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.

Home-roasting coffee?

I’m pretty sure home-baked bread is good for me and in a best case scenario it also tastes better than loaves bought from the bakery. Now I’ve been roasting coffee in that same oven I use for baking and after about 6 kg of raw coffee transformed into espresso beans I’m quite taken with the prospect of it all. In the latest case the blend was made up of 80% “India Monsooned Malabar AA” and 20% “India Cherry a/b Robusta” from Caffè Fausto.

I just shovel enough raw coffee onto a tray lined with baking paper so that the beans lie next to each other and not on top of each other and heat the oven to 200°C-220°C. In they go and after about 20-25 minutes and a little bit of tossing around, the beans are done. This way of roasting coffee also reveals the “hot spots” of the oven. In areas where after 15 minutes the most coloring of the beans is visible, there is a hot spot of the oven, in my case on the left and right hand side close to the walls. After roasting, the kitchen smells like smoke, liquorice, leather and coffee. The waves of steam billowing out of the oven when the door is opened are a bit freightening but so far no accidents apart maybe from a mild headache after being exposed to the smoke for more than 5 minutes.

There is a point where the beans start to sweat and quickly turn black. I found after that point almost all coffee tastes the same and I wouldn’t want to consume it on a regular basis. But a little oil escaping from the hot bean and a dark color is fine and helps to bring out the intensity that I like in a shot of espresso or in my “latte”.

When the beans are done it is probably best to cool them quickly to stop the cooking process and “seal” the aroma. There is a skin around the raw bean which is shed during roasting and needs to be removed in order to be able to produce caffè with crema. Also any remaining pieces of that skin can mess up the grinder. Between each Kilogramm of home-roasted coffee I grind a pound of professionally-ground coffee in an attempt to clean it but don’t know if it is necessary.

3-days breakfast rolls

The nice thing about these rolls is that the morning you need them, you just take a tray out of the fridge and pop it in the oven. The other nice thing is that they take two days of waiting for the dough. I had planned to make the dough very smooth by adding some lard, which was also used frequently by bakers when there were no chemical ‘improvers’, but I find they made the crust a bit hard. Perhaps that’s what lard does, but I might use butter or oil next time. Or a little Quark.

3-days breakfast rolls (makes 6-8 rolls)

Pâte fermentée

• 100g strong white flour
• 65 water
• 2g sea salt
• 1g fresh yeast

Mix and knead briefly. Let stand for 2 hours at room temperature until expanded. Then put into fridge overnight, for 12-18 hours. The next day take out of the fridge 2 hours before using it in the dough.

Soaker

• 100g water, hot, approx. 80°C
• 40g coarse spelt meal
• 30g sunflower seeds
• 30g rolled oats
• 6g sea salt

Mix and let stand covered at room temperature for 3-20 hours, depending on your time frame (which shouldn’t be a problem if you’re making 3-days-rolls)

Dough

• Soaker
• Pâte fermentée
• 100g strong white flour
• 100g whole-spelt flour or wholemeal flour or whole-rye flour
• 50-100g warm water, to make a loose dough
• 20g lard
• 5g barley malt
• 3g fresh yeast
• More sunflower seeds, rolled oats and any rye meal for sprinkling on top

Mix to a sticky dough using your favorite method, either by hand or machine. Let rise for 60-90 minutes until well-risen. Divide, shape into rolls, moisten the surface and dunk into a bowl of additional seeds. Line a small baking sheet with baking paper, put rolls on it and put in fridge overnight.

On baking day, get tray out of fridge, heat the oven to 260°C and put the tray in the oven. Wait 20-25 minutes until rolls’ color is a rich golden brown. If not eating them all, store in a freezer bag and toast the next morning, which sometimes brings out the most sensational whole-grain flavor.

Roggenvollkorn ohne Hefe

Bäcker Süpke, in his blog, reported about whole-grain breads as interpreted by Baking academy in Weinheim. As he mentioned that this loaf was made without commercial yeast and had a singularly dense crumb, I quickly went through the cupboard to see if I had the ingredients, which are rye meal, rye meal and rye meal. My supply of rye grains was good for 1,5kg of rye bread.

The result is a moist loaf that is sliced thin to release its strong flavor and aroma. Very good. Will post translated recipe ASAP.

A sandwich day

German Type 550 flour performs okay-ish when baking French or Italian bread using a cool dough that ferments over a couple of hours with little yeast, strengthening it by giving it folds. But the relationship between flour and water fizzles when making sandwich breads like toast- or Pullman loaves These doughs need to stand tall, undergo a relatively warm fermentation period and are mixed at high speed. I added a little gluten to help the dough rise quite a bit over the top of my baking frame. Gluten absorbs flavor, I am reluctant to add it, but it makes sense to me here, as dense slices of sandwich breads are no fun. If using American flour, adding gluten is not necessary and I believe most varieties of strong white flour in the UK also give super results.

I like my sandwich with spicy pastes or spreads. The chickpea flavor of the one I’ve used here is very good in combination with turkey and a couple of cucumber slices. You could add tahini and garlic to the chickpea spread to make hummus and congratulate the people behind the biggest serving of hummus ever made.

Sandwich bread

Sponge (= biga)

• 70g strong white flour
• 42g cold water
• 1g fresh yeast

Mix together, knead briefly and let stand covered at cool room temperature for 12-16 hours. It shoud look very inflated.

Dough

• Sponge
• 280g strong white flour
• 180g warm water
• 8g butter, softened
• 8g sea salt
• 5g powdered gluten
• 4g fresh yeast
• 4g sugar
• 0.5g malt

Mix on highest speed for 4-5 minutes or until the dough comes away from the sides of the bowl.
Let rise for 45 minutes, then shape into a sandwich loaf and prove for 45-60 minutes.
Bake at 230°C for 10 minutes, then reduce heat to 210°C and bake for further 30-35 minutes until brown on top.

Chickpea sandwich spread

• 100g dried chickpeas, soaked overnight in water
• 1/2 tsp cumin
• 1/4 tsp cardamom seeds
• pinch of powdered chile
• 1/4 tsp salt
• pepper to taste
• 1 tbsp olive oil
• 3 or 4 dried tomatoes, soaked overnight in water
• 5-10 tbsp water

Cook the chickpeas for about 60-90 minutes until soft. Roast the cumin and cardamom in a pan and as it starts to release aromas, grind the two spices in a mortar. Blitz everything on the ingredient list together except the dried tomatoes, chop those. If necessary, put through a sieve; chickpeas can be quite tough even cooked. Season with additional salt and pepper. Add the tomatoes to the finished smooth paste.