The formula
factor = servings you want ÷ servings the recipe makes
Where it comes from
Scaling a recipe is a rule of three applied to every ingredient, and it takes no shortcuts: the factor is the same for all of them, salt and leavening included. What does not scale is time and temperature, because they depend on thickness rather than quantity: twice the batter in the same tin takes far more than twice as long, while the same batter split between two tins takes exactly as long as the original.
How to work it out by hand
- Divide the servings you want by the servings the recipe makes
- Multiply every amount by that factor
- Round sensibly: half a teaspoon can be adjusted, leavening cannot
- Leave the times and temperatures exactly as they were
What is worth knowing
Three things scale badly and it is worth knowing them. Baking powder tripled leaves an aftertaste, so on a big factor it is better to fall slightly short. Salt in a fermented dough scales exactly, because it holds the yeast back in proportion. And the liquid in a stew scales less than everything else, because what evaporates depends on the surface of the pan and not on what is in it: twice the ingredients in the same pot usually leaves too much broth.