A cup measures volume and a gram measures weight, therefore the number of grams cannot be given because it is entirely dependent on what is in the cup. A cup of something heavy weighs more in grams than a cup of something light.
Cup-to-gram measurements are often used in cooking, but the item being used must be known. For instance, 1 cup of butter weighs 227 grams, while 1 cup of granulated white sugar weighs 201 grams. In the United States cooking recipes call for cups, tablespoons and teaspoons. In most of the world the metric system is used, consisting of liters, milliliters, grams and kilograms.