By size or weight - I never seem to know ...
Here's some general guidelines I have used in the past:
Small onion = 4 ounces by weight or about ½ cup chopped
Medium onion = 8 ounces, or about 1 cup chopped
Large onion = 12 ounces, or about 1½ cups chopped
Jumbo onion = 16 ounces, or about 2 cups chopped
The terms are not always completely accurate so use your best judgement. I've often seen large onions that were as big or bigger than "jumbo" according to this data.
While not scientific, I think some ingredients are best left to the idea of artistic interpretation -- or in chef vernacular, "to taste". Onions are the perfect example of this. Like onions just so-so? use medium sized ones. Love 'em? Go large. Hate 'em? Go mini...and dice it really, really small.
NOTE: Skip jumbo. It's a bad category regardless of your affinity for the root. For most all veggies, it's ideal to buy small or medium, because smaller sizes maintain better flavor. The larger ones have often gained their girth through water weight...making for pithy textures and disappointing taste. Think watered-down chicken soup.
This may not help you distinguish between small and large, but will put relative sizes in perspective: Remember that volume is proportional to the cube of the girth. So it doesn't take much additional girth to increase volume substantially.
- An increase of 25% in girth nearly doubles the volume.
- An increase of 50% will more than triple the volume.
- And doubling the girth gives you eight times the yield.
If you look at the recommendations of the US National Onion Association you'll see that a small onion can be anything between 1" and 2.25" in size. In sheer volume the difference is staggering. Then if you chop or slice it the next inaccuracies appear. How thinly or finely do you chop. Then the taste, the amount of volatiles in the onion play a role; after all the volatiles give onion its taste and smell.
So, it is up to your personal taste. Use it as a guideline, chop an onion, taste it raw and cooked and then add as much as you would like.