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Back-Of-The-Envelope Calculation

Back-Of-The-Envelope Calculation

What Is a Back-Of-The-Envelope Calculation?

A back-of-the-envelope calculation is a casual mathematical calculation, often performed on a scrap of paper, like an envelope. A back-of-the-envelope calculation utilizes estimated or adjusted numbers to create a ballpark figure quickly. The outcome ought to be more accurate than a conjecture, as it includes putting remembered to paper, however it will be less accurate than a proper calculation performed utilizing exact numbers and a bookkeeping sheet or calculator.

Figuring out a Back-Of-The-Envelope Calculation

A back-of-the-envelope calculation may be utilized to decide if further research and more nitty gritty calculations are justified. In the STEM disciplines (science, technology, engineering, math) such calculations are typical for the people who out of nowhere become roused by a thought or need to perform a quick exercise to estimate a number.

The way that a back-of-the-envelope calculation references working out a thought or calculation on an envelope is intended to show how little planning goes into the analysis. The individual is either so rushed or not bothered, that they will find anything material is close by that they can compose on.

For commonplace masterminds sitting at a coffee shop who just need to estimate the number of cars that pass through a bridge toll booth, the number of customers that visit a quick easygoing restaurant during lunch hour, or earnings per share (EPS) of a company in five years, back-of-the-envelope calculations are as valuable in outlining these quantitative concepts.

Roused writing on the back of an envelope since the beginning of time has prompted huge revelations by great people, and it assists ordinary individuals with business thoughts or investors with trading thoughts to get a beginning.

The magnificence of a back-of-the-envelope calculation is that it requires no research and depends on the assessor's current information, not needing any further data that isn't currently known at the time. Typically, the general subtleties or accurate sources of info aren't so important as showing up at some kind of clearer image of the problem in question.

Fermi Problem

Back-of-the-envelope calculations are at times alluded to as Fermi problems, named after physicist Enrico Fermi. Fermi was known for having the option to make close approximations to problems with the most slender of data, and at times without any data whatsoever. Enrico Fermi won the Nobel Prize in material science in 1938.

Real World Example

At the 2017 World Government Summit, Elon Musk made sense of how aliens from space could arrive at Earth: "I'll provide you with some back-of-the-envelope calculations. Any advanced alien civilization that was whatsoever keen on populating the universe, even without surpassing the speed of light, assuming you're just moving at around 10% or 20% the speed of light, you could populate the whole cosmic system in, suppose, 10 million years, perhaps 20 million, max."

Here, Musk utilized no itemized analysis nor did he perform any research. He thought of the numbers and the calculation while talking, in view of his own insight, to show up at an estimate to the problem he was examining.


  • Back-of-the-envelope calculations are more accurate than an estimate yet not quite so refined and accurate as a conventional analysis.
  • This type of calculation is utilized as an estimate to show up at a ballpark figure when required quickly.
  • These types of calculations are likewise alluded to as Fermi problems.
  • A back-of-the-envelope calculation is a quick and casual mathematical calculation.
  • A back-of-the-envelope calculation requires no research yet rather depends on the assessor's current information.