Knowing the difference will make you an ace cake baker.
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Most cake recipes call for flour. That's specific, yet vague, which is why we usually turn to all-purpose wheat flour that's supposed to cover all the bases, and it usually does. Some cake recipes, however, specify cake flour. What's the difference?

Cake flour is very finely milled soft winter wheat that makes it lighter and softer than other types of flour. It also has lower protein content, around 7 to 8 percent protein compared to 10 to 12 percent for all-purpose or 14 to 16 percent for bread flour. High protein flour develops more gluten, adding strength and elasticity to the dough and final baked good. That's what we need for a dense, chewy loaf of bread, but not what we want for tender cake or other delicate baked goods. Low-protein cake flour helps cakes turn out light and fluffy with a fine, close crumb. All-purpose flour is widely used (and the default whenever a recipe simply calls for flour) because it's middle ground between flours that are higher or lower in gluten.

Replacing all-purpose flour with cake flour in all cake recipes sounds like a great idea, but it isn't an even swap and might not improve all cakes. All-purpose flour weighs about 4.5 ounces per cup while cake flour weighs about 4 ounces per cup, so to substitute one for the other can affect the ratio and proportion of the other ingredients in the recipe and change how the cake turns out.

The best advice is that when a recipe specifies cake flour, use it. 

These days there are several reliable brands of cake flour in the grocery store, but at one time Swans Down was so common and familiar that many home bakers wrote that instead of the words "cake flour" in their recipes.