What does arithmetically mean?
"Arithmetically" is a formal adverb meaning in a manner that relates to arithmetic — that is, according to the basic operations of addition, subtraction, multiplication, and division. It appears most often in mathematical and academic prose, where it carries two related senses. First, it can describe something done by straightforward numerical calculation: a figure verified arithmetically has been checked by plain computation. Second, and more distinctively, it describes growth or change that proceeds in an arithmetic progression, increasing or decreasing by a fixed amount at each step — a population growing arithmetically might add one thousand people every year. This contrasts sharply with "geometrically," which denotes change by repeated multiplication and hence far faster expansion. The contrast was made famous by Thomas Malthus, who argued in the late eighteenth century that food production increases arithmetically while population tends to grow geometrically. The word derives from Greek "arithmos," meaning number, via Latin and French, and belongs to the same family as "arithmetic" and "arithmetician."
adverbIn a way that relates to arithmetic; according to the rules or methods of arithmetic, especially as opposed to geometric or other forms of reasoning.
- In accordance with the methods of arithmetic; by simple calculation with numbers.
- In an arithmetical progression — increasing or decreasing by a constant amount (as opposed to geometrically).
"The population grew arithmetically, adding a fixed number of people each year rather than doubling."
"The sequence continues arithmetically, rising by seven with each term."
"She checked the invoice arithmetically before approving it, line by line."
When Malthus warned that food supply grows arithmetically while population grows geometrically, he turned a humble adverb into one of history's most consequential ideas.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of arithmetically
"Arithmetically" derives from the Greek "arithmetikos," from "arithmos" (number), which passed into Latin as "arithmetica" and then into Middle French before entering English. The noun "arithmetic" was established in English by the early modern period, and the adverb formed from it with the suffix "-ly" followed later. Cognates sharing the Greek root include "arithmetician" and, more distantly through the broader family of number-related terms, words such as "logarithm."
Related word forms
How arithmetically is actually used
The word is formal and largely confined to mathematical, scientific, and academic writing. Its most famous use is in discussions of arithmetic versus geometric progressions, notably in Malthus's writings on population.
Easily confused with arithmetically
'Arithmetically' describes change by constant addition (e.g. +2, +2, +2), while 'geometrically' describes change by constant multiplication (e.g. ×2, ×4, ×8).