This is the full explanation of how to scale a recipe to a different diameter tin BUT same height tin.
Calculate the area of each tin: Pi x r²
Divide the area of the tin you want to use into the area of the pan size in the recipe.
The product will give you the multiplier.
Multiply the weight of each ingredient with the multiplier to determine the amount of each ingredient to use.
Since this recipe is written for two tins, and you only want to bake one tin, you will have the added step of dividing the weight of each ingredient in half, then apply the multiplier.
Step by Step instructions:
Step 1: find the radius by dividing the diameter of the circle.
20 cm tin / 2 = 10 cm
30 cm tin / 2 = 15 cm
Step 2: Square the radius (r²)
10 cm x 10 cm = 100
15 cm x 15 cm = 225
Step 3: multiply r² by Pi
(Pi = 3.14)
3.14 x 100 = 314 (area of pan in recipe)
3.14 x 225 x 1 = 706 (area of pan you want to use)
Step 4: Divide the area of the pan you want to use into the area of the pan in the recipe.
706/314 = 2.248
Round up to 2.25
The multiplier is 2.25.
ADDED STEP because you only want to bake one tin: divide all the ingredients in the recipe in half
225g plain flour / 2 = 112.5
350g caster sugar / 2 = 175g
Repeat with all the ingredients
Note on leavening, vanilla and eggs:
Convert the amount of leavening and vanilla from volume measurement to weight. Then divide the weight of the leavening (vanilla) in half because you want to use one tin.
Baking POWDER
1 tsp baking POWDER = 3g
1 1/2 tsp baking powder x 3 = 4.5 g
4.5g / 2 = 2.25g for one tin
Baking SODA
1 tsp baking SODA = 6g
1 1/2 tsp baking SODA x 6g = 9g
9g / 2 = 4.5g for one tin
Vanilla extract
1 tsp vanilla extract = 4g
2 tsp vanilla extract x 4g = 8g
8g / 2 = 4g for one tin
EGGS:
This recipe does not specify the size of the egg. I do not know how eggs are graded in the UK, so no clue as to what the average weight of an egg typically used in baking for recipes formulated in the UK. In the US most recipes call for large eggs. The weight of a large egg in the US for baking is 50g WITHOUT the shell. So weight the type of egg you typically use in baking to determine the weight. Divide the weight of the two eggs in half since you want to bake one cake. Then multiply the weight of the egg with the multiplier.
STEP 5: multiply the weight of each ingredient with the multiplier.
112.5g plain flour x 2.25 multiplier = 253g plain flour
175g caster sugar x 2.25 multiplier = 393.75g
2.25g baking POWDER x 2.25 multiplier = 5g baking powder
3g Baking SODA x 2.25 multiplier = 6g baking SODA
4g vanilla extract x 2.25 multiplier = 9g vanilla extract
Repeat Step 5 with the weight of all ingredients.
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Regarding baking time. Bake to internal temperature NOT time.
Approximately 20 minutes into baking look at the cake. If it had risen to the top of the tin or close to it AND it looks set in the center, lightly touch the center of the cake. If the finger imprint remains, continue baking and perform the touch test every five minutes.
If the finger imprint springs back up, then use an instant read Thermometer to check the internal temperature in the CENTER of the cake.
Bake until internal temperature is between 96°C (205°F) - 100°C (210°F).
Do not let the cake reach a temperature beyond 210°F (99°C). Beyond this temperature and too much will evaporate and the cake will be dry.
You cannot bake by time because every oven performs differently. In addition the type of tin used affects the rate of baking.
Beware of baking tins made of dark metal. The dark color coating on the tins conduct heat much more intensely than a natural metal cake tin. The batter in contact with the metal will bake and set way faster than the center. This produces a cake with a very dry, thick tough crust and a dry crumb in the center.
These tin also cause the cakes to rise higher in the center and crack. The reason being is the batter in contact with the tin sets to soon. The leavening in cake batter continues to create rise in the center of the cake as it’s baking at a slower rate. As the center rises above the outer edge of the cake it cracks open. It’s like a volcano effect.
Anodized aluminum also conducts heat much more intensely than a natural metal tin. So it will also produce a dark, dry tough crust.
The rule with dark metal coated tins and anodized aluminum is to reduce the oven temperature by 15°C (25°F)
Fan forced ovens also bake hotter as the fan circulate the heat all around the tin.
This recipe has a baking temperature of 160°C (320°F). This is a pretty good baking temperature. I bake most of my cakes at this temperature in a conventional oven. And I use natural metal pans.
If you are going to use a dark metal tin Or anodized aluminum AND the oven fan, You can probably still bake at the temperature noted in the recipe. But keep a close watch on the cake.
Ganache
The recipe makes a total of 400 g ganache (200 g chocolate +200 g double cream = 400 g)
So the recipe uses 200g ganache per 20 cm (8 in) layer. That’s pretty much the standard.
Divide the cake size you are going to make into the cake size from the recipe.
30 cm / 20 cm = 1.5
1.5 is your multiplier
200g ganache times 1.5 = 300g ganache
Recipe for ganache is a 50-50 blend of chocolate and double cream. To make 300 g of ganache simply divide it by 2
For 300g ganache use:
150g chocolate
150g Double cream
