What does modulo mean?
Modulo is a mathematical and computing term used when a calculation is performed with respect to a specified modulus. Given an integer and a positive modulus, modular arithmetic focuses on the remainder obtained by division; for example, 17 modulo 5 is 2. The same operation is used in programming to test properties such as whether a number is even, to extract digits, and to perform calculations in cyclic structures. In formal notation, expressions such as “x modulo n” or “x mod n” are common. The term is closely associated with modular arithmetic, in which numbers that leave the same remainder are treated as equivalent. Although “mod” is more familiar in computing, “modulo” is the standard full form and is widely understood in technical and academic contexts.
prepositionWith respect to a specified modulus, especially when calculating the remainder on division by that modulus. In computing, it refers to an operation that returns the remainder after one integer is divided by another.
- With respect to a specified modulus in modular arithmetic.
- In computing, with respect to the remainder produced by an integer division operation.
"The repeating sequence can be calculated modulo 7, so each result lies between 0 and 6."
"Two integers are equivalent modulo 5 when they leave the same remainder when divided by 5."
"The programmer used the modulo operator to determine whether the input was even."
Modulo arithmetic makes numbers wrap around: clock arithmetic, calendar cycles, and many computer systems use it to keep calculations within a fixed range.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does modulo come from?
The word comes through Italian modulo from Latin modulus, a diminutive of modus, meaning “measure” or “manner.” The mathematical sense developed from the use of a modulus as a measure or divisor in modular calculations. English usage became established in mathematical writing before the abbreviated form “mod” became common in computing.
Related word forms
How modulo is actually used
In formal mathematics, “modulo” is normally read as “with respect to a modulus” and is commonly paired with the symbol “mod,” as in “12 mod 5.” In programming, “modulo” and “mod” often refer to the remainder operation, although the behavior for negative numbers can differ between systems and languages.
Easily confused with modulo
A modulus is the positive integer used as the divisor in modular arithmetic, whereas modulo indicates that a calculation is performed with respect to that divisor.
Mod is the informal or programming abbreviation of modulo, while modulo is the fuller standard term.