Scaling a recipe up

Why does quadrupling a recipe ruin a dish that four separate batches make perfectly?

You have cooked a dish twenty times for two people and it is reliable. Tonight there are eight, so you multiply every line of the recipe by four, reach for the big pot, and produce something disappointing: a sauce that never thickened, meat that went grey instead of brown, a bake that is scorched at the rim and wet in the middle.

Here is the strange part. If you had cooked the same amount of food as four separate batches in the original pan, one after another, it would have come out right every time. Same ingredients, same quantities, same cook. So whatever went wrong was not in the ingredient list. What is it that four small batches preserve and one big batch destroys?

Start with what you actually multiplied. You multiplied masses — grams of onion, millilitres of stock, spoons of salt. Ask the obvious follow-up: does everything that matters to the dish scale with mass?

Consider the pot. You have four times the food, so four times the volume. But the pot has not grown in every direction equally; it cannot. Volume grows with the cube of a length, while surface grows with the square. Quadruple the volume of a similarly shaped vessel and its linear size grows by the cube root of four, about 1.59, so its surface area grows by four to the two-thirds — about 2.5 times, not four. The food has four times as much inside and only two and a half times as much boundary.

Now ask what happens at that boundary, because a surprising amount of cooking does. Heat enters through it. Steam leaves through it. Browning happens on it. So per spoonful of food, you have given yourself roughly 63 percent of the heating surface, 63 percent of the evaporating surface, and 63 percent of the browning surface you had before. Does the sauce that would not thicken start to make sense? Reduction is evaporation, evaporation is a surface process, and you asked a surface that grew by 2.5 to service a volume that grew by 4.

Then there is the burner, which did not scale at all. It delivers roughly the watts it always did into four times the thermal mass. What does that do to the time the dish spends coming up to temperature? It stretches it — and every rate that depends on time rather than on your intention stretches with it. More minutes below browning temperature is more minutes of stewing. A large dough or a large pot of stock also holds its own heat: with less surface per unit mass it sheds warmth slowly, so a big batch of dough ferments faster and further than a small one left in the same room, and a big pot of stock cools through the warm range for hours after you switch off.

And the grey meat? When you tip four times the meat into a pan whose base area grew by 2.5 at best — or, more likely, did not grow at all — two things happen at once. The pan's stored heat is dumped into a much larger cold mass, so the surface temperature crashes below the range where browning proceeds usefully. And the meat now sits crowded, so the water it releases cannot escape from a surface that is mostly covered. Water boiling off holds the surface near 100 degrees Celsius, and the browning reactions that give roast flavour need it well above that. So the meat steams. Four separate batches never crowd the pan and never crash its temperature, which is precisely why they work.

Do you notice what all three failures share? Every one of them is a quantity tied to area or to time, and you scaled only the quantities tied to mass.

It is tempting to conclude that recipes simply "do not scale", but that is too strong. Quantities that are pure ratios do scale cleanly: salt as a fraction of mass, the acid in a brine, the hydration of a dough. What does not scale is anything set by geometry or by the clock — pan area, evaporation, come-to-temperature time, cooling time, how deep the heat must travel to reach the middle.

That gives you the repair, and it is not arithmetic. Restore the ratio you actually depended on. Use a wider pan rather than a taller one when the point was evaporation or browning. Brown in batches and combine. Hold back a portion of the liquid, since a big pot loses less to steam and will end up thinner if you add the same proportion. Expect timings to change in both directions: longer to reach temperature, and often shorter at temperature once the mass is holding its own heat.

There is an honest caveat here. Professional and industrial kitchens do not scale recipes at all in this arithmetic sense; they re-develop them at the target size and re-time them by measurement. The reasoning above tells you which dial slipped and roughly why, but it will not hand you the corrected number — for that, you still have to taste, probe, and adjust.

• Why does the same square-cube reasoning explain why a large animal overheats where a small one freezes?
• What does a food scientist mean by "heat transfer coefficient", and why does stirring change it?
• Why does scaling a recipe down fail in its own way, particularly for baking and for anything relying on a crust?

Every term the collection defines is gathered in the glossary.