The Kitchen Formula Calculator v3

Part 6  The Kitchen Formula Calculator v4 & The Logical Structure Of A Recipe

The Problem With Volume Measurements

There’s an important change to common recipe writing habits to be made if using The Kitchen Formula Calculator. Just as for bread formulae, and using Baker’s Percentages, using Cook's Percentages mandates that recipes be written using weight, not volume measures. This has not been typical kitchen practice, in fact it’s rarely so except in operations serious about staying in business, some enlightened Chefs, or operations with very significant production levels (Oscar Meyer hotdog, or Krispy Kreme donuts). Using weight measures offers advantages if we can put away our cups, and spoons, and beakers. First of all, the ratio of one weight to another is so much easier to compare than comparing the ratios of volume measurements such as 1/3 cup versus 1/8 teaspoon. Can you immediately conjure how many eighths of teaspoons fit into a third of a cup? When I first started as a Chef's apprentice in 1979 I was surprised to find out that most of my fellow cooks had no clue. Fathoming what are cups, pints, quarts and gallons was the limit. In any case, measuring ingredients by weight is far more precise. No one has ever precisely scooped out 1 cup of flour, or a cup of black eyed peas, nor can anyone do it again and again. Each cup is a bit different from the next. This fact has largely been ignored because cooking is a far more flexible process than bread baking. Nevertheless, the workers at the Smucker’s jam factory are not scooping ingredients, or using spoons. Recipe formulation is precise. Ensuring the batch by batch production cost is reliably consistent matters greatly.

There are other important operational reasons why a cook’s recipe is more usefully written in weights, not measures. Eventually, any cook, whether professional or at home, always has to re-scale the yield of a recipe to match changes in the expected demand, or to perform a recipe costing. In both cases, ingredient volume to weight conversions become necessary. Even home cooks do recipe re-scaling regularly, and while they don’t typically do recipe costings, it might occur on occasion, and even small businesses need to know and control production costs, not just in order to determine a sales price that makes sense, but to remain in business. How does one compare the volume of 1/8 teaspoon to 1/3 cup? When performing a recipe cost one doesn’t convert the 25 kilogram sack of flour, or 5 kilo bag of beans to teaspoons. One has to convert all the recipe ingredients from volume measures of flour, beans, herbs, spices, salt, sugar, etc to weights, and then calculate the value of the weight of each ingredient used in the recipe to the cost per unit of the bulk pack for each. Usually this is done in grams and kilograms. Doing ingredient volume to weight conversions requires you know how many teaspoons, and tablespoons inhabit a cup because one recipe might stipulate a cup of beans, another just a tablespoon. We do not want to do separate calculations for such stuff. We simply calculate the cost of one cup of beans, and divide that by our understanding of numbers of tablespoons and teaspoons per cup to obtain ingredient costs for these. 

Do you know how many tablespoons can fit into a cup; how many teaspoons one can pull out of a tablespoon? The answer is sixteen of the former, three the latter. Thus, forty-eight teaspoons per cup, sixteen per third cup, and 128 of one-eigth teaspoons per 1/3rd cup. Imagine thirty cooks getting that right, and of course, that's accounting for one ingredient! Doing volume to weight conversions are a headache, but only because the recipe was written using volume measures. Recipes using weight measures are not problematic, but still require some computation, and there is no Chef who loves to do recipe costings. Even home cooks occasionally do such stuff because they're interested to know what their oatmeal cookie recipe costs, and maybe if they change this ingredient or that, they’d have an equally tasty cookie that costs marginally less to produce. In any case, if such conversions are done on the fly, it’s always going to be more or less accurate. Using The Kitchen Formula Calculator provides a way to do it with ease, and precision, and immediacy.

Suppose you are obliged by your Chef (or your auntie) to be very precise, maybe for the sake of doing a recipe test, or menu costing. Even if you can properly calculate how many eighths of a teaspoon are in one third of a cup, this doesn’t always help because it doesn’t account for how ingredients can vary as they fill a cup or spoon on any given day. No one can fill a cup with flour to the same level twice in a row, so how can I expect 30 cooks to do it the same way? Nor does it account for the fact that a cup of one type of salt is quite different from another type of salt, both are different from a cup of butter, and a teaspoon of baking powder is not the same as a teaspoon of sugar. To do an accurate accounting of how much it costs to make a recipe, one must convert these volume creatures to numbers, i.e. into weights, and specifically to gram weights because these are much more precise and easy to deal with than ounces. Ultimately, we are obliged to refer to one or another of the many volume to weight conversion tables that can be found in cookbooks, or online. While many abound, none consistently agree what a cup of bread flour weighs, or a cup of egg whites. Why can’t the various conversion charts agree? It’s because Ingredient density changes depending on location, weather conditions, storage, and if the ingredient is, by its nature, able to be compacted. Flour is a classic example of such, but one of many. If you own a laboratory, and staff it with trained scoopers equipped with very precise spoons, cups, beakers, and equally precise digital scales, you’d still get variations in conversions, possibly from the same lab on different days, or if your head flour scooper was off, and his assistant was doing the dipping. So, why not just write recipes using ingredient weights, aided by the visualization of what's most important, the ratios involved? This is what Cooks Percentages, and The Kitchen Formula Calculator does.

Why do we do recipe costings? Because we want to make money; it’s a business, or we are on a home budget, and want to find ways to save expenses. We need to know how much it costs to make so we can sell it at an acceptable margin, or substitute less expensive ingredients, or less of some, and yet make a representative and tasty product. Doing recipe costing is something most chefs loathe to do, and because they are less than delighted, they typically do it without rigor, and because controllers don't know the difference, and rely on their Chefs to be sincere (and because they have other stuff to do) these figures are generally accepted. After some time, when the food cost goes fubar, folks like me are called in to unfubar it, and the first thing we do is to analyze the Chef’s recipe, plate and menu costing; often doing it all over again from scratch. Imprecise recipe costings mean that a finished plate offering from the menu is likely improperly calculated, as will be the overall cost of the menu. This has implications for when we desire to do “menu engineering”, i.e. to analyze what the various parts of a menu do for the overall goal of making profit, and what to do about specific aspects of the menu to get it more on target with expectations, and needs.

Perhaps you do not conduct nightly menu costings as part of preparing your family dinner. Well, there are other scenarios in professional settings that make weights more practical than measuring volumes of stuff. Perhaps for the cook, volumes work just fine, but not for controllers, owners, or investors. In any case, since a kitchen recipe allows some leeway, and because cook cooks to taste, then it makes no practical difference to them if a recipe is written in weight measures. A good cook doesn't always pull out his spoons when measuring mise en place for a recipe, the cook will learn to visualize what 2 Tablespoons of chopped chives is. So it is if the recipe calls for 5 grams of chopped chives. Understanding the general ratio of ingredients is all that’s necessary, but tasting while it is in process is crucial. Nevertheless, using weight measures is more precise. If a cook only needs a general understanding of the ratios of ingredients in a recipe, doesn't it make sense to provide a very accurate general understanding?

How does all this matter for understanding the idea of Cook’s Percentages, and why The Kitchen Formula Calculator is useful?

What’s most troublesome about relying upon volume measures is that making recipe yield adjustments is quite problematic. To upscale or downscale the yield of a recipe, we’re obliged to doing some ingredient volume to weight conversions to recalculate each for the adjusted yield, or by using some recipe multiplier, and using that to determine how many more or less tablespoons, teaspoons, cups (and usually some ingredients in ounces and pounds). In very simple recipes it’s easy enough to just double the numbers of teaspoons, tablespoons and cups called for, but for such stuff as eights of teaspoons, thirds of cups, it soon gets to be not so simple, and because it is not so simple, errors occur. It is even more problematic if we want to cut the recipe by a fraction. Then our multiplier is something like .5 or .33, or .75.

For example, if you need to increase the recipe yield by a factor of 1.5, what is one-third cup x 1.5; one-eighth teaspoon x 1.5? Most folks will not figure this out correctly. Or, if the recipe must be downscaled, what is .5 of one-third, .5 of three-fourths? Though not very complex math, workshops are busy places, recipes have multiples of ingredients, each one requires the calculation. People make mistakes.

To further illustrate the problem, and also to illumine the value of knowing the mathematical structure of a recipe, consider the following example. A recipe for Tomato Soup yields 1 liter (a volume measure), roughly the same as saying, it equals 1 kilogram (a weight measure). Each ingredient in the recipe can be seen as a percentage that references either the total volume of the formula, 1 liter, or the total weight, 1 kilogram. What percentage of the whole does each ingredient represent? You simply cannot get useful information using volume measures. It may be the case that 1 liter of Tomato soup contains 65 tablespoons, but 1 tablespoon of salt, and 1 tablespoon of flour, and 1 tablespoon of oil are not the same thing. Each weighs differently. It's really not very useful data to know that the amount of chopped tomatoes required, if analyzed as the percentage of tablespoons versus the total number of tablespoons in 1 liter of Tomato Soup is a certain percent value. To make sense of a recipe’s mathematical structure, we must use weights. It's only when we understand the mathematical relationships, ingredient ratios, that we can upscale/downscale a recipe with ease and precision. 

You might be good with numbers, easily performing calculations in your head. Most are not. Even so, if able to figure out how many eighths of teaspoons of all ingredients comprise 4 quarts of Tomato Soup, and then to assign a percentage to each ingredient, what’s that do for you? It’s just painfully arrived at trivia. You can neither upscale or downscale using such data.

The Kitchen Formula Calculator makes sense of formula mathematics. 

It does so by using Cook’s Percentages. 

It does so without error, and it does so immediately, but one must first convert any volume measures of stuff to weights. Doing such conversions always involves some degree of error because scooping out a perfectly level spoonful, cup, or beaker full of stuff is error prone, and variations can be caused by ingredient settling, and atmospheric fluctuations as well. Nevertheless, for all recipes not bread, cooking stuff like Tomato Soup is not exact. Such marginal error as will occur when converting volumes to weights is ok. What we want is for it to be close enough, “good enough for government work”. In any case, when it comes to doing volume to weight conversions, close enough is all we can do. 

To perform volume to weight conversions, cooks reference any number of reputable ingredient volume to weight conversion charts, but with the understanding that there's a margin of error in all of them. Consider this: according to King Arthur Flour, 1 teaspoon of Vital Wheat Gluten weighs 3 grams. According to another reference, Aqua-Calc.com it weighs 2.5 grams, but when I measured one teaspoon of my own cache it weighed only 1.8 grams. According to Aqua-Calc.com a cup of egg whites is 243 grams, King Arthur doesn’t tell you this. The King only tells me that 1 large egg white (1-1.25 ounces) weighs 1-1.25oz, or 30-35grams. So, there’s a 16% margin of error built in to their conversion. If you want accuracy, then you’ll be obliged to figure out what is the weight of the actual egg you are using, and then do so every time you do the recipe, or just convert your recipe from the very unspecific "1 egg white" to something specific like 30 grams. My own measurements show that a single egg white from a “large” egg can vary from 34-38 grams. Since grams are quite small increments compared to ounces, being off by one or two is no big deal (except for certain very sensitive ingredients). As a standard, when I write a recipe I use 18 grams as the weight of an egg yolk, 36 grams per egg white. It works. Some sources claim 1 cup of all purpose flour weighs 125 grams, and bread flour too, but this is clearly not going to be the case. Why? Because bread flour, and all purpose flour have different densities. They’ve been milled and sifted differently. They will weigh differently per cup. Such bulk ingredient types, as are flour and grain, tend to settle. They're compact-able. Changes in weather has effects on ingredients too. The best we can do is refer to the same conversion chart again and again, so that, whatever is the margin of error in that chart, at least it's the same margin of error consistently, hopefully. Or, you can do as I do, create your own chart using your own measurements in grams.

Think about this for a moment! Doesn’t this fact alone stand as argument for not writing formulae using volume measures? The only reason we are reduced to wasting time like this is because we have bad habits. We grew up with cups, spoons, and beakers, but no simple, lightweight,and extremely accurate scales...but now we do. 

Weight measures do not fluctuate. Five grams of anything, will always be five grams, whereas one cup of something will almost never weigh the same amount twice. You may be afraid of metrics since you were raised in a place accustomed to using American Standard or Imperial systems of measures. So, why use grams? Actually, grams are optional, scaling is not. Use ounces if you like, the scale can be set one way or the other. However, because grams are so much more precise than ounces (there are 28.35 grams in an ounce) setting the scale to the gram weight mode makes sense. A typical home recipe often includes small quantities of some ingredients; leavening agents, spices, herbs. For these we habitually resort to the “convenience” of teaspoons, 1/2, 1/4, 1/8 tsp, but even a cheap digital scale can display gram weights in hundredths of grams. It’s just as easy to weigh 4 grams of cinnamon as it is to scoop it out. The only difference is this: when I scoop 1 teaspoon of cinnamon for my oatmeal cookie recipe, I usually add it to the mixing bowl. Instead, I scoop it, put it in a little receptacle of my digital scale, note how much it weighs, and then put it in my mixing bowl. After which, I always just add the weight of the cinnamon to my mixing bowl. Some scales can give accurate results to hundredths of a gram. Why is it that we should use grams, not ounces? Because by using the gram weight mode setting on the scale, if I don’t scale an ingredient precisely all the time (I scaled 210g, but 208 was called for) the difference in grams is quite negligible especially considering the built in leeway cooks have when preparing most kitchen recipes; two grams is less than 1/14th of an ounce. On the other hand, if scaling ingredients using ounces, the human error variations can become not so forgivable. If the metric system is boggling for you, or if you are otherwise committed to not learning new things, take heart, you don't need to understand, you only need set the scale to grams by pressing a button. The scale understands for you. In any case, The Kitchen Formula Calculator displays all ingredient weights, and formula yields in both grams and ounces. 

In summary, the "same" volume measure of an ingredient will not weigh the same every time it is measured, but a weight is a weight is a weight, every time. A teaspoon of salt cannot be scooped the same twice in a row. Converting a teaspoon of salt to a weight measure, we gain the ability to compare it mathematically to the other ingredients in a recipe as ratios, one to another. When we do so, these are what I call the ingredient Cook’s Percentages. Understanding this, and by using The Kitchen Formula Calculator, a cook can re-scale a recipe with ease, and precision. Since the calculator also has built in tables for performing recipe costings, it's an invaluable tool for professionals, or occasionally interested home cooks. An important difference from Baker’s Percentages which always add up to more than 100% is that Cook’s Percentages always add up to a total of 100%. Bar graph logic versus pie chart logic.

Why do Cook's Percentages matter?

Re-Scaling recipes is always a fact in kitchens. Here’s a simple example of a common problem in food production operations that home cooks grapple with as well. A recipe yields eight portions, but I have nine guests, and two days later, six more have requested the same preparation. I would prefer not to have extra portions. I want exactly nine portions today, and six next time. In this very typical case one needs a conversion tool, to upscale the recipe this time, and to downscale it later this week. The tool has typically been a pocket calculator. In order to adjust recipe yield a multiplier is required. To calculate it, the cook divides the increased or decreased portions required by the original yield. Thus, 9 portions divided by the 8 portion original yield equals a 1.125 multiplier. Again, for 6 portions, divide 6 by 8, to arrive at a .75 multiplier. These values can now be used to recalculate new ingredient quantities for each occasion. Multiply each ingredient’s weight (or volume measurements) in the original formula using the appropriate multiplier to arrive at an adjusted value. It’s a tedious process, especially for complex formulae; error prone as well. Bearing in mind that in professional kitchens the yield required depends upon portions needed which can often be in the hundreds. It’s important to make proper calculations.

Besides, the obvious opportunity for screwing up, there’s another problem if performing recipe yield adjustments with a pocket calculator. The result obtained from the process described above is useful for the immediate occasion only. What if next week you need to do the same preparation again, but this time you'll need fifteen, or fifty portions? What if production demands change day to day as is normal in commercial settings? Using your pocket tool means you do it all over again every time the production requirement changes, or as some Chef’s do, they’ll build in multipliers to the recipe; 2x, 3x, 4x etc. This is better than starting from scratch every time, but it’s an inefficient method compared to what The Kitchen Formula Calculator, based on Cook's Percentages can do. 

Scaling up formula yield, or scaling it down is a very frequent necessity for all cooks. What’s needed is a tool that can give the result on demand, repeatedly, precisely, effortlessly. There are numerous kitchen recipe database programs that can do this, but so does The Kitchen Formula Calculator. It functions as effectively as a program designed to do this sort of thing, doesn't require a lot of user guide, and it has the benefit of being free. If you want to use it, you can.