October 12th, 2010

Cake pan size conversion ~ The formula ~

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One of the many baking questions I get asked is how to scale a cake recipe to fit another size or shaped pan.
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There is an universal formula you can use:
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(volume of the preferred tin) ÷ (volume of the original tin)
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For this, you need to find out the volume of the two tins.
The formulas to work out the volume of a pan according to shapes are the following:
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ROUND
(3.14 x half the diameter x half the diameter x height)
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SQUARE or RECTANGLE
(length x width x height)
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NOVELTY CAKE TIN
First work out the volume of tin by weighing how much water goes in. Water is 1g = 1 cm³
(The mass of 1 cubic centimetre water at 3.98°c equal to a gram. (it’s the temperature at which it is at maximal density roughly). So we can use that number you’ve weighed as the measure of volume.
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MULTI-CAVITY TIN (like a muffin pan)
Again, work out the volume by pouring water in one cavity, & multiply that with how many cavities there are. Weigh it in grams, & use that number as the volume.

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Here are two examples:

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To convert from an 8″ ROUND cake tin (with 2″ height) to 10″ ROUND cake tin (with 3″ height) you’d do this:
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(3.14 x half the diameter x half the diameter x height) ÷ (3.14 x half the diameter x half the diameter x height)

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(3.14 x 5 x 5 x 3) ÷ (3.14 x 4 x 4 x 2) = 2.34375
So here we now know that we need to multiply the recipe by 2.4 times.
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But if the height of the pans are the same, use this simpler formula:
(dimension of preferred tin ÷ dimension of original tin) x (dimension of preferred tin ÷ dimension of original tin)
For example,
(10÷8) × (10÷8) = 1.25 x 1.25 = 1.5625
So here we now know that we need to multiply the recipe by 1.6 times.
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To convert an 8″ ROUND cake tin A to 10″ SQUARE cake tin B (when height is the same):
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(length x width) ÷ (3.14 x half the diameter of A x half the diameter of A)

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(10 x 10 ) ÷ (3.14 x 4 x 4) = 1.99
So here we now know that we need to multiply the recipe by 1.99 times. (I like to round it to 2)
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Please note:

– If both tins in question are of same height, you don’t need to measure the height for each.
– The examples are in inches, but of-course the same formula works in centimeters too!
– When I get long answers like 1.5625, I personally like to round it UP to 1.6.
– Although the oven temperature should remain the same for both occasions, the baking-time will change.
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It’s all probably elementary bit of maths for you all, but for me it certainly isn’t! There is a reason why I’m a baker & not a mathematician…