PizzaSuperFreak,
Rather than just give you the answer to your downsizing question, I will show you how to calculate the amount of dough and the quantities of ingredients you will need to make a dough ball for a 10-inch pizza. You used volume measurements, which will entail a few more steps, but that just means a bit more work.
To begin, let's first calculate how much dough you will need for the 10-inch pizza. The calculation is simple. The expression for doing this is:
W = 3.14 (or Pi, the Greek letter) x R x R x TF,
where W is the weight of the amount of dough needed, R is the radius of the pizza to be made from that weight of dough (in our case, R = 10/2 = 5), and TF is the thickness factor. For a thin NY style pizza, the TF value that is most commonly used is 0.10. So, solving for W in the above expression, we get W = 3.14 x 5 x 5 x 0.10, or 7.85 oz. as the weight of the dough ball you will need to make a 10-inch pizza. Unfortunately, that number alone doesn't tell us how to determine how much of each of the ingredients to use to make that 7.85 oz. dough ball. For this, we need baker's percents. Since your recipe uses volume measurements, they have to be first converted to weight measurements.
To do this, I took your original recipe and weighed the KA bread flour and the water, and for the rest of the ingredients I used conversion factors to convert from volume measurements to weight measurements since my scale can't weight the very light ingredients. For purposes of the exercise, I left out the VWG, although if it were to be used, it too would have an assigned baker's percent. I also weighed some larger quantities of regular salt and Kosher salt (my brand is Morton's) and found that they were pretty much equal in weight. So, it shouldn't matter much which form of salt is used in your recipe for the 10-inch case. For the weight of water, I used 8.33 oz. per cup, which is the standard conversion factor and more accurate than actually weighing a cup of water (which I did anyway just to see if there was a significant difference). Taking your recipe, the weights come out as set forth below. The weights won't be super accurate simply because the volume measurements are not accurate measurements. I have intentionally carried the calculations out to several decimal points so that you can see the actual numbers when you use your own calculator:
2 3/4 c. KA bread flour = 13.15 oz.
1 c. water = 8.33 oz.
1 t. salt = 0.196875 oz.
3/4 t. olive oil = 3/4 x 0.1645833 oz., or 0.1234374 oz.
1 t. ADY = 0.133333 oz.
Now, if we add up all the weights from the above recipe, we get a total of around 21.94 oz. That is the weight of the dough ball you would use to make the 16-17 inch pizza that I referenced in my earlier post. To downsize the recipe to use for our 10-inch pizza, we will need the baker's percents. Let's start with the flour. For baker's percent purposes, the flour is always assigned 100%. All of the other baker's percents for the recipe key off of that number. So, for the baker's percent for water, we divide the weight of the water (8.33) by the weight of the flour (13.15), and that gives us 0.63346, or roughly 63%. That is the magical "hydration" number you read so much about. Dividing the weights of each of the rest of the ingredients in the recipe by the weight of flour, we get the following baker's percents table (where I have rounded out to two places for the sake of simplicity):
KA bread flour, 100%
Water, 63%
Salt, 1.5%
Olive oil, 0.94%
ADY, 1%
Now we are ready to calculate the amounts of each of the ingredients for the 7.85 oz dough ball for the 10-inch pizza. To do this, we first add up all of the baker's percents. In our case, the sum of the baker's percents (100 + 63 + 1.5 + 0.94 + 1) comes to 166.44. To simplify the further calculations, we divide that number by 100, and this gives us 1.6644. The first thing we do with that number is to divide it into 7.85. That gives us the weight of the flour to be used in the 7.85 oz. dough ball, or 4.7164143 oz. To calculate the amounts of the remaining ingredients, all we have to do is multiply the weight of flour by each of the baker's percents listed in the above table. So, for example, the weight of water is 4.7164143 x 63%, or 2.971341 oz. Doing the same calculations for the remaining ingredients, we get the following (again I have rounded the numbers to two places):
KA flour (100%), 4.72 oz.
Water (63%), 2.97 oz.
Salt (1.5%), 0.07 oz.
Olive oil (0.94%), 0.04 oz.
ADY (1%), 0.05 oz.
You will note that if you add up all the above weights, they come to 7.95 oz. Unfortunately, we are not out of the woods yet. Unless one has a Frieling scale that can weigh very light ingredients, we have to convert the weights of salt, olive oil and ADY to volume measurements. One teaspoon of salt weighs 0.196875 oz., one teaspoon of olive oil weighs 0.1645833, and one teaspoon of ADY weighs 0.133333 oz. (these are all numbers that Steve and others at this site came up with some time ago). Dividing each of the weights set forth above by these respective numbers, we end up with the final recipe, as follows:
KA bread flour (100%), 4.72 oz.
Water (63%), 2.97 oz.
Salt (1.5%), 0.36 t., or a bit over 1/3 t.
Olive oil (0.94%), 0.24 t., or about 1/4 t.
ADY (1%), 0.375 t., or 3/8 t.
To convert the flour and water to volume measurements to benefit those who do not have scales or digital scales, I often measure out the weights of flour and water using my digital scale and convert back to volume measurements using measuring cups and spoons. In this case, the 4.72 oz. flour becomes about 1 c. plus 2 T., and the 2.97 oz. of water becomes about 3/8 c.
And there you have it. You will have to do some experimenting with all these numbers since they started out as volume measurement. Also you will have to make adjustments to kneading times and bake times and temperatures.
Peter
