L W}{4}$	`L` and `W` are the ellipse's full inside axes.

For each group, multiply one pan's area by its count n to obtain total area A. Multiplying by inner wall height H gives that group's brim capacity C.

A = n a C = A H

Subscripts o and t mean original and target. Each fill fraction f is the entered percentage divided by 100. The original batter depth is b_o, and the target fill-limit depth is b_lim. These determine original recipe batter volume V_o and target usable capacity U_t.

\begin{array}{l} b_{o} = H_{o} f_{o} b_{lim} = H_{t} f_{t} \\ V_{o} = A_{o} b_{o} U_{t} = A_{t} b_{lim} \end{array}

The equal-depth multiplier M_d compares total base areas. The capacity multiplier M_c compares the target's chosen usable volume with the original batter volume, not simply the two brim capacities.

\begin{array}{l} M_{d} = \frac{A_{t}}{A_{o}} \\ M_{c} = \frac{U_{t}}{V_{o}} = \frac{A_{t} H_{t} f_{t}}{A_{o} H_{o} f_{o}} \end{array}

Use M_d as the selected multiplier M for Equal depth, or M_c for Target capacity. The two factors agree when original batter depth and target fill-limit depth agree. Wall heights and fill percentages do not change the equal-depth factor, although they still determine volumes and whether the planned depth fits.

Multiplying the original batter volume by M gives scaled batch volume V_s. Divide by target count n_t for batter per target pan V_pan. Dividing scaled or original volume by total target area gives scaled target batter depth b_s or target depth without scaling b_u.

\begin{array}{l} V_{s} = V_{o} M V_{pan} = \frac{V_{s}}{n_{t}} \\ b_{s} = \frac{V_{s}}{A_{t}} b_{u} = \frac{V_{o}}{A_{t}} \end{array}

The remaining volume R is Space below target fill limit. The allocation P is Batch share per target pan, expressed as a percentage of the scaled batch.

R = U_{t} - V_{s} P = \frac{100}{n_{t}}

To apply the result to an ingredient, multiply its original quantity q_o by the selected factor. Its scaled quantity q_t stays in the same ingredient unit.

q_{t} = M q_{o}

Fill-limit comparison

Fit compares the unrounded scaled target batter depth with the target fill-limit depth. A tolerance ε of 0.000000001 cm prevents tiny numerical differences from being treated as a meaningful mismatch.

Exact conditions for the three fill-limit messages, including the numerical tolerance.
Message	Condition
Below fill limit	$b_{s} < b_{lim} - ε$
At fill limit	$b_{lim} - ε \leq b_{s} \leq b_{lim} + ε$
Above fill limit	$b_{s} > b_{lim} + ε$

This tolerance is not an allowance for inaccurate measurements or cake rise. Two depths that look identical after display rounding can still fall on opposite sides of the chosen limit.

Units, accepted ranges and precision

Inch measurements are converted using exactly 2.54 cm per inch. Areas are reported in cm², depths in cm and volumes in mL, because one cubic centimetre equals one millilitre. These output units remain the same when the entered dimensions use inches. Multipliers are dimensionless.

Inclusive input limits after converting lengths to centimetres.
Input quantity	Minimum	Maximum	Unit or requirement
Inside diameter, side, length or width	0.1	254	cm
Inner wall height	0.1	50.8	cm
Pan count in each group	1	20	Whole pans
Original fill and target fill limit	1	95	%

Both endpoints are accepted. These are input limits, not recommended pan sizes or filling levels. Width is needed separately only for rectangles and ovals.

Calculations retain unrounded values. Ordinary quantities display up to two decimal places, and multipliers up to four. Nonzero quantities with a magnitude below 0.01 use scientific notation with three digits after the decimal point; positive multipliers use that notation below 0.0001. Rounded per-pan amounts may not sum exactly to the rounded batch total. Display precision does not make the entered measurements more accurate.

Where the geometry applies

The model assumes straight walls, a level batter surface and identical pans within each group. An oval is treated as a true ellipse, not a rounded rectangle. Tapered, Bundt, tube and irregular pans need measured usable volume rather than these base-area formulas; there is no direct measured-volume input here. Ingredient scaling also assumes the same recipe proportions produce proportionally more or less batter. No batter density, finished-cake expansion or serving-size model is included, so a volume in mL is not an ingredient weight in grams or a serving count.

Worked Examples:

A 20 cm round recipe in a 24 cm round pan

For one pan on each side, Equal depth, 5 cm walls and 60% fills, the base areas are approximately 314.16 cm² and 452.39 cm². Their ratio gives a recipe multiplier of 1.44×. The estimated 942.48 mL original batch becomes 1,357.17 mL at the same 3 cm batter depth. An ingredient originally weighing 250 g therefore becomes 360 g. This is 44% more batter, not the 20% increase suggested by comparing diameters alone. Keeping the original batch unchanged would instead give a target depth of about 2.08 cm.

A wider pan with only 2 cm walls

Keep the original 20 cm round pan, 5 cm wall height and 60% fill, but give the 24 cm target pan a 2 cm wall and a 60% fill limit. Equal depth still calls for 3 cm of batter and reports Above fill limit. Selecting Target capacity changes the multiplier to 0.576× and the estimated batch to 542.87 mL. Its depth is 1.2 cm, exactly the chosen fill-limit depth, so the message becomes At fill limit. The wider but shallower pan calls for less of the original recipe under these assumptions.

Two oval pans replaced by three round pans

Suppose the original recipe fills two elliptical pans measuring 30 cm by 20 cm, and the replacements are three round pans with 24 cm diameters. With 5 cm walls, 60% fills and Equal depth, total base areas are approximately 942.48 cm² and 1,357.17 cm². The multiplier is 1.44× for the complete two-pan recipe. The scaled batch is approximately 4,071.50 mL, with 1,357.17 mL per target pan at 3 cm depth. Each target pan receives one third of the batch, displayed as 33.33%; multiplying the original recipe by three again would overcount the target pans.

References:

NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically, National Institute of Standards and Technology, August 18, 2025.
The essential alternative baking pan sizes, King Arthur Baking, April 23, 2019.