How this calculator works
A cake pan is a simple container, so its capacity is the area of the base multiplied by its depth. A round pan uses the area of a circle, pi times the radius squared, and a square or rectangular pan uses length times width. Two pans of the same capacity can still bake differently: a wide shallow pan exposes more batter to the oven and browns faster, while a narrow deep pan insulates the centre. The multiplier here matches batter volume, which is the first step in scaling a recipe. Keep an eye on the batter depth, and adjust the baking time if it changes much.
Formula
round pan volume = pi x (diameter / 2)^2 x depth. rectangular pan volume = length x width x depth. recipe multiplier = new pan volume / original pan volume. For example, an 8 in round pan 2 in deep holds 3.14 x 10.16^2 x 5.08 = 1,647 mL.
Worked example
A recipe is written for a 9 in round pan 2 in deep, with a capacity of 2,085 mL. You want to use a 9 x 13 in rectangular pan 2 in deep, which holds 3,834 mL. The multiplier is 3,834 / 2,085 = 1.839, so every ingredient is multiplied by about 1.84. The batter is shallower in the rectangular pan, so start checking earlier than the original time.
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Frequently asked questions
Can I swap an 8 in round pan for a 9 in round pan?
A 9 in round pan holds 26.6 per cent more than an 8 in pan of the same depth, so the recipe needs a 1.27 multiplier. If you keep the original quantities, the batter will be shallower and the cake will bake faster and may be drier. Matching volume is the reliable way to swap pans.
How many cups does a standard cake pan hold?
An 8 in round pan 2 in deep holds about 7.0 US cups, a 9 in round 2 in deep about 8.8 cups, and a 9 x 13 in pan 2 in deep about 16.2 cups. The table above uses the exact US customary cup of 236.588 mL.
Does pan colour or material change the result?
Yes. Dark non-stick pans absorb more radiant heat and can brown the base too quickly, so many bakers lower the oven temperature by about 10 to 15 °C. Glass and ceramic pans heat more slowly. The capacity calculation is unaffected, but the baking time and temperature may need adjusting.
How full should I fill a cake pan?
Most cake recipes fill the pan between one half and two thirds full, leaving room for rise. If the converted batter would fill the new pan more than about two thirds, bake the excess in a second smaller pan or reduce the recipe rather than risk a spill.