There are 7.09 grams in one-quarter of an international avoirdupois ounce, which is the most commonly used measure of ounces, as of 2014. There are 7.78 grams in one-quarter of a troy ounce, which is commonly used for measuring the mass of precious metals.
An avoirdupois ounce is one-sixteenth of an avoirdupois pound. There are 7,000 grains in an avoirdupois pound, 437.5 grains in an ounce, or 109.38 grains in a quarter-ounce. A grain weighs 0.06 grams. In an international yard and pound agreement signed in 1959, the United States and countries of the Commonwealth of Nations agreed that an avoirdupois ounce is equal to 28.35 grams.