What does moduli mean?
Moduli is the plural of modulus, a term used most often in mathematics and engineering. In number theory, a modulus is a positive integer used to determine whether two integers have the same remainder when divided by it. Equivalently, it defines a congruence class: integers are congruent modulo a given modulus when their difference is divisible by that number. The plural moduli therefore refers either to the chosen integers or to the collection of multiples associated with them. In physics and materials science, a modulus is a measure of a material’s response to deformation, so elastic moduli and shear moduli describe how resistant materials are to particular forms of stress. The word is predominantly technical, though its mathematical sense is common in advanced school and university mathematics.
noun (plural)The plural form of modulus. In mathematics, moduli are constants used in congruences; in physics and engineering, moduli are numerical measures of properties such as elasticity or stiffness.
- The plural of modulus, especially a mathematical integer used to express equivalence under congruence.
- Plural of modulus used for numerical measures of stiffness, elasticity, or other material properties.
"The test compares the measured elastic moduli of the two composite materials."
"All integers in the same residue class share a common modulus."
"The laboratory reported different elastic moduli for samples produced at distinct temperatures."
The headword is already plural; its singular form is “modulus.”
"Each calculation specifies one of several possible moduli."
One mathematical modulus defines a congruence class; its multiples, the moduli, form an entire family of equivalent remainders.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does moduli come from?
“Moduli” is the regular plural of the noun “modulus,” formed by adding the Latin plural ending -i. “Modulus” was borrowed from Latin, where it means “small measure” and derives from modus, meaning “measure,” “manner,” or “extent.” The same Latin root also underlies English words such as “moderate,” “modest,” and “modulate.”
Related word forms
How moduli is actually used
The word is normally plural because it is the inflected form of the singular noun “modulus.” In technical mathematics, it should not be confused with the unrelated plural “moduluses,” which is occasionally encountered in nontechnical or older usage.