11.8: Modulus Operator

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Let’s take the example one step further: suppose you have a measurement in inches and you want to convert to feet and inches. The goal is divide by 12 (the number of inches in a foot) and keep the remainder.

We have already seen the division operator (/), which computes the quotient of two numbers. If the numbers are integers, it performs integer division. Java also provides the modulus operator (\%), which divides two numbers and computes the remainder.

Using division and modulus, we can convert to feet and inches like this:

quotient = 76 / 12;   // division
remainder = 76 % 12;  // modulus

The first line yields 6. The second line, which is pronounced “76 mod 12”, yields 4. So 76 inches is 6 feet, 4 inches.

The modulus operator looks like a percent sign, but you might find it helpful to think of it as a division sign (÷) rotated to the left.

The modulus operator turns out to be surprisingly useful. For example, you can check whether one number is divisible by another: if x \% y is zero, then x is divisible by y. You can use modulus to “extract” digits from a number: x \% 10 yields the rightmost digit of x, and x \% 100 yields the last two digits. Also, many encryption algorithms use the modulus operator extensively.