Quick Answer
1/4 cup equals approximately 59 grams of water.
For common kitchen ingredients, 1/4 cup is about 31 grams of all-purpose flour, 50 grams of granulated sugar, 55 grams of packed brown sugar, 57 grams of butter, and 46 grams of uncooked white rice.
The exact gram amount changes by ingredient because cups measure volume and grams measure weight.