A US cup is 8floz or 240ml, but as lucyr said, everything has different weights. 1c water weighs 240g but as far as I remember, 1c flour weighs about 120g, and 1c walnuts weighs 100g, etc.
You can find a list of ingredients with grams per cup in some cookbooks, but it really is much easer to buy a set of cups.

Have fun

med