What is a more professional term for the phrase 'back-of-the-envelope' calculation, used by scientists and such as a word for a very basic, general first calculation?

  • Simple? Please include an example phrase where the term would be used. "Back-of-the-envelope" is a perfectly good expression. The reason I wouldn't use it in a peer-reviewed paper isn't because its register isn't "professional" enough but because such calculations have no business being reported in a journal. – terdon Dec 3 '17 at 16:55
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    I respectfully disagree - many peer-reviewed papers use these types of calculation as a basis for their studies, one example? Cao & Caldeira (2010) Atmospheric carbon dioxide removal: long-term consequences and commitment. Environmental Rearch Letters ,5. – Alex Spence Dec 3 '17 at 17:21
  • Similarly many numerical approaches need a set of initial values known as guesses. A robust technique should give answers independent of the guesses, but a good guess can make the model converge much more quickly. Testing a range of guesses can be important. – Chris H Dec 3 '17 at 17:36
  • @AlexSpence but that's my point. If it is good enough to go in a journal, and you consider it a back of the envelope calculation, then call it a back of the envelope calculation. I assumed you meant a quick approximation, which is why I asked you for an example sentence in the first place. Otherwise, there's nothing wrong with the expression "back of the envelope" and indeed, it appears quite often in published papers. – terdon Dec 3 '17 at 18:06
  • Preliminary model (one assumes the scientists can manage the maths involved, but are having difficulty formulating a definitive equation). – Edwin Ashworth Dec 3 '17 at 23:02

Zeroth-order approximation.

In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth.

This not only has the advantage of sounding more formal, it implies a pathway toward more formal approximations.


In some cases estimate fits. I prefer rough estimate to reinforce the motion of arbitrary assumptions. With respect to your comment, initial estimate has a nice ring to it, and easily leads to ... based on which is often appropriate.

Back-of-the-envelope calculation is more generally accepted than the (presumably only British) synonym fag-packet calculation (or -- sketch etc.) Another useful but fairly informal word is guesstimate, which you'll find in plenty of dictionaries.


You can say preliminary or cursory calculations.

  • And how would the meaning of those phrases compare with "back-of-the-envelope calculation"? Is it really just a change of register, or does it change the meaning? We're generally looking for answers that give some detail, not just one-liners. – David Richerby Dec 3 '17 at 23:07

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