After searching, one site states:
I would figure that the granulated product would have more waste space/void per cup, and therefore one would use a lesser volume of 10x to achieve an equal measure of sweetening. Is there an aspect of this which I’ve missed?
One of the neater science demonstrations I’ve seen done was the following: a guy took two identical containers and filled them each with steel balls of differing size, tapping them down to be sure they were as tightly packed as possible. He then poured water into both of them to fill up the extra spaces, and asked us to guess which container contained more water.
The answer was that both of them had the same amount of water, to a very good approximation. The reason is that the most efficient packing for spheres is something called “hexagonal close-packed”, and as long as both containers have this same type of packing, the percentage of the space inside the containers which was occupied by spheres is constant. Sure, the gaps are larger inside the container containing the larger balls, but there are a lot fewer of those gaps than there are in the container with the smaller balls. Those two tendencies exactly cancel each other out, and the occupied percentage of the containers remains the same regardless of the size of the balls.
So what does this have to do with your question? Well, the only way that your measuring cup can contain a different amount of sugar is if the grains tend to pack in substantially different ways in granulated vs. confectioner’s sugar. It’s possible that they’re different shapes; it’s possible that air gets trapped more efficiently in confectioner’s sugar; who knows? But it can’t just be a function of the size of the grains.
I have a few friends who actually study this kind of thing for their research. I’ll ask them if they have a fancier answer than this.
Granulated sugar is cubical, that gives very tight packing.
The powdered stuff is irregular. Despite the smaller size of the bits, it doesn’t pack so well.
Incidently, if you ever find yourself out of powdered sugar, or need some without cornstarch, you make it very quickly by tossing a bit into one of those whirling blade type coffee grinders
1 3/4 of sifted confectioners sugar. Sifting introduces air into the mix and makes it a decidedly non-optimal packing. If you get 1 3/4 cup of sifted confectioners sugar and then squeezed on it really hard, I bet you could get close to 1 cup.
I agree completely with that analysis, but the site referenced in my OP claims 1 3/4 packed confectioners = 1 cup granulated, which didn’t process well. The irregular grain structure explanation sems to have weight-thanks to all who have contributed thusfar.