Start by writing the factor down
Divide the servings you want by the servings the recipe makes. Twelve cookies from a recipe for twenty-four is a factor of 0.5; nine servings from a recipe for six is 1.5. Every ingredient amount is multiplied by that one number, so write it at the top of the page before you touch a measuring cup.
Multiply the original amount, not a number you have already rounded. Half of 1⅓ cups is ⅔ cup exactly; if you first round 1⅓ to 1¼ you end up 2 teaspoons short, which is enough to matter in a small batch of dough. The recipe scaler on this site keeps the unrounded value for you and lists every line at once.
Halving awkward cup measures
US cup measures divide cleanly into tablespoons: 1 cup is 16 tablespoons and 1 tablespoon is 3 teaspoons. Half of ¼ cup is 2 tablespoons. Half of ⅓ cup is 2 tablespoons plus 2 teaspoons. Half of ¾ cup is 6 tablespoons, and half of 1½ cups is ¾ cup. The table below covers the measures that appear most often.
When a halved amount lands on a fraction your cups cannot measure, weigh it instead. Half of ⅔ cup of flour is ⅓ cup, but half of ⅔ cup of butter is easier as 76 grams on a scale than as 5 tablespoons plus 1 teaspoon by the spoon.
Doubling is easy for ingredients and hard for pans
Doubling every ingredient doubles the volume of batter or dough, but a pan holds what it holds. A doubled cake recipe needs a second pan of the same size, not a taller layer in one pan; a taller layer bakes slower in the middle and can sink or stay raw while the edges dry out. Two pans on one rack also change the airflow, so rotate them halfway through.
Cooking time does not double. A doubled soup takes longer to come to a simmer but not twice as long to cook once it does. A doubled tray of cookies takes the same time per tray. Use the original time as a guide, check early and rely on doneness cues such as colour, texture and internal temperature rather than the clock.
What not to scale in proportion
Eggs come in whole numbers. Half of three eggs is one egg plus one beaten egg measured by weight or spoon (a large egg is about 50 g out of the shell, so use about 25 g). Doubling a recipe that calls for one egg to two eggs is fine; scaling by 1.5 needs the same beaten-egg trick.
Salt, spices, chilli and strong flavourings are a matter of taste and often need a little less than the full factor when you scale up, because they are easy to add later and impossible to remove. Leavening in baking generally scales with the flour, but very large batches can need proportionally less; follow a tested recipe for big quantities rather than multiplying a small one by four.
Liquids in a braise or stew are set by the pan, not the factor. A doubled stew in a wide pot may need less than double the stock to cover the meat. Add liquid until the recipe's description is met, then adjust seasoning at the end.
Keep a note with the recipe
Write the factor and the pan you used beside the recipe. The next time you scale it, you can repeat what worked instead of re-deriving it. If the result was different from the original, note what you changed: the pan, the time, or an ingredient you adjusted by taste.