Vol. XXIII · The Everyday Cook Plate 3 of 12scaling a recipe, doubling, halving, baker's percentages, pan size, baking time, square law, eggs, seasoning, evaporation, batch size, recipe conversionTH

Scaling a Recipe.

A cake recipe doubled into the same tin overflows, burns at the edges and stays raw in the middle. The ingredients were right; the geometry was not.

Scaling the ingredients is arithmetic: multiply every quantity by the same factor — easiest when the recipe is in grams (I.5) or in baker's percentages (XXIV.2). What does not scale by the ratio is everything that depends on shape and time. A deeper batter or a thicker roast takes longer to heat through, roughly with the square of the depth (II.2). A larger pot loses proportionally less water to evaporation, so a doubled stew or rice needs less than double the liquid (XXI.3). A larger pan crowds less or more depending on its area, which changes browning (XV.3).

Seasoning deserves care: salt scales with the food, but strong spices and chilli are perceived non-linearly and cooks usually start at about three-quarters of the scaled amount and adjust (I.7). Eggs round to whole numbers, so small recipes are best scaled in grams of beaten egg. Yeast and chemical leaveners scale with flour, but rising time depends on dough temperature, not on the size of the batch (XXIV.6). The workshop scales a cake.

Below: a pound cake for a 20 cm round tin scaled by the factor you choose: the quantities, the eggs, the tin that keeps the batter at the same depth, and how the baking time at the centre would grow in the original tin (square law of II.2).

What you will learn
Workshop
Original recipe for a 20 cm round tin: 200 g each of flour, sugar and butter and 4 eggs (200 g). Same depth: area scales with the factor, so diameter × √factor. Same tin: depth × factor, and the time to heat the centre × factor² by the square law — an upper bound, since heat also enters through the sides.

Multiply the grams, then fix the geometry

Doubled, the pound cake needs 400 g each of flour, sugar, butter and egg; to bake at the same depth it needs a tin of about 28 cm across (or two 20 cm tins), not the original one, in which the batter would be twice as deep and its centre could take up to four times as long to set while the edges overbake. Tripled, about 35 cm. In practice, use two tins, or a larger tin and a lower oven, and test with a skewer.

A checklist for scaling anything: convert to grams; multiply; round eggs, and weigh the beaten egg if precision matters; choose pans by area so depth stays the same; for roasts, expect the time to grow with thickness, not weight (II.2), and use a thermometer (I.4); for stews, soups and rice, add liquid more gradually than the ratio suggests and reduce at the end (XXII.8); season to three-quarters, then taste; for big batches, check that the burner and pot can bring the larger mass to temperature in reasonable time (II.6), and cool it in shallow containers (XII.7).

At the stove

Halve a recipe you know well. Write down every change beyond the arithmetic that you had to make — pan, time, heat — and keep the note with the recipe.

Fannie Farmer's Boston Cooking-School Cook Book (1896) popularised level, standard measurements in American recipes so that they could be repeated and scaled; metric weights, used by professional bakers everywhere, make scaling simpler still.

Terms

Scaling factor
The number every quantity is multiplied by.
Pan area
What sets the depth of a batter for a given amount.
Square law
Heating time grows with the square of thickness (II.2).
Baker's percentage
Each ingredient as a share of the flour weight (XXIV.2).
Ingredients scale by the ratio; shape and time do not. Keep depth by scaling the pan's area, expect time to follow thickness squared, add liquid and seasoning gradually, and round eggs by weight.

Sources

  1. A teaching value chosen for the course: the right order of magnitude and shape, not a measurement of a particular food.