CONSIDER the Parmesan problem: Imagine that you’re making lasagna with a recipe that calls for topping it with “a cup of grated cheese.”

This was a straightforward instruction when the box grater was the only way to shred cheese. In the last few years, though, more cooks have bought Microplanes, which can turn a small chunk of Parmesan into mountains of billowy ribbons of cheese. And there lies the difficulty: the heavier shavings of a box grater can fill a cup with twice as much cheese as a Microplane’s fluffy snow.

J. Kenji Lopez-Alt, the managing editor of the blog Serious Eats, once asked 10 people to measure a cup of all-purpose flour into a bowl. When the cooks were done, Mr. Lopez-Alt weighed each bowl. “Depending on how strong you are or your scooping method, I found that a ‘cup of flour’ could be anywhere from 4 to 6 ounces,” he said. That’s a significant difference: one cook might be making a cake with one-and-a-half times as much flour as another.

Professional chefs have long argued that there is nothing simple about a simple cup of flour. Nor is there anything foolproof in that cup of grated cheese, a half-cup of diced carrots or a tablespoon of butter. When you fill a measuring cup or spoon with any ingredient, the amount you get depends on a number of factors: how small you’ve sliced it, how tightly you’ve packed it in, how carefully you’ve scooped and whether you manage to get all of it out of the spoon. (Consider the mess of getting all the honey out of a tablespoon measure.)