calculus

Etymology

It is borrowed from Latin calculus (“small stone, pebble; reckoning”),^{[2][3][4][5][6]} a diminutive of calx (“small stone, limestone”), the source of chalk.^[2][4][7][8] In Latin the word was used of a pebble or counter in a game of draughts, of a stone for reckoning on an abacus or counting board, and hence of reckoning and calculation, and of a stone used in voting.^[2][7][9] It also meant a stone in the bladder or kidneys.^[7][6] The same Latin word is the source of calculate.^[3][5][10]

Earliest recorded meaning

A system of calculation in higher mathematics: 1666 in Barnhart and Merriam-Webster,^[3][6] 1672 in the OED, from the Philosophical Transactions of the Royal Society.^[2] Etymonline gives the 1660s.^[4]

Semantic evolution

The word first named a method of calculation in mathematics, and the main modern sense is short for differential calculus and integral calculus,^[4][11][12] branches of mathematics that Newton and Leibniz developed independently.^[13] In the late 17th century it also meant computation in general (1684–1817, now obsolete).^[2][12] In medicine, from 1732, it is a stone or concretion formed in the body, such as a kidney stone;^[2][4] Johnson (1755) knew only this sense, "the stone in the bladder".^[14] It is also used of tartar on the teeth.^[6][4] In logic and mathematics it is any formal system of calculation with symbols, as in predicate calculus.^[13][12]

Timeline

• 1666 – a system of calculation in higher mathematics.^[3][6]
• 1672 – first OED quotation, for the mathematical sense.^[2]
• 1684 – computation, calculation (obsolete by 1817).^[2]
• 1732 – in medicine, a stone formed in the body.^[2][4]
• 1755 – Johnson defines it as the stone in the bladder.^[14]

Meanings

Noun

1. The branch of mathematics that deals with derivatives and integrals, made up of differential and integral calculus.^[13][12][6]
2. Any method or system of calculation or reasoning with symbols; in logic, a formal system.^[13][12][6]
3. In medicine (plural calculi), a stone-like concretion of mineral salts in a hollow organ or duct, as a kidney stone.^[13][6][2]
4. Tartar on the teeth.^[6]
5. (obsolete) Computation, calculation.^[2][12][6]

Word family

• precalculus
• differential calculus
• infinitesimal calculus
• integral calculus

Related words

• calcify
• calcium
• calculate
• chalk

References

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