I have three sources for what 1 cup cake flour weights. Americas Test Kitchen says 113 grams, Calculateme.com says 130 grams and JoyofBaking.com says it is 120 grams.
Which is the correct conversion from volumetric to weight based measurements for a cup of cake flour?
Who’s right? In a way, all of them are.
The weight equivalent of volumetric measurements will depend on the packing, which in turn will depend on the baker.
The probably lowest value you will get if you use slightly older flour, stored in a dry environment, sieved, then spooned into the measuring cup and leveled. That’ll be pretty close to, I’d say 110 g. In contrast, a flour from a humid environment, that has settled during transport and storage and was then scooped directly with the measuring cup - you can get easily close to 150g in that case.
Admittedly, the latter isn’t good practice, but it shows the difference and the Achilles heel of measuring by volume. When a recipe requires precision and reliability, it’s usually written in weight-based measurements and ratios. In daily use, many recipes have enough tolerance built in for the kind of errors introduced by volumetric units, and some will explain the method (e.g. “spooned and leveled”). In baking there’s often a final step that says add “1-3 tablespoons of milk” or “as needed” - aiming to get the batter to the desired consistency.
If you need true precision, use a scale. There are e.g. macaron recipes that start with weighing the eggs, then weigh the other ingredients based on that. Likewise commercial recipes that will list “350g egg” instead of seven eggs - which is roughly the same amount, but not necessarily exactly the same.
As Juliana mentioned in a comment, the weight (mass) of a particular volume (in this case 1 cup) of something depends on its density. If you are measuring water, which has a very consistent density, then you can convert easily. If you are measuring walnuts, which could be packed tightly or loosely, then the conversion will have to be very rough. Flour is somewhere in between which is why there are different measurements.
This is why most regular or professional bakers use weights rather than volume measurements, although I understand that in some parts of the world volume measurements are still typical. If you trust the recipe writer, then a recipe written using volume measurements should not require perfect precision anyway so I would just go for a weight somewhere in the middle of the estimates you have found.
If the recipe is in a cookbook you may even have a section at the start/end giving conversions, or giving instructions for how to measure the volume (for example by tapping the cup to allow the flour to settle).
In addition to the built-in uncertainty when measuring flour by volume, not all cake flour (or AP flour, or whole wheat flour) is the same. A theoretical perfectly-measured cup of one brand may not weigh exactly the same as a cup of another brand.
The best thing to do is to start with a recipe that provides weights. I believe JoyOfBaking does this for all her recipes, and ATK does for most if not all of their baking recipes.
If you want to stick with a recipe that only includes volume measurements, I would either:
