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final hydration formula

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cranbo's picture
cranbo

final hydration formula

I'm no math whiz, but I'm trying to figure out my overall hydration, and could use some help with the math.



Let's assume I have 1000g of dough
700g (70% of dough) is at 55% hydration
300g (30% of dough) is at 100% hydration (my starter)


What would my total dough hydration be?


 


 

AnnaInMD's picture
AnnaInMD

took awhile, heh

cranbo's picture
cranbo

Hi AnnaInMD


Thanks! My question is how did you figure it out?


I ended up building a spreadsheet to enable me to do similar calculations. Really what I was looking for was a way to determine overall hydration when you are using a range of pre-ferments (like firm sourrdough starter, scrap dough, biga, poolish, etc)


It looks like this:


Overall hydration calculation sheet


 


To use it:
First, I type in all your bakers percentages in Column B
Next, I enter initial flour weight in yellow box in Column D
Then, I enter hydration percentages for each starter in the "Hydration" column (Column C)

For each starter, my spreadsheet calculates flour + water amounts to create that hydration percentage.


I total the flours in the dough & starters ("Flour Total" in pink), as well as the liquids ("Water Total" in blue)

Water Total / Flour Total = Overall Hydration (pictured in green box)


Yay!


Hope this helps someone else that's feeling as math-challenged as I am right now :) And please let me know if my math is wrong.

AnnaInMD's picture
AnnaInMD

700(.55) + 300(1.00) = 1000X


385 + 300 = 1000X


685/1000 = X


68.5 = X


 


:)

tgrayson's picture
tgrayson

It doesn't take algebra, just grade school math:


 


.70(55) + .30(100) =  68.5


 


 

Daisy_A's picture
Daisy_A

Hi AnnaInMD,


I found cranbo's question relevant, as I am faced with having to work out similar things at the moment. Please, what steps did you go through to get this answer? Is there some kind of formula or equation to use? I am getting better at hydration but it really is challenging my maths. at the moment to combine multiple hydrations.  With thanks, Daisy_A

Candango's picture
Candango

Unless my understanding of this is way off, I show the final hydration should be about 66%.  OK, How to get there?  As follows.


Start with your two known amounts, Starter (300 g of 100%) and rest of dough (700g at 55%).  SO total dough is 1000g at x% hydration.


First, the starter:  A = flour, B = water.  With 100% hydration, A=B.


So 2 A = 300 g.  A = 150 g flour; B = 150 g water.


 


Second, the rest of the dough.


B + A = 700 g.


B (water) = 55% A (flour). 


So A + .55A = 700 g.  1.55 A = 700.  A = 700/1.55.  = 452 g.


B = 700 - 452 = 248 g


As a proof, divide 248 by 452, getting 54.8% (close enough)


 


Now add the water: 248 + 150 = 398


And the flour: 452 + 150 = 602


Adding these gives you the final dough of 1000 g


For the final hydration, divide the water (398) by the flour (602) and get 66%, unless I goofed somewhere along the line.  It would be nice to have a spreadsheet program to figure this out, and if I did it on a regular basis, I would look into one, but the challenge of figuring ir out is part of the Fun (?), no?


 


 

Daisy_A's picture
Daisy_A

Thanks candango - great to have the maths.


I can now work out overall dough hydration when I have the total formula worked out by counting the flour and water rates of all soakers, starters etc. so I can divide total water by total flour. Only been able to do this in the past couple of weeks.


However estimating potential hydration at the interim stage like this was beyond me. Obviously it is good to be able to do this before working out the total formula as it may govern which starter is used (I have both liquid and stiff). Spreadsheets are useful but I don't want to go into the computer everytime and I would like to be able to do the calculations, so will study your example here. Thanks again, Daisy_A

davidg618's picture
davidg618

David G

ananda's picture
ananda

Hi Daisy_A,


Decide on your final desired hydration.


Look at your starters, soakers, etc and calculate how much water they account for.


Take that away from your final hydration figure.


The figure you are left with is the amount of water still needed to give you the correct hydration in your overall dough formula.


Best wishes


Andy

Daisy_A's picture
Daisy_A

Thanks Andy,


This is actually what I want to do and why I'm interested in the maths. Will try working backwards.


Agree with you that it would be good to work with doughs in the 60s at the moment so am looking to tune my formulae to that hydration. Turns out that when I did the chart for the Barm Bread in retrospect I accidently transposed the water figure for the two loaf dough - should have read 125g with optional 50g (which I used) not 250g with optional 50. The loaf I made was therefore 69% hydration and not 95%! Makes a lot more sense.


This has been best hydration for me so far and still got good oven spring. Anything beyond that is testing my current shaping skills. Did try to make another bread based on the wrong formula - that was a bit of a 'mare but I did manage to rescue it!


Now have a 69% loaf proving so hopefully it will come out okay. Proofing times are changing from day to day, however, with the changeable weather. Was nice to do a yeasted bread with the croissants as the rise was a bit more predictable.


Just finishing up Jan Hedh lemon bread - wow that formula produced a lovely loaf.   Best wishes,  Daisy_A

davidg618's picture
davidg618

I'm not trying to push my spreadsheets. I made them for my use, and they serve me well. However, on the ocassions when I've mentioned them I was getting requests for them.


My spreadsheets begin where Andy suggests: with the amount (weight) of dough I want to make, and what %Hydration I want the final dough to contain.


I also provide for 1 preferment (sourdough starter, biga, poolish, etc.) Its entered by it's weight, and %Hydration also.


The sheets calculate the total flour and water needed to produce the desired dough, and also calculates the contributions of flour and water from the preferment.


Subsequently, you add the flours and liquids you want in the dough. The sheets keep a running total of both the flours and liquids (water, milk, oil, eggs, eggwhites, beer, etc.). You need only to match the running totals to the calculated totals. With a minimum of hand calculation you can account for soakers, and additional preferments by simply calculating their flour and liquid contributions and entering them as such.


It also calculates the needed salt (at 2% of the total flour weight), and provides space for yeast in the preferment (biga, poolish) or dough, and other additions (malt powder, nuts, fruit). The salt is included in the running total dough weight, but not the other additions aren't. They are either too small to be significant, or, my choice was things like nuts, and semi-dried fruits (raisins, craisins, olives,etc.) don't contribute to the dough's strength significantly, nor alter the %Hydration significantly.


The spreadsheets written in Excel (.xls format) are protected, i.e. calculated cells are locked, but there is no password needed to unlock them so you can customize the sheets to your needs if you choose to.


There is also a Starter Calculator Spreadsheet. It does the math for the way I build all my sourdough formula-ready levains from the seed cuture I store in the refrigerator. I use three builds over 24 hours, adjusting the %Hydration in thirds if the formula calls for a starter hydration different from the 100% hydration of the seed culture. My way is a little more labor intensive, and takes about a third longer than the single build most bread book formulas call for, but it's consistent, and produces a very lively formula-ready levain. The link to my blog entry about the three-build method:


http://www.thefreshloaf.com/node/12766/building-formulaready-levain-starter


If you're interested the spreadsheets are available, free, at:


http://glitzandglitterboutique.com/davidg618/spreadsheets.html


David G

dlstanf2's picture
dlstanf2

David, I went through your spreadsheet and found some weight errors and a couple of other little issues.


Biggest problem was you gram to ounce conversion. Your are using 29.57353, when it should be 28.3495. Why are you using 29.57353?

davidg618's picture
davidg618

Thank you. I found the error in the conversion months ago, and thought I had fixed it. I had on my own sheets, but obviously didn't on the web site.


To put it in perspective, the error results in about a 1.5oz error for each kilogram of weight if you start with metric, and about 20g error for each pound of weight if you begin with English units. Converted formula remain viable, only a little bigger, or smaller. Nonetheless, I apologize for any inconvenience its caused others.


I've removed the web page posted above, rather than correct them.


David G