Back-of-the-envelope calculation
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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.
Note that the term is an idiom; back-of-the-envelope calculations need not be performed on an envelope, or even written on paper; they could be performed on a computer. The defining factor is the use of simplified, scaled-down models.
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In the hard sciences, back-of-the-envelope calculation is often associated with physicist Enrico Fermi,[1] 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.[2][3]
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. This method of getting approximate and quick answers became informally known as the Fermi method.
Another related anecdote involves the wife of Albert Einstein visiting a star observatory. She asked the reason for the fancy, complicated equipment. The observatory director answered that by them they "unveil the secrets of the universe". She answered: "Well, my husband reveals the secret of the universe with a pencil and a used envelope".[citation needed]
