# Modulus vs. Modulo

## Difference Between Modulus and Modulo

#### Modulusnoun

(mathematics) The base with respect to which a congruence is computed.

#### Modulopreposition

(mathematics) Given a specified modulus of.

*21 and 84 are congruent to each other modulo 9, since both numbers leave the same remainder, 3, when divided by 9.*

*Thus 21 modulo 9 is 3, because when 21 is divided by 9, the remainder is 3.*

#### Modulusnoun

(mathematics) The absolute value of a complex number.

#### Modulopreposition

(technical) Except for differences accounted for by.

*"A is the same as B modulo C" means A is the same as B except for differences accounted for by C.*

#### Modulusnoun

(physics) A coefficient that expresses how much of a certain property is possessed by a certain substance.

#### Modulopreposition

(extended use) With due allowance for (a specified exception or particular detail).

*The "tail recursion modulo cons" technique allows functions that would be tail recursive but for a cons call to be transformed into a tail recursive form.*

*All mammals, modulo the monotremes, give birth to live young.*

#### Modulusnoun

An operator placed between two numbers, to get the remainder of the division of those numbers.

#### Modulonoun

(computing) The operation or function that returns the remainder of one number divided by another.

#### Modulusnoun

an integer that can be divided without remainder into the difference between two other integers;

*2 is a modulus of 5 and 9*

#### Modulusnoun

the absolute value of a complex number

#### Modulusnoun

(physics) a coefficient that expresses how much of a specified property is possessed by a specified substance