Think back to your fourth grade arithmetic. When you divide two numbers, you have a dividend (the number on top), a divisor (the number on the bottom), a quotient (the answer), and a remainder (what's left over). In computer science, this kind of division is very important. However, we're usually more interested in the remainder than in the quotient. When we're interested in the remainder, we call the operation a modulus (or modulo, or mod). For instance, one of the examples on your fourth grade arithmetic text might have been 13 ÷ 3 = 4 (with a remainder of 1). As computer users, we're more interested in 13 mod 3 = 1. It's really the same operation, though. Modulo is also used in expressions like "modulo wildcards," which means "everything but wildcards."

A BASIC operator which produces the remainder left after a division operation. The command is MOD.

Taking the remainder after division. For example, 4 mod 2 = 0 since four is divisible by two but 5 mod 2 = 1 since 1 is the remainder (i.e., 5 - 4 = 1).

The word modulo (Latin, with respect to a modulus of ___) is the Latin ablative of modulus which itself means "a small measure." It was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. Ever since however, "modulo" has gained many meanings, some exact and some imprecise.

This article discusses the usage of the term modulo as a form of mathematical jargon. It does not discuss the precise meaning of the mathematical concept.