Aback-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as anenvelope. It is more than aguess but less than an accuratecalculation ormathematical proof. The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions.
A similar phrase in the U.S. is "back of anapkin", also used in the business world to describe sketching out a quick, rough idea of a business or product.[1] In British English, a similaridiom is "back of afag packet".
In the natural sciences,back-of-the-envelope calculation is often associated with physicistEnrico Fermi,[2] who was well known for emphasizing ways that complex scientific equations could be approximated within anorder 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 solveFermi problems.[3][4]
Fermi was known for getting quick and accurate answers to problems that would stump other people. The most famous instance came during thefirst atomic bomb test inNew Mexico on 16 July 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.[5][6]
Perhaps the most influential example of such a calculation was carried out over a period of a few hours byArnold Wilkins after being asked to consider a problem byRobert Watson Watt. Watt had learned that the Germans claimed to have invented a radio-based death ray, but Wilkins' one-page calculations demonstrated that such a thing was almost certainly impossible. When Watt asked what role radio might play, Wilkins replied that it might be useful for detection at long range, a suggestion that led to the rapid development ofradar and theChain Home system.[7]
Another example isVictor Weisskopf's pamphletModern Physics from an Elementary Point of View.[8] In these notes Weisskopf used back-of-the-envelope calculations to calculate the size of a hydrogen atom, a star, and a mountain, all using elementary physics.
In a video interview for theUniversity of California, Berkeley on the 50th anniversary of the laser, Nobel laureateCharles Townes described how he pulled an envelope from his pocket while sitting in a park and wrote down calculations during his initial insight into lasers.[9]
During lunch with NFL commissionerPete Rozelle in 1966,Tiffany & Co. vice president Oscar Riedner made a sketch on a cocktail napkin of what would become theVince Lombardi Trophy, awarded annually to the winner of theSuper Bowl.[10]
An important Internet protocol, theBorder Gateway Protocol, was sketched out in 1989 by engineers on the back of "three ketchup-stained napkins", and is still known as the three-napkin protocol.[11]
UTF-8, the dominant character encoding for theWorld Wide Web,[12] was designed byKen Thompson andRob Pike on a placemat.[13]
TheBailey bridge is a type of portable, pre-fabricated, truss bridge and was extensively used by British, Canadian and US military engineering units.Donald Bailey drew the original design for the bridge on the back of an envelope.[14]
TheLaffer Curve, which claims to show the relationship between tax cuts and government income, was drawn byArthur Laffer in 1974 on a bar napkin to show an aide to PresidentGerald R. Ford why the federal government should cut taxes.[15]
Upon hearing that theS-IV 2nd Stage of theSaturn I would need transport from California to Florida for launch as part of theApollo program,Jack Conroy sketched the cavernous cargo airplane, thePregnant Guppy.[16]
TheVideo Toaster was designed on placemats in a Topeka pizza restaurant.[17]
Robert Metcalfe's earlyEthernet diagrams from his days at Xerox PARC back in the early 1970s might be the most famous napkin sketches in the technology industry.
As the prospect of system meltdown loomed, the men began scribbling ideas for a solution onto the back of a ketchup-stained napkin. Then a second. Then a third. The "three-napkins protocol," as its inventors jokingly dubbed it, would soon revolutionize the Internet. And though there were lingering issues, the engineers saw their creation as a "hack" or "kludge," slang for a short-term fix to be replaced as soon as a better alternative arrived.
He sketched the original design for the Bailey Bridge on the back of an envelope as he was being driven to a meeting of Royal Engineers to debate the failure of existing portable bridges
[Conroy] listened to the conversations around him, then picked up a cocktail napkin and a ballpoint pen. And with the precision he'd learned during the brief months he'd attended engineering school many years before, he drew an airplane that had never been built, to carry a rocket that had never been launched, to take man to a place nobody had ever been before.Jack Conroy had just sketched the airplane that would become the Pregnant Guppy.
Montgomery suggested thatJenison meet his friendBrad Carvey, who had been working on projects involving robotic vision. The three of them got together in a pizza restaurant in Topeka and started drawing block diagrams on the placemats.
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