LATIN DICTIONARYLexicon Latīnum
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“extravagance” in Latin

The English word extravagance itself goes back to Latin vagus, through extra.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

extravagance
Wandering beyond fixed limits, error (in a speech); oratio vagans [Vid: DIGRESSION].
Impetuosity (of passions, etc.), intemperantia: libidinum intemperantia: cupiditatum caecus impetus (after cupiditates in alium caeco impetu incurrentes). Extravagances, stulte facta: he committed many extravagances, multa stulte fecit.
Lavish expenditure, effusio: profusio (as act): sumtus effusi or profusi (lavish expenses): profusa luxuria (excessive inclination for luxury, splendour, sensual indulgence, etc.): nimia liberalitas.

Quick answer

What is the Latin word for extravagance?
The usual Latin words for “extravagance” are errō, intemperāns, effūsiō; also profūsiō, profūsus. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.