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
    Commented Dec 3, 2017 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. Commented Dec 3, 2017 at 17:21
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    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
    Commented Dec 3, 2017 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
    Commented Dec 3, 2017 at 18:06
  • Preliminary model (one assumes the scientists can manage the maths involved, but are having difficulty formulating a definitive equation). Commented Dec 3, 2017 at 23:02

3 Answers 3


[Making a] Zeroth-order approximation [Wikipedia].

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.

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    'First approximation' is probably the everyday equivalent of the technical 'zeroth approximation'. The Wikipedia article mentions this. Commented Jun 15, 2023 at 16:43

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. Commented Dec 3, 2017 at 23:07

In some cases estimate fits. I prefer rough estimate to reinforce the notion 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.

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