What does modulus mean?
A modulus is a formally defined numerical measure used to describe the size, strength, or other characteristic of a mathematical or physical quantity. Its best-known mathematical use is the distance of a complex number from the origin: the modulus of 3 + 4i, for example, is 5. In physics and engineering, a modulus expresses a response to force or deformation, as in the modulus of elasticity, which measures a material’s resistance to being stretched or compressed. The word is therefore broader than simply “size”; it suggests a quantity defined by a precise relationship or convention. Although it is used across English-speaking countries, it belongs mainly to technical and academic registers. For general readers, the complex-number sense offers the clearest introduction, while the engineering senses are important in materials science and mechanics.
nounA modulus is a numerical quantity that expresses the size, magnitude, or measure of a property, especially in mathematics, physics, and engineering. In complex numbers, it is the distance of a number from the origin; in mechanics, it may denote a quantity such as a material’s stiffness or its ratio of stress to strain.
- A numerical quantity expressing the magnitude or measure of a mathematical or physical property.
- The distance of a complex number from the origin, equal to the square root of the sum of the squares of its real and imaginary parts.
- A coefficient expressing the relation between two physical quantities, such as stress and strain in a material.
"The modulus of the complex number 3 + 4i is 5, because it is the distance from 3 + 4i to the origin in the complex plane."
"The modulus of 5 + 12i is 13."
"The material has a high modulus of elasticity, indicating that it resists deformation under stress."
The plural is moduli, with the final i pronounced as a separate syllable in technical mathematical usage.
"The moduli of these complex numbers are equal."
In the complex plane, a complex number’s modulus is simply the length of the line from the origin to the point representing that number.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does modulus come from?
The word comes from Latin modulus, meaning “a small measure,” a diminutive related to modulus in the sense of a standard or measure. It entered English in the 17th century and initially referred to a numerical measure or standard. Its development in mathematics and mechanics reflects the broader Latin root associated with measuring, from which words such as moderate, modest, and measure also developed.
Related word forms
How modulus is actually used
The term is primarily formal and technical. In mathematics, it is especially associated with complex numbers and modular arithmetic, while in physics and engineering it commonly appears in names such as modulus of elasticity and modulus of resilience.
Easily confused with modulus
Magnitude generally means size or importance, whereas modulus usually refers to a formally defined numerical measure, such as the distance of a complex number from the origin.