# Modulus vs. Modulo: What's the Difference?

## Modulus and Modulo Definitions

#### Modulus

Abbr. m or M(Physics) A quantity that expresses the degree to which a substance possesses a property, such as elasticity.

#### Modulo

(Mathematics) With respect to a specified modulus

18 is congruent to 42 modulo 12 because both 18 and 42 leave 6 as a remainder when divided by 12.

#### Modulus

The square root of the product of a complex number and its complex conjugate.

#### Modulo

Correcting or adjusting for something, as by leaving something out of account

This proposal is the best so far, modulo the fact that parts of it need modification.

#### Modulus

Abbr. mod A natural number used as a specified divisor in modular arithmetic.

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#### Modulo

(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.

#### Modulus

The number by which a logarithm in one system must be multiplied to obtain the corresponding logarithm in another system.

#### Modulo

(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.

#### Modulus

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

#### Modulo

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

In the Lisp programming language, 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.

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#### Modulus

(mathematics) The absolute value of a complex number.

#### Modulo

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

#### Modulus

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

#### Modulus

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

#### Modulus

A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength, efficiency, etc.; a parameter.

#### Modulus

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

2 is a modulus of 5 and 9

#### Modulus

The absolute value of a complex number

#### Modulus

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