coefficient

Etymology

It is formed from English co- + efficient,^{[2][3][4][5][6]} probably influenced by New Latin coefficiēns, used in mathematics in the 16th century,^[4][6] and by French coefficient.^[2][6] The Shorter Oxford, the Oxford Dictionary of English, Hoad and Collins take it directly from the New Latin word,^{[7][8][9][10]} which is formed from co- (“together”) and efficiēns (“accomplishing”),^[8][3] the present participle of efficiō (“to work out, accomplish”).^[11][10] Etymonline, Klein and Weekley credit the French mathematician François Viète (died 1603) with introducing the term into mathematics.^[4][5][11]

Earliest recorded meaning

As an adjective, cooperating to produce a result: 1665, in the Philosophical Transactions of the Royal Society.^[2][7] The noun is first recorded in Kersey's dictionary of 1708–15,^[2][6][3] although Etymonline dates it to about 1600.^[4]

Semantic evolution

The first meaning, a joint agent or factor in producing an effect, follows the parts of the word.^[2][4] Kersey's dictionary already had the algebraic sense, a number placed before and multiplying another quantity, and the differential coefficient, the rate of change of a function.^[2] Johnson (1755) gave both the general and the algebraic sense.^[12] From 1829 physicists used it for a multiplier that measures a property of a particular substance and is constant for it.^[2] The adjective is now rare or obsolete.^[7]

Timeline

• c. 1600 – a joint agent, in Etymonline's dating.^[4]
• 1665 – adjective, cooperating to produce a result.^[2][7]
• 1708 – in algebra, a number multiplying a quantity; also differential coefficient.^[2]
• 1708–15 – a joint agent or factor.^[2][6][3]
• 1829 – in physics, a multiplier measuring a property of a substance.^[2]

Meanings

Noun

1. In mathematics, a number or constant written before and multiplying a variable or unknown quantity: in 7y, the coefficient of y is 7.^[10][3][2]
2. In physics, a number that measures some property of a substance or system and relates one physical quantity to another.^[10][3][2]
3. Something that acts together with another to produce an effect; a joint agent or factor.^[3][2]

Adjective

1. (rare) Acting together to produce an effect.^[3][7][2]

Word family

• coefficiently

Related words

• efficient
• effect
• efficiency

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n o Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e f g h Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
4. ^ a b c d e f Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
5. ^ a b Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
6. ^ a b c d e Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
7. ^ a b c d e Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
8. ^ a b Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
9. ^ Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
10. ^ a b c d Collins English Dictionary (2023), Glasgow: HarperCollins
11. ^ a b Weekley, Ernest (1921), An Etymological Dictionary of Modern English, London: John Murray
12. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.