coefficient

coefficient — noun

1. In algebra, a number or symbol that is written before a variable and tells you h

1.nounB2
Definition

In algebra, a number or symbol that is written before a variable and tells you how many times that variable is included in a term. For instance, in the expression 4y, the coefficient 4 shows that y is taken four times.

Example

In the equation 5x + 3 = 18, the coefficient of x is the number 5.

coefficient of [variable] before an equals sign

Theo noticed that the term 9b² has a coefficient of 9.

coefficient in a squared term

Common collocations
  • leading coefficient
  • numerical coefficient
  • negative coefficient
  • positive coefficient
  • coefficient of x
Synonyms
  • multiplier

    Emphasises the multiplying function; less common in classroom algebra, more used in statistics and economics.

  • factor

    Broader term — any number that divides into or combines with others; not specific to the number in front of a variable.

  • numerical factor

    Formal phrasing; used in textbooks to distinguish the number from the variable part of a term.

Grammar Patterns

coefficient of [variable]

Usage Note

Often appears with 'of' followed by the variable: ‘the coefficient of x’. A variable with no written number has an implied coefficient of 1.

Common Mistakes

The number 3 in 3× is called a constant.
The number 3 in 3x is called a coefficient.
A constant stands alone (like the 5 in x + 5), while a coefficient multiplies a variable.
The coefficient of x in x² + 2x is 2.
The coefficient of x² is 1 and the coefficient of x is 2.
Each power of a variable has its own coefficient.

2. A number used in science and engineering to express how much of a specific physi

2.nounB2
Definition

A number used in science and engineering to express how much of a specific physical property a material or system has. Examples include the coefficient of friction between two surfaces and the coefficient of thermal expansion of a metal.

Example

The friction coefficient between rubber tyres and dry asphalt is roughly 0.9.

friction coefficient + material pair

Engineers calculated the thermal expansion coefficient of steel before building the railway track.

Common collocations
  • friction coefficient
  • drag coefficient
  • coefficient of expansion
  • coefficient of restitution
  • absorption coefficient
  • safety coefficient
  • temperature coefficient
Synonyms
  • index

    Used in specific fields like optics (refractive index); narrower in meaning.

  • constant

    A value that stays fixed under given conditions; a coefficient is one type of constant.

  • modulus

    Refers specifically to a measure of a physical property such as elasticity; more technical than coefficient.

Grammar Patterns

coefficient of [property]

[property] coefficient

Usage Note

Most commonly appears in compound terms such as 'friction coefficient' or 'coefficient of expansion'. Each scientific field has its own specific coefficients with standard symbols.

Common Mistakes

The rate of friction is 0.5.
The coefficient of friction is 0.5.
'Coefficient' refers to a fixed measure of a property, not a rate of change.

Synonym discussion

Sense: noun/1

In algebra, a coefficient specifically multiplies a variable (the 4 in 4x). A factor is a broader term — any number that divides evenly into a product or combines with others through multiplication. For instance, 2 and 3 are both factors of 6, but neither is a coefficient unless placed before a variable. A constant is a fixed value that does not change, such as the +5 in 2x + 5; it is not tied to a variable. A multiplier is close to coefficient but is more often used in economics or statistics to describe an amplifying effect (e.g., the fiscal multiplier). A parameter is a quantity that defines the behaviour of a system or equation — it can include coefficients as one type. In everyday classroom algebra, 'coefficient' is the precise term for the number in front of a variable; use 'factor' only when talking about divisibility, and 'constant' when referring to the standalone number in an expression.

factor ↗constant ↗multiplierparameter ↗

Common collocations

Nouns

  • correlation coefficient
  • coefficient value
  • coefficient estimate

Phrases

  • coefficient of determination
  • coefficient of friction
  • coefficient of expansion
  • coefficient of restitution
  • coefficient of variation

Prepositions

  • coefficient of

Etymology

LatinFrenchEnglish

Borrowed in the mid-1600s from French 'coefficient', which came from Latin 'co-' meaning 'together with' and 'efficiens' meaning 'producing or bringing about'. The original idea was 'something that works together with something else to produce a result' — in the case of a mathematical coefficient, it works together with a variable to form a term. The scientific meaning (a number measuring a property) developed in the 1700s as physics and chemistry grew as experimental fields.