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The modulus of a vector r, usually written |r|, or sometimes simply r, is defined to be the length of the vector r. If r is written in terms of three orthonormal vectors (ie: mutually perpendicular vectors of unit length), i, j and k such that:

r = xi+yj+zk,

the modulus of r is the square root of x2+y2+z2.

It should be noted that the modulus of a vector is a scalar.

Modulus is also a synonym for:

In materials science modulus (or elastic modulus) is a measure of the stiffness of a material. See also Young's modulus

In computer programming, the modulus operator gives the remainder of integer division, ie modular arithmetic. Mathematicians tend to call this modulo, for example:

13 = 3 modulo 10
13 = 3 mod 10

This is because 10 is here the modulus of the congruence, and modulo (a Latin ablative) stands for 'to the modulus'.

C programmers will write:

13 % 10 = 3.