﻿

# Back-of-the-envelope calculation

The phrase back-of-the-envelope calculations refers to rough calculations that, while not rigorous, test or support a point. They are far more than a guess but far less than a proof. The phrase is generally used in mathematics, physics and engineering. It refers to the practice of quickly jotting down calculations on the nearest available piece of paper, such as the back of an envelope.

The term is an idiom; "back-of-the-envelope" calculations need not be performed on an envelope, or written on paper, or even written down at all. The defining factor is the use of simplified, scaled-down models.

History

In the hard sciences, "back-of-the-envelope calculation" is often associated with physicist Enrico Fermi, [ [http://www.encyclopedia.com/doc/1G1-78334537.html Where Fermi stood. - Bulletin of the Atomic Scientists | Encyclopedia.com ] ] who was well known for emphasizing ways that complex scientific equations could be approximated within an order of magnitude using simple calculations. He went on to develop a series of sample calculations which are called "Fermi Questions" or "Back-of-the-Envelope Calculations" and used to solve Fermi problems. [ [http://serc.carleton.edu/quantskills/methods/boe/ Back of the Envelope Calculations ] ] [ [http://www.nap.edu/html/hs_math/be.html High School Mathematics at Work: Essays and Examples for the Education of All Students ] ]

Fermi was known for getting quick and accurate answers to problems which would stump other people. The most famous instance came during the first atomic bomb test in New Mexico on July 16 1945. As the blast wave reached him, Fermi dropped bits of paper. By measuring the distance they were blown, he could compare to a previously computed table and thus estimate the bomb energy yield. He estimated 10 kilotons of TNT; the measured result was 18.6.

Another example is Victor Weisskopf's pamphlet "Modern Physics from an Elementary Point of View". [Lectures given in the 1969 Summer Lecture Programme, CERN (European Organization for Nuclear Research), CERN 70-8, 17 March 1970.] In these notes Weisskof used back-of-the-envelope calculations to calculate the size of a hydrogen atom, a star, and a mountain, all using elementary physics.

A similar phrase is back of a napkin.

Examples

* When British engineer James Nasmyth was asked to build a bigger hammer after the workpiece was too big for existing fall hammers, Nasmyth, after a little thought, sketched out on a piece of paper the design for the steam hammer.
* There is a commonly held legend that economist Arthur Laffer first explained the Laffer Curve on the back of a napkin.
* Legend has it that the original Southwest Airlines "Texas Triangle", connecting its major cities (Dallas, Houston, San Antonio) was created on the back of a napkin.

ee also

*Sanity test
*Rule of thumb

References

* [http://www.cs.northwestern.edu/~paritosh/papers/BotEStrategiesAAAI05.pdf Analysis of Strategic Knowledge in Back of the Envelope Reasoning, a paper presented at 20th National Conference on Artificial Intelligence, AAAI 2005. (PDF)]
* [http://www-cse.ucsd.edu/classes/sp97/cse141/botec.html Syllabus at UCSD]

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• back-of-the-envelope calculation — A back of the envelope calculation is a figure that was arrived at quickly or by using estimation as if someone had grabbed the first scrap of paper they found and made a quick guess …   The small dictionary of idiomes

• Back-Of-The-Envelope Calculation — An informal mathematical computation, often performed on a scrap of paper such as an envelope. A back of the envelope calculation uses estimated and/or rounded numbers to quickly develop a ballpark figure. The result should be more accurate than… …   Investment dictionary

• back-of-the-envelope calculation —    This expression refers to a quick approximate calculation done informally, as on the back of an envelope.     I don t need the exact amount. Just give me a back of the envelope calculation …   English Idioms & idiomatic expressions

• back-of-the-envelope — adj, always used before a noun informal : done to provide a rough idea of something I can t tell you the exact amount, but my back of the envelope [=rough] calculation indicates a cost of about \$300,000 …   Useful english dictionary

• on the back of an envelope — (informal) Said of a calculation that is performed quickly and without scrupulous regard to accuracy • • • Main Entry: ↑envelop * * * on the back of an envelope phrase quickly and without thinking about all the details The proposal was no doubt… …   Useful english dictionary

• Back of a napkin — #REDIRECT Back of the envelope calculation R from merge …   Wikipedia

• List of minor characters from The Hitchhiker's Guide to the Galaxy — The following is a list of minor characters in the various versions of The Hitchhiker s Guide to the Galaxy , by Douglas Adams.AgrajagAgrajag is a constantly reincarnated entity who ends up being killed multiple times by Arthur Dent. First… …   Wikipedia

• rough calculation — /ˌrʌf ˌkælkjυ leɪʃ(ə)n/ noun a way of working out a mathematical problem approximately, or the approximate result arrived at ● I made some rough calculations on the back of an envelope …   Dictionary of banking and finance

• List of minor The Hitchhiker's Guide to the Galaxy characters — The following is an alphabetical list of the minor characters in the various versions of The Hitchhiker s Guide to the Galaxy, by Douglas Adams. The descriptions of the characters are accompanied by information on details about appearances and… …   Wikipedia