Carrots come in all shapes and sizes, so asking how many it takes to make a single glass of juice is like asking how many dogs it takes to fill up a bed. (Although in the latter case, the answer can be a single chihuahua, if they're determined to grab the center spot.) As a general rule, you may need between 9 and 11 medium-sized supermarket carrots to yield a single cup of juice. A more accurate way to determine the number of carrots needed to produce eight ounces of liquid, however, would be to weigh them. Eighteen ounces of carrots is necessary to fill up an 8-ounce glass. Yep, that's a lot, but carrots are much denser and less juicy than apples (you only need 14 ounces of those) or watermelon (a mere four ounces will work).
If you don't have a juicer and are using your blender to extract the juice from chopped carrots, you'll need to add liquid to facilitate the process. While this will dilute the carrot juice, a complementary flavor such as orange juice can add some much-needed sweetness and tang, while coconut water will supply nutrients of its own. In this case, you can get by with as few as three carrots as long as you use a sufficient amount of fluid to make up the difference.