back-of-the-envelope
UK[ˌbæk əv ði ˈenvələʊp]US[ˌbæk əv ði ˈenvəloʊp]
adj
(of a calculation or estimate) done quickly and simply, using approximate figures, as might be done on the back of an envelope.
Etymology
The phrase "back-of-the-envelope" emerged in the mid-20th century as a vivid metaphor for informal, preliminary calculations. It evokes the image of a person hastily jotting down rough figures or a simple diagram on the only available scrap of paper—the back of an envelope. The logic hinges on the contrast between the formal, detailed work done in ledgers or notebooks and the spontaneous, approximate nature of work done on an improvised surface. This idiom encapsulates a pragmatic approach to problem-solving, where a quick, conceptual estimate is valued over precise but time-consuming computation.
Analysis
This is a fixed adjectival phrase composed of common English words. It is not productively formed from classical morphemes but is a metaphorical idiom. The key components are the noun 'envelope' (from French 'envelopper', to wrap) and the prepositional phrase 'back of the'.
Examples
We started with a back-of-the-envelope calculation to see if the project was even feasible.
His back-of-the-envelope sketch of the design was surprisingly close to the final product.
Before commissioning a full study, the manager asked for a back-of-the-envelope estimate of the costs.