There are 16 cups in 1 gallon. One easy way to calculate relationships between measurements of volume is to use an online calculator.
To calculate how many cups are in one gallon, a person must know that there are 2 cups in 1 pint, there are 2 pints in 1 quart and there are 4 quarts in 1 gallon. From this, a person can come to the conclusion that there are 4 cups in 1 quart. Since there are 4 quarts in 1 gallon, the person can then multiply 4 times 4 to determine that there are 16 cups in 1 gallon.