Friday, October 17, 2008

Conversion Factors

Let's face it: not all restaurant recipes were conceived at the volume that is needed in a professional kitchen. In fact, most recipes were initially developed for a much smaller group of people, and then adapted for large-scale use. Converting these recipes isn't difficult, and it gets easier with a little knowledge of conversion factors.

To find the conversion factor (CF) of a recipe, you need two factors: the amount that the recipe currently yields, and the amount that you need it to yield. For instance, let's say you have a recipe that yields 6 servings, and you need to feed 50 people. 50 divided by 6 is 8.333, so you have a CF of 8. If you needed to go the other way, you would have 6 divided by 50, which is 0.12.

But that's only part of the process. Let's look at the ingredient list on my oatmeal cookie recipe:

1 cup butter
1/2 cup white sugar
1 cup brown sugar
2 eggs
1 1/2 tsp vanilla extract
1 cup all-purpose flour
1 tsp baking soda
1 tsp salt
1 1/2 tsp cinnamon
3 cups oats
1 cup raisins

This recipe yields 38 cookies. Let's say I want to convert it to a nice round number, like 250. This gives us a conversion factor of 6.578947368. You can round it if you want. In fact, a lot of bakers would look at this number on the calculator and just call it 6.5, which is probably okay, as long as you use the same CF for each ingredient. In a computer program, you might want to hang onto the unrounded number. For now, I'm going to stick with 6.5.

Your next task is to convert each individual ingredient. This is easy. Multiply the old amount by the conversion factor to get the new amount.

The problem with this is that converting some amounts is non-trivial. 1 1/2 tsp times 6.5 = 9 3/4 tsp. What the heck do you do with that? It gets even more fun when you do it with a lot of commercial software. First, the software requires you to enter decimal values, not fractions like we're used to seeing in recipes. 1.5 X 6.578947368 = 9.868421053. Yeah, good luck with that. Does it help to know that 9 3/4 tsp = 3 Tbsp + 3/4 tsp? It would have been nice if the computer gave us something like that.

Here's the best thing to do: convert each amount to ounces first, apply the CF, and then convert back to the most reasonable value. This is nice, since we have an ounce measurement in both weight- and volume-based recipes. Of course, if you just used metric, this would already be tons easier, but that's just not as common in America as we might like it to be. Let's go ahead and do the whole ingredient list:

Ingredientsold amount
old amount
 CF new amount
new amount
butter1 cup8 fl ozX6.5=52 fl oz6 1/2 cups
white sugar1/2 cup4 fl ozX6.5=26 fl oz3 1/4 cups
brown sugar1 cup8 fl ozX6.5=52 fl oz6 1/2 cups
eggs2 ea2 eaX6.5=13 ea13 ea
vanilla1 1/2 tsp0.25 fl ozX6.5=1.625 fl oz3 Tbsp + 3/4 tsp
ap flour1 cup8 fl ozX6.5=52 fl oz6 1/2 cups
baking soda1 tsp0.1667 fl ozX6.5=1.08333 fl oz2 Tbsp + 1/2 tsp
salt1 tsp0.1667 fl ozX6.5=1.08333 fl oz2 Tbsp + 1/2 tsp
cinnamon1 1/2 tsp0.25 fl ozX6.5=1.625 fl oz3 Tbsp + 3/4 tsp
oats3 cups24 fl ozX6.5=156 fl oz1 gallon + 3 1/2 cups
raisins1 cup8 fl ozX6.5=52 fl oz6 1/2 cups

Well, if you ever need to scale that recipe to make 250ish cookies, I've just done the work for you. But some of you are out there looking at the decimal points, wondering how the heck I got "1/2 tsp" out of 0.08333 fl oz. Some of you are also wondering why I said "fl oz" instead of just "oz".

First, let's talk about ounces. We have two types, ounces by weight (a.k.a. dry ounces or oz/wt) and ounces by volume (a.k.a. fluid ounces or fl oz). As far as water is concerned, there are 16 oz by weight in a pound and 16 fl oz in a pint. You've heard the saying, "a pint's a pound the whole world round", right? Well, it's not entirely true. First of all, the saying is only in reference to water. A pint of flour will not weigh a pound. Interestingly, a pint of butter will weight a pound. Secondly, it's also slightly inaccurate. A pint of water actually weighs approximately 16.7 oz. Even worse, the weight of the pint of water will vary even more, depending on its temperature. At commercial volumes the difference is certainly enough to matter, but for home use it's not usually a big deal.

Let's talk about the 0.08333 fl oz thing. I could just tell you that it's 1/2 tsp and hope you believe me, but I'd like you to know why it's 1/2 tsp. First, let's look at our standard volume conversion chart.

1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fl oz
1 fl oz = 2 Tbsp
1 Tbsp = 3 tsp
1 pinch = approx 1/8 tsp (usually non-liquid)
1 dash = approx 1/8 tsp (usually liquid)

That tells us that there are about 16 pinches in a Tablespoon and 32 pinches in a fluid ounce. If we were to convert our standard measurement chart to decimal, and use only ounce conversions, here's what we'd get:

1 gallon = 128 fl oz
1 quart = 32 fl oz
1 pint = 16 fl oz
1 cup = 8 fl oz
1 Tbsp = 0.5 fl oz
1/2 Tbsp = 0.25 fl oz
1 tsp = 0.16667 fl oz
1/2 tsp = 0.08333 fl oz
1/4 tsp = 0.0416667 fl oz
1 pinch/dash = 0.0208333 fl oz

This actually gives us a pretty good baseline for writing recipe software. The user tells the program how much a recipe currently yields and how much they want it to yield. The program converts the entire recipe to ounces, performs the CF calculations, and then converts it back to the closest measurement.

Even if you're not planning on writing recipe software, the above chart is still handy. I know I would be lost in the kitchen without a calculator, but the calculator is still going to give me decimals. Why not print out the chart above and keep a copy with your kitchen calculator? That will save you a little bit of time when scaling your recipes.

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