Scaling a recipe

A recipe for 4 becomes a recipe for 6 when every amount is multiplied by 6/4 = 1.5.

Water for three packets of noodles

Start with something smaller than a recipe. A made-up packet of instant noodles says 550 ml of water for one packet. Cooking three in one pot, you need 550 × 3 = 1,650 ml, not 550 plus a splash. The water for three packets is three times the water for one. Recipe scaling is that same move, applied to every ingredient at once.

Pancakes for 6 from a recipe for 4

A made-up pancake recipe for 4 people uses 300 g of flour, 2 eggs and 250 ml of milk. You are cooking for 6. Each ingredient has to change, and they all change by the same factor, called the scale factor: the servings you want divided by the servings the recipe makes. Here it is 6/4 = 1.5. Flour becomes 300 × 1.5 = 450 g, eggs 2 × 1.5 = 3, and milk 250 × 1.5 = 375 ml.

One factor keeps flour and milk at 6 : 5

The recipe is really a set of ratios. Flour to milk is 300 : 250, which is 6 : 5. If you scaled the flour by 1.5 and the milk by 2, the ratio would change to 450 : 500 = 9 : 10 and the batter would come out thinner. Multiplying every amount by the same number keeps every ratio between ingredients the same; that is what makes the bigger batch taste like the original. In the language of the last unit, each ingredient is in proportion to the number of servings.

From 6 servings down to 4: multiply by 2/3

The scale factor can be less than 1. To turn a recipe for 6 into a recipe for 4, the factor is 4/6 = 2/3. A recipe that uses 3/4 cup of sugar for 6 needs 3/4 × 2/3 = 6/12 = 1/2 cup for 4. Fractions make this tidy. With decimals, 2/3 is 0.666..., and rounding it to 0.67 before multiplying adds a small error to every ingredient, so keep the fraction as long as you can.

What to do with 1 1/3 eggs

Some answers are not practical. Scaling 2 eggs by 2/3 gives 1 1/3 eggs. One choice is to beat 2 eggs and use two thirds of the mixture by weight; another is to round to 1 egg and accept a small change. A third is to pick a scale factor that gives whole eggs: the recipe for 4 uses 2 eggs, so a recipe for 2, 6 or 8 keeps whole eggs, but a recipe for 5 does not.

Only 200 g of flour in the cupboard

Sometimes one ingredient limits you. You have only 200 g of flour, and the recipe for 4 uses 300 g. The scale factor is now 200/300 = 2/3, and every other ingredient gets the same factor: 250 × 2/3 is about 167 ml of milk. The batch serves 4 × 2/3, about 2.7 people. This is the same proportion as before, with the flour setting the number instead of the guests.

Everything above scales ingredient amounts only. Pan size, cooking time and oven temperature do not simply follow the scale factor, so a recipe book or the cook's own judgement is the guide for those.