## Baker’s math – a handful of practical examples

A bit of number crunching is a baker’s daily business. Here are a few calculations I feel myself forced to use rather frequently (except the last one, which is more of a very theoretical nature). Note that these calculations do not work for volumes like cups (or handfuls, gills or shovels) but only for weight / mass measures. I like to use g and kg, but if you prefer ounces, stones, atomic mass or any weight unit, fine. Weight reflects the number of molecules of the ingredients that connect with each other. Volume doesn’t.

### Straightforward scaling, etc.

**1. How do I calculate the hydration of a dough? **

**Answer: ** Hydration is given by weight of water to weight of flour (and all other dry mass that will bind water except salt and yeast). Example: The recipe uses 600g of flour and 400g of water. The hydration is 400 / 600 = 2/3 = 0.666… = 67%. Note that liquids in general are not 100% water. Full fat milk for example has about 87% of water. When calculating hydrations, you have to take this into account where large amounts of it are used.

**2. I got a recipe from the internet that uses X grams of flour but I want make a loaf using Y grams flour. How to fix this?**

**Answer:** Scale every ingredient with factor X / Y. Example: The recipe calls for 700g of flour, but you want to use 500g of flour. Multiply every weight in the recipe with 500 / 700 = 5 / 7 = 0.71…

**3. I made a dough with a hydration of X %. If I use Y lb. of flour, how much dough will I have not taking into account salt, yeast and all other small quantities?**

**Answer: ** You will have exactly (1 + X/100)*Y lb. of dough. Example: Hydration is 68% and 1 lb. of flour is used. This will yield 1.68 * 1 lb = 1.68 lb. = 1 lb. 10.9 oz. = 762g of dough.

### More hydrations

**4. I have a recipe here that uses a hydration of X %. I want to have exactly Y kg of dough, neglecting salt, yeast and other small quantities. How much flour do I need?**

**Answer: ** You will need Y / (1 + X/100) of flour. Example: Recipe has hydration of 70% and you want to make 300g of dough. Flour needed is given by 300g / 1.7 = 176.4g.

**5. I wanted to make a dough with X % hydration and used Y g of flour. Now I accidentally added Z g of water, which is way too much. Since I can’t take out the water, how much flour do I add now to get the correect hydration?**

**Answer: ** You will have to add (Z / X) – Y of flour. Example: 500g of flour is in the bowl and you want 65% hydration. You accidentally added 430g of water, which is too much. Then you must add (430g / 0.65) – 500g = 162g of flour.

### Further playful examples

**6. During baking dough for a medium-sized loaf of bread will lose 20% of its own weight. I am using a hydration of X % and need the baked loaf to weigh Y g. How much flour do I need for such a loaf?**

**Answer: ** You will need (1 / 0.8) * Y / (1 + X/100)) lb. of flour. Example: You want 750g loaves and are using a hydration of 71%. You will need (1 / 0.8) * 750g / 1.71 = 548g of flour.

**7. I want to test the effect of a specific ingredient on height of finished loaf of bread baked in a rectangular tin (which then is a measure for dough volume). I have made 8 different loaves using the following quantities of the ingredient: 0%, 2%, 4%, 6%, 8%, 10%, 12% and 14%. I have measured the height and have the feeling the greatest height is somewhere in the middle, but where is it exactly?**

**Answer: ** If the greatest height is somewhere in the middle you probably have results like shown in the picture below. Even with such a small amount of samples it is possible to graphically determine the maximum by drawing the resulting curve. In this case the best bread volume would be at around 5% of the ingredient.

Cool article

Here’s another one for you: how would I calculate total (overall) hydration of my dough, if I am using a starter with a different hydration?

Let’s say my starter hydration is 100% (1:1 flour-to-water).

I am using 25% starter (by weight of flour in dough).

I am hydrating my dough at 50%.

What is my total hydration?

Sorry, the math is killing me tonight… :( Thx for your help!!!!

cranbo29 May 2010 at 13:25

25% of starter at 100% is 12.5% water and 12.5% flour. The total hydration then is given by

(50 + 12.5)/(100 + 12.5) * 100 % = 55.55… %

Thanks, I think I will addd something similar to the post

theinversecook29 May 2010 at 14:57

I quite like calculating these maths ! :-P

Nat9 June 2010 at 15:42

Really? Me too, but I’m really bad at doing them in the head.

theinversecook9 June 2010 at 16:01

I only use calculator, haha, except some simple calculations like dividing a weight of 3 loaves into 1. But I do think these conversions are one of the interesting parts in making bread. O I just remember you blogged about how much the length of a bread should increase for doubling in size. For a boule it’s 2 to the power 1/3 right? Really useful and should be highly promoted!! I believe not many people thought about it.

Nat10 June 2010 at 11:20

I wish I had a calculator in my scale. If the boule is approximated by perfect symmetry of a sphere, 2^(1/3) is right, I think.

I totally agree. The sentence

Let the dough double in size.is ambiguous.

theinversecook12 June 2010 at 16:02

that’s great really is the best thnig that i can see in this sites

recette tiramisu frameboise13 April 2011 at 00:49