Multiplying a recipe is arithmetic for most of it and judgement for the rest. The multiplier itself is trivial — desired servings over original servings — and the value in doing it properly is knowing which four ingredients to ignore it for.
What scales cleanly
Flour, sugar, butter, eggs, liquid, meat, vegetables — anything that is mostly bulk scales directly with the multiplier. Doubling a stew doubles all of it.
Weight is easier to scale than volume. Doubling 250 grams is obvious; doubling three quarters of a cup means working in eighths and hoping your measuring spoons agree with the recipe's.
This is a good argument for converting a recipe you use often into grams once, after which scaling it is trivial forever.
Salt and spice scale less than proportionally
Perceived saltiness and heat do not increase linearly with the amount, and a dish scaled up with the seasoning multiplied exactly tends to come out over-seasoned.
The working rule among cooks is to scale seasoning to about halfway between one and the multiplier, then taste and correct. For a doubled recipe that means roughly 1.5 times the salt to start.
Strong spices — clove, cardamom, star anise, chilli — need the most restraint. Aromatics like onion and garlic scale fine.
Leavening is the one that fails visibly
Baking powder and soda produce gas, and the batter has to be able to hold it. In a larger, deeper batter the bubbles have further to travel and more weight above them.
A doubled cake with doubled baking powder often rises fast, then collapses in the middle. The usual guidance is to scale chemical leavening by less than the multiplier on anything above about 1.5 times — around 75 to 85 percent of proportional.
Yeast is different and scales normally, because fermentation is a slower process that self-regulates against temperature and time.
Time never scales
Cooking time depends on how far heat has to travel, which depends on the depth and shape of the food — not on how much of it there is.
A doubled stew in a wider pan takes about the same time. The same doubled stew in a taller pot takes longer and reduces less, because the surface area to volume ratio changed.
Doubling a cake into a deeper tin can add half again to the time and usually wants the oven 15 to 25 degrees Fahrenheit lower so the outside does not overbake waiting for the centre.
Pan and pot capacity
The other constraint is physical. A doubled recipe needs twice the pan area, which is not twice the pan dimensions — a pan twice as long and twice as wide is four times the area.
For anything that browns, pan area matters more than capacity. Food crowded into a pan steams rather than browns because the moisture cannot escape fast enough.
When in doubt, use two pans. It is the single most reliable way to scale a recipe that involves any browning at all.