Kitchen math

Why does twice the thickness take four times as long, and what changes when you scale up a recipe?

Kitchen math: which rule calculates what?

Three rules set cooking times in the kitchen. All three are approximate, because a real piece of meat or vegetable is not a perfect slab. But they are enough to make a decision when the recipe does not cover your case.

1. The square rule. Heat and salt move into food from the outside. The time it takes to reach the center grows with the square of the thickness.[1] A piece twice as thick takes about four times as long; three times as thick, about nine times as long. That is why meat cut thicker than the recipe says takes far longer than the difference in thickness suggests.

Time when the thickness changes

An approximate calculation for the same shape, the same heat and the same starting temperature. For poultry and ground meat, only a thermometer tells you it is done.

about 45 minutes

2. Heat is faster than salt. Heat and salt follow the same rule, but heat moves much faster. A turkey breast roasts in a few hours, while salt takes 24 hours to reach its center.[2] That is why salting and marinating start hours before cooking. Salt added during cooking stays on the surface of the meat.

3. Time and temperature can stand in for each other. Collagen turns into gelatin slowly at low temperature and quickly at high temperature.[3][4] The price of high temperature is lost water. That is why the same shank turns tender quickly in a pressure cooker and slowly over low heat, but may come out drier from the pressure cooker.

What changes when you scale up a recipe?

When a recipe grows, ingredient amounts rise by the same ratio, but cooking time, evaporation, resting, spices and pan use do not.

  • Time: Cooking time rises with the square of the thickness. That is why meat twice as thick takes about four times as long.
  • Evaporation: Evaporation is proportional to surface area. Twice the food in the same pot thickens much later. That is why you use a wide pot.
  • Resting: A large piece of meat rises another 3–5 °C (5–9 °F) after you take it off the heat. That is why you take the meat off slightly before the doneness you want. Poultry and ground meat, however, stay on the heat until they reach their safe internal temperature.
  • Spices: Spices do not scale at the same ratio as the ingredients. So scale the salt by the weight of the dish, add about 75% of the calculated amount of spice, then taste and finish.
  • Pan: In a crowded pan the temperature drops and the meat releases water. That is why you cook meat in batches.

Sources

Sources for the science numbers. A number is written as a number only when it was read in its source; anything that could not be read is written without a number.

  1. A Mathematical Model for Meat Cooking (arXiv 1908.10787, 2019)
  2. America's Test Kitchen, Salting Turkey: How Long Is Long Enough?
  3. Tornberg, Effects of heat on meat proteins (Meat Science 70, 2005)
  4. Alahakoon ve diğ., Optimisation of Sous Vide Processing Parameters (Food and Bioprocess Technology 11, 2018; ön işlemli sığır döşü)