Friday, 17 May 2013

How to adjust a cake recipe for different sized tins

Picture from the awesome web comic xkcd.com


Picture this - you've got a recipe for a gorgeous sounding cake, you've got the ingrediants to make it, the time to give it your full attention, the burning desire for something sweet.... the one thing you don't have is the correct sized tin.  So what do you do?  Do you give up on the idea or do you have a go at reducing the recipes quantities?  But how much by?  Do you use an educated guess or do you go for something a bit more precise?  It may seem a bit of a daunting task but by using Science! (or at least maths) it's one that's surprisingly easy to accomplish.  All it needs is a tape measure, a calculator and a piece of paper.

For this example I'm going to use a simple Victoria Sponge recipe.  This recipe calls for the use of two round 20cm sandwich tins.  However seeing as it's just going to be myself, my husband and our son who'll be eating it I don't want to make that much cake.  I could use the recipe to make cupcakes I suppose but it's just not the same.  Instead I'm going to use a couple of very dinky little cake tins that I picked up in our local pound shop.  The recipe calls for

225g caster sugar
225g butter
4 eggs
225g self raising flour

but obviously that's going to be way too much mix for the little tins I have.  So how do I go about reducing the recipe?

The first thing to realise is that it's all about volume.  If that recipe is meant for two 20 cm tins then the first thing to do is work out the volume of the tins.

1 Measure the inside of your cake tin.  This is the diameter.  Half it and you'll have the radius (r) of the tin

2 Measure the depth (d) of the tin.

3 Now comes the maths.  First you need to work out the area of the tin.  To do this you need to use the basic formula of 3.14 x (r x r) which in the case of a 20 cm cake tin is 3.14 x (10 x 10) which gives us an answer of  314.

4 You then need to multiply this by the depth of the tin to work out the volume of the cake tin needed.  So it'd be 314 x 4 which is 1256.  Because the recipe calls for 2 cake tins the total volume of the cake is 2512

5 I repeat this process with the smaller cake tins I will be using.  These are 12 cm in diameter, 4 cm deep.  So the maths is

Area of the circle - 3.14 x (6 x 6) = 113

Volume of the cake tin - 113 x 4 = 452

Volume of 2 cake tins - 452 x 2 = 904

6 Since 904 is approximately 1/3 rd of 2512  I will need to use 1/3 of the amount of mixture (in this case I'd have a bit of mixture left over which I'd probably turn into a couple of cupcakes)  The new recipe is thus

75 g caster sugar
75g butter
2 eggs (it'd be nearly impossible to get 1/3 of 4 eggs so I'll use two)
75g self raising flour

This method can not only be used to scale down recipes but also scale up.

Now that's all very well and good for round cakes but what if you only have a square tin?  Well that can be worked out fairly easily as well.

1 Measure the height (h) depth (d) and width (w) of your tin.  Now all you have to do is h x d x w.  Which in the case of my 18 cm square tin is 7.5 x 18 x 18 = 2430

Hope that wasn't too scary and if you have any questions about the maths please ask!

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