# What is the difference between modulo and modulus?

Throughout my education in computer science, I feel like I've heard the terms "modulo" and "modulus" used interchangeably. It looks like even Wikipedia claims that "modulo" is "sometimes called 'modulus'" (see the first sentence of the page on 'modulo').

I've looked into this issue a little and it seems that "modulo" finds singular use in modular arithmetic (e.g. "19 and 64 are congruent modulo 5"). In addition, I've seen the symbol % be referred to as "modulo."

Meanwhile, "modulus" appears to have several definitions, including "absolute value" and "constant factor" as well as referring to the "5" in "modulo 5."

Is it ever correct to use these terms interchangeably in the context of computer science? Are they simply different types of words that represent the same idea (such as "run" and "runner")? Are there important differences in other disciplines?

Bonus: Etymologically, what gave rise to these two terms?

• It's the other number that's "sometimes called 'modulus.'" ​ ​ – user12859 Feb 13 '16 at 3:19
• @D.W. I believe what Ricky addressed this—the wording in the first paragraph is slightly ambiguous but "sometimes called 'modulus'" refers to some concept in the first paragraph which I now believe I mistakenly thought was modulo. – intcreator Feb 13 '16 at 3:55