## Basic math question... How to change the hydration in a starter?

OK, my mother starter is 100% hydration. For a recipe I am working on, I want to use a 70% hydration starter.

If I start with 150 grams of 100% starter, how do I build this to 450 grams of 70% hydration starter? The math escapes me. The problem is that the 70% figure isn't 70% of 450, but 70% of the total flour weight. However, how do I arrive at the total flour weight? It would seem a simple problem, but none of the figures I am coming up with work.

I know that 100% hydration starter is 50% flour and 50% water. A 70% hydration starter should be 42.8571% water (100/70). This doesn't work, however. Obviously, I am miscalculating.

**Understand that I am not asking what the total flour weight is in 450 grams of 70% hydration flour, but how to arrive at that figure.**

I would gladly do a search, but I have no idea how to word this in search terms.

After posting this, I remembered what Peter Reinhart wrote in The Bread Baker's Apprentice:

Total flour weight = total weight / total percentage.

TFW = 450 / 1.70 (170%) = 265 +-.

So, 450 grams of 70% hydration starter would be 265 grams flour and 186 grams water. That is actually 451 grams, but I would need a scale that measures in fractions of a gram to get this perfect. The extra is better anyway as some with inevitably stick to the bowl.

450 grams at 70% hydration is 264 grams of flour and 185 grams of water. You currently have 150 grams of 100% starter which is 75 grams of flour and 75 grams of water. Subtract the 75 grams of flour from the 264 and subtract the 75 grams of water from the 185 grams of water. This means you have to add 189 grams of Flour and 110 grams of water.

Hope this helps,

Randy

In baker's maths, a 100% hydration starter has 100% water and 100% flour.In baker's maths, a 70% hydration starter has 70% water and 100% flour.

The total weight of the 70% starter therefore is 170% (of the flour weigh).

This means, in a 70% starter, you'll have (70 / 170 =) 41,17% of water compared to the total weight of the starter. This is close enough to your result that it might have confused you. It confused me as I was estimating in my head if your calculation could have been right.

Now you want 450g of sourdough. This is about 185g of water and 265g of flour (which is 69.8... % hydration).

Now, let's say, you want about 15% of the flour as starter. Overall formula:

Mix it, let it ferment for 12 to 18 hours, and you'll get 450g of 70% sourdough/starter/levain/leaven, ... :)

I would start with 140 grams of 100%-hydration starter. Why? Because it contains 70 grams of water, so you know that there needs to be 100 grams of flour for that amount of water to get to 70% hydration. The starter contributes 70 grams of flour, so add 30 grams of flour. Now you have 170 grams of 70% starter. To build up from there, just add the amount of flour and water needed in the proper ratio.

The simplest way would be to make 510 grams of starter (since 3*17=51). Add 200 grams of flour and 140 grams of water to the 170 grams of starter. I usually make a little more starter than a recipe calls for because you invariably lose some stuck to the bowl and utensils.

That would have been smart! *hangs head in shame*

Well, why does the recipe call for a 70% starter in the first place? It has different characteristics in taste and creates a different balance between yeast and bacteria.

This is why I would built a fresh starter with a smaller part of the old one as seed. If it is just about the hydration, of course, you can use more of your old starter and just adjust the hydration with either water or flour.

Well, I am new to sourdough, so I am probably doing this wrong. As I stated, my mother starter is 100%. I am trying to convert the 100% starter to a firm (if 70% can be considered "firm") starter before addition to the final dough. I am starting with 150 grams of 100% starter and building that into 450 grams of 70% starter over the course of two days.

If I am doing this incorrectly, please let me know why and what would be the correct method. Right now, everything I am doing is an experiment, as I am completely phasing out my use of commercial yeast. This is new and uncharted territory for me!

As to the math question, I answered it myself, or rather, Peter Reinhart did, in my reply. Still, thanks everyone for the help!