## DEFINITION of 'Back-Of-The-Envelope Calculation'

A back-of-the-envelope calculation is an informal mathematical computation, often performed on a scrap of paper such as an envelope. A back-of-the-envelope calculation uses estimated or rounded numbers to quickly develop a ballpark figure. The result should be more accurate than a guess, as it involves putting thought to paper, but it will be less accurate than a formal calculation performed using precise numbers and a spreadsheet or calculator.

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## BREAKING DOWN 'Back-Of-The-Envelope Calculation'

A back-of-the-envelope calculation might be used to determine whether further research and more detailed calculations are warranted. In the STEM disciplines (science, technology, engineering, math) such calculations are commonplace for those who suddenly become inspired by an idea or want to perform a quick exercise to estimate a number.

At the 2017 World Government Summit, Elon Musk explained how aliens from outer space could reach Earth: "I'll give you some back-of-the-envelope calculations. Any advanced alien civilization that was all interested in populating the galaxy, even without exceeding the speed of light, if you're only moving at about 10 or 20 percent the speed of light, you could populate the entire galaxy in, let's say, 10 million years, maybe 20 million, max." For mundane thinkers sitting at a coffee shop who just want to estimate the number of cars that pass through a bridge toll booth, the number of customers that visit a fast-casual restaurant during lunch hour, or earnings per share of a company in five years, back-of-the-envelope calculations are as useful in framing these quantitative concepts as Mr. Musk predicting the chances of aliens invading our skies. Inspired scribbling on the back of an envelope throughout history has led to great discoveries by great men and women — and it helps ordinary people with business ideas or investors with trading ideas get a start.

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