# The Math of Modern Cooking

When diving into modern cuisine, one quickly encounters recipes with highly-specific weights, percentages, ratios, and other math-y things that might be a little jarring at first. Precision is very important in modern cooking - this allows you to get consistent results every single time, and reproduce the work of others exactly as they made it. Rest assured you don't need to break out your college math textbook or be a mental arithmetic genius to succeed - the math of modern cooking is quite simple. Trying to remember the rules while juggling ten other tasks while cooking is no fun though, so this page is a cheat sheet you can use when you need it.

Sections:

### Finding a Percentage of a Weight

Hydrocolloids and other modern ingredients are often used in very specific percentages. For example, you may want to thicken a sauce by using 0.2% of its weight in xanthan gum, or make a fluid gel using a 1% concentration of agar agar. To compute a percentage of the weight of an ingredient, first convert your percentage to a decimal, then multiply by the weight in question.

Let's say we have 75 grams of sauce and want to add 0.2% xanthan gum. To compute 0.2% of 75 grams, we first convert 0.2% from a percentage to a decimal by dividing by 100:

$$\frac{0.2}{100} = 0.002$$

Then multiply by the weight of our ingredient.

$$0.002 \times 75 = 0.15$$

Thus we need to add 0.15 grams of xanthan gum.

This is probably the most common task in all of modern cooking, so it's the one most worth remembering. Or, here's a handy-dandy calculator for your convenience:

What is

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### Scaling Ratios

Sometimes recipes are given as ratios which need scaling depending on how much of an ingredient you have or your desired yield. Let's say you want to try the Modernist Cuisine technique of using fish sauce to rapidly "age" your beef. They give the recipe as a ratio: use 3 grams of sauce for every 100 grams of beef. You have a steak weighing 250 grams - how much sauce do you need?

First, we can simplify the ratio by dividing the quantities:

$$\frac{3}{100} = 0.03$$

This means we need 0.03 grams of sauce for every 1 gram of steak. Then just multiple by the weight of our steak:

$$0.03 \times 250 = 7.5$$

Thus we need 7.5 grams of sauce for our 250 gram steak.

### Reverse-Engineering Percentages From Weights

Sometimes you'll be reading a recipes that gives the weights of all ingredients, without specifying their percentages. For example, Corey Lee's Benu cookbook includes a garlic fluid gel recipe that calls at one point for 250 grams of milk and 5 grams of low-acyl gellan gum. In case you're wondering, "what percentage is that by weight?", it's easy to figure out. Just divide the quantity in question by the other weight, and then multiply by 100 to convert from a decimal back to a percentage.

$$\frac{5}{250} \times 100 = 2\%$$

Thus the recipe uses a 2% concentration of low-acyl gellan gum. One note: sometimes you need to be careful when determining the other weight to use when dividing. In this case it's easy, since there's only the one ingredient (milk) in question. Other times it may be comprised of several ingredients put together, in which case you'll need to add their weights together first.