back-of-the-envelope

A reference to a calculation or an idea that occurs to one being jotted down on an available scrap of paper, such as the back of an envelope.[1]

• (Received Pronunciation) IPA^(key): /ˌbæk‿əv ðiː ˈɛnvələʊp/, /-ˈɒnvələʊp/, /-ˈɒnvləʊp/
• (General American) IPA^(key): /ˌbæk‿əv ði ˈɛnvəˌloʊp/, /-ˈɑnvəˌloʊp/, /-ɛnvəˌlop/

• Audio (AU)

  (file)

• Hyphenation: back of the en‧vel‧ope

back-of-the-envelope

1. (idiomatic, informal) Especially of a calculation, estimation, or other reasoning, or an idea: approximate, rough, simplified. [from 20th c.]

   Synonyms: (UK) back-of-the-fag-packet, (US) back-of-the-napkin

   We can do some back-of-the-envelope calculations before all the facts come in.

   • 1964 February 20, Edgar M[aurice] Cortright, witness, “Statement of Edgar M. Cortright, Deputy Associate Administrator for Space Science and Applications, NASA; Accompanied by Dr. John F. Clark, Director of Sciences, Office of Space Sciences and Applications”, in 1965 NASA Authorization: Hearings before the Subcommittee on Space Sciences and Applications of the Committee on Science and Astronautics, U.S. House of Representatives, Eighty-eighth Congress, Second Session on H.R. 9641 (Superseded by H.R. 10456) […] No. 1, Part 3 […], Washington, D.C.: U.S. Government Printing Office, →OCLC, page 1548:

     [T]he original estimates are frequently back-of-the-envelope-type estimates made internally without detailed engineering studies, if you go all the way back to Day 1.

   • 1966 March 17, Arthur M[elvin] Okun, witness, “Council of Economic Advisers: Salaries and Expenses”, in Departments of Treasury and Post Office and Executive Office Appropriations for 1967: Hearings before a Subcommittee of the Committee on Appropriations, House of Representatives, Eighty-ninth Congress, Second Session […], Washington, D.C.: U.S. Government Printing Office, →OCLC, page 713:

     We joke about having to make back-of-the-envelope calculations, while in the university environment we might spend 2 or 3 weeks computerizing the calculations. I might say, however, that making back-of-the-envelope calculations and later checking them out on computers has impressed me that we have developed a considerable skill in back-of-the-envelope calculations.

   • 1979 February 22, Thomas F[rancis] Eagleton, “Department of Labor: Labor-management Services Administration: Statement of Jack A. Warshaw, Deputy Assistant Secretary for Labor-management Relations [...]”, in Departments of Labor and Health, Education and Welfare and Related Agencies Appropriations for Fiscal Year 1980: Hearings before a Subcommittee of the Committee on Appropriations, United States Senate, Ninety-sixth Congress, First Session: Part 1 […], Washington, D.C.: U.S. Government Printing Office, →OCLC, page 464:

     On one defense item, somebody kept referring to it as a back-of-an-envelope cost estimate. Do you have a back-of-an-envelope cost estimate?

   • 1996, Tony Aspromourgos, On the Origins of Classical Economics: Distribution and Value from William Petty to Adam Smith (Routledge Studies in the History of Economics)‎, Abingdon, Oxfordshire; New York, N.Y.: Routledge, published 2000, →ISBN, →ISSN:

     Apart from those manuscripts which were intended as more or less complete, self-contained works, [William] Petty left a huge body of papers, much of which amounts to fragments and hastily written private notes – many the seventeenth-century equipvament of back-of-the-envelope calculations and comments. These papers constitute a further testament to his sustained investigation of economic and political subjects.

   • 1996, T[homas] W[illiam] Körner, “Biology in a Darkened Room”, in The Pleasures of Counting, Cambridge, Cambridgeshire: Cambridge University Press, published 2002, →ISBN, part II (Meditations on Measurement), pages 112–113:

     The reader will not need to be warned that the calculations involved are of the back of an envelope type and statements of the form ‘a equals b’ should be read ‘a equals b approximately’ or even ‘with a bit of luck, a and b will be of the same order of magnitude’.

   • 1998, Paul Lawrence Rose, “The Bomb as Reactor: The U235 Bomb Misconceived, 1940”, in Heisenberg and the Nazi Atomic Bomb Project: A Study in German Culture, Berkeley; Los Angeles, Calif.; London: University of California Press, →ISBN, page 115:

     Misapplying a basic feature of diffusion theory, [Werner] Heisenberg arrived at an impossibly high figure for a critical mass of pure U235. This was done by means of a seductively simple "back of an envelope" calculation in 1940, […]

   • 1999 winter, David A[lexander] Wolf, “Wow! The Earth! Just a Little E-mail from a Guy in Outer Space”, in Peter Warshall, editor, Whole Earth: Access to Tools, Ideas, and Practices, San Rafael, Calif.: Point Foundation, →ISSN, →OCLC, page 89, column 1:

     Back of the envelope calculation: I've traveled roughly 17 million miles since we left the crew quarters at Cape Kennedy, not including the van ride to the pad … in fact, Earth seems a bit dreamlike these days, as we are connected only by crackling voices on the radio and the photographs brought along and our memories.

   • 2010, David G. Thomson, quoting Pradeep Sindhu, Mastering the 7 Essentials of High-Growth Companies: Effective Lessons to Grow Your Business‎, Hoboken, N.J.: John Wiley & Sons, →ISBN:

     I remember very distinctly in October 1995, after I completed my paper design, I had an epiphany. This back-of-the-envelope design was five years ahead of its time.

   • 2010 March, Kirk McKusick, Sean Quinlan, quoting Sean Quinlan, “GFS [Google File System]: Evolution on Fast-forward”, in Moshe Y[a’akov] Vardi, editor, Communications of the ACM, volume 53, number 5, New York, N.Y.: ACM Media, →DOI, →ISSN, →OCLC, page 45, column 3:

     [I]t quickly became apparent that the natural mapping we had thought of—and which seemed to make perfect sense back when we were doing our back-of-the-envelope estimates—turned out not to be acceptable at all.

   • [2021 March 24, Christian Wolmar, “Railways Must Sell Themselves and Offer a Better Product”, in The Railway Magazine, number 927, Sutton, London: IPC Transport Press, →ISSN, →OCLC, page 46:

     Now, those Treasury mandarins unfamiliar with the railway might assume on the back of an envelope that if only 80% of trains are running, then that will cost 20% less. If only it were that simple.]

• back-of-an-envelope

• napkin math

• back-of-the-envelope calculation on Wikipedia.Wikipedia
• “back-of-the-envelope, adj.”, in Merriam-Webster Online Dictionary, Springfield, Mass.: Merriam-Webster, 1996–present.