Back-of-the-envelope calculation
Encyclopedia
A back-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as the actual back of an envelope
. It is more than a guess
but less than an accurate calculation
or mathematical proof
.
The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions.
A similar phrase is "back of a napkin
", which is also used in the business world to describe sketching out a quick, rough idea of a business or product.
, 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 problem
s.
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. 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.
Envelope
An envelope is a common packaging item, usually made of thin flat material. It is designed to contain a flat object, such as a letter or card....
. It is more than a guess
Guess
The word guess commonly refers to a conjecture or estimation. To "guess" is to make a prediction without sufficient information or knowledge.Guess may also refer to:*Guess , an American name-brand clothing line...
but less than an accurate calculation
Calculation
A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition...
or mathematical proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
.
The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions.
A similar phrase is "back of a napkin
Napkin
A napkin, or face towel is a rectangle of cloth used at the table for wiping the mouth while eating. It is usually small and folded...
", which is also used in the business world to describe sketching out a quick, rough idea of a business or product.
History
In the hard sciences, back-of-the-envelope calculation is often associated with physicist Enrico FermiEnrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
, who was well known for emphasizing ways that complex scientific equations could be approximated within an order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
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 problem
Fermi problem
In science, particularly in physics or engineering education, a Fermi problem, Fermi question, or Fermi estimate is an estimation problem designed to teach dimensional analysis, approximation, and the importance of clearly identifying one's assumptions...
s.
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
New Mexico
New Mexico is a state located in the southwest and western regions of the United States. New Mexico is also usually considered one of the Mountain States. With a population density of 16 per square mile, New Mexico is the sixth-most sparsely inhabited U.S...
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. 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.