What does coefficient mean?
A coefficient is a number or known quantity that multiplies a variable or measures a particular property within mathematics and science. In an algebraic expression such as 7x, the 7 is the coefficient of x — it scales the variable by a fixed amount. Beyond pure algebra, scientists use coefficients to quantify specific relationships: the coefficient of friction describes how much two surfaces resist sliding past one another, while statisticians rely on correlation coefficients to express how strongly two variables move together. The word comes from Latin roots meaning 'acting together,' reflecting the way a number cooperates with a symbol to produce a result. Coefficients appear throughout equations in economics, chemistry, and engineering, making this a foundational technical vocabulary word for anyone working with quantitative data or formulas.
nounA numerical or constant factor that multiplies a variable in an algebraic expression, or a number measuring a specific physical property or effect (such as friction or thermal expansion). More broadly, a value that serves as a measure of some characteristic of a system or phenomenon.
- Mathematics: a numerical or constant factor multiplying a variable or term in an algebraic expression.
- Physics/engineering: a numerical measure of a specified property or effect, such as the coefficient of friction or expansion.
- Statistics: a value expressing the degree of relationship between variables, as in a correlation coefficient.
"In the equation 5x + 3, the coefficient of x is 5."
"Simplify the expression by combining like terms so each variable has a single coefficient."
"The drag coefficient of the new car design was significantly lower than that of its predecessor."
Standard plural; used when referring to multiple factors in an expression or several measured values in scientific contexts.
"The polynomial has three nonzero coefficients."
The word 'coefficient' literally means 'acting together' — because in early algebra, numbers and variables were imagined as cooperating to produce a product.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of coefficient
Coefficient derives from New Latin 'coefficient-', the present participle stem of 'coefficere', formed from Latin 'co-' (together) and 'efficere' (to bring about, to effect), which itself combines 'ex-' (out) and 'facere' (to do or make). The term entered English in the early 17th century, originally in a broader sense of 'jointly producing an effect' before narrowing to its modern mathematical use. It shares the root 'facere' with English words such as efficient, office, and facilitate.
How coefficient is actually used
Primarily a technical term used in mathematics, physics, statistics, and engineering; rarely encountered in casual conversation. In everyday mathematical speech, 'the coefficient of x' is the standard phrasing.
Easily confused with coefficient
A coefficient is the number multiplying a variable, while a constant is a standalone fixed value not attached to any variable.