A beer recipe is a grain bill, a hop schedule, a yeast and four numbers: the gravity it should start at, the gravity it should finish at, the bitterness and the colour. The ingredients travel between brewers perfectly well. The numbers do not, because they were achieved on somebody else's kettle, with somebody else's crush, sparged at somebody else's pace. This is why a recipe that reads 1.052 so often comes out at 1.044 in your fermenter, and it is a scaling problem rather than a mistake.
What the four numbers mean
Original gravity is the sugar in the wort before fermentation and sets the strength. Final gravity is what is left and sets how the beer feels in the mouth; a beer that finishes at 1.014 tastes fuller than the same beer at 1.008 even at identical strength. Bitterness in IBU balances the malt, and colour describes what it looks like. Only the first is fixed by the grain bill, the other three depend on your mash temperature, your yeast and your water as much as on the recipe.
Efficiency is the number that moves
A recipe's grain bill implies a gravity only if you extract the same share of the sugar the author did. That share is brewhouse efficiency, and it is a property of your crush, your sparge and your kettle, not of the beer. Work it out once: gravity degrees times litres into the fermenter, divided by the potential of the grain bill times its weight. Pale malt gives roughly 300 degrees per kilogram per litre. If a recipe assumes 75% and you get 62%, scale the whole grain bill up by the ratio and the gravity lands.
Scaling to a different batch size
Grain and hops scale with the volume in the fermenter, not with the volume in the kettle: the kettle volume includes a boil-off that does not change proportionally if your boil length stays the same. Work out the water first, then scale the grain by the ratio of finished volumes, then scale the bittering hops by the same ratio and adjust for the different gravity, because a stronger wort extracts less bitterness from the same weight of hops.
Write down what happened
The most useful recipe you will ever own is the one you brewed last month with your own figures written on it: the strike temperature that actually landed on target, the boil-off you measured, the efficiency you got, the gravity it finished at and how it tasted. That turns the next brew from a prediction into an adjustment. It is also the thing this site's paid plan keeps, so that the next brew day starts from the last one rather than from a default.
Questions people ask about beer recipes
Where do good beer recipes come from?
Competition-winning recipes and the style guidelines behind them are the usual starting point, and they are freely published. What is worth more than any particular recipe is a record of what your kit did with the last one.
Why is my gravity always lower than the recipe says?
Efficiency, then the crush. A gap set for a shop-bought grain bill leaves whole kernels, and whole kernels are sugar you paid for and did not extract. Measure your efficiency and either fix the crush or scale the grain.
Can I substitute a hop the recipe calls for?
For bittering, yes, if you match the alpha acid contribution rather than the weight, half the weight of a hop at twice the alpha acid is the same bitterness. For late and dry hopping the substitution is a flavour judgement and weight matters less than character.
How do I convert a recipe from all-grain to extract?
Replace the base malt with a weight of extract that gives the same gravity (dry malt extract contributes considerably more per kilogram than grain does, because none of it is husk and none is lost to efficiency) and steep the speciality malts. The hop schedule and the yeast are unchanged.