Back of the envelope calculations are not meant to be very accurate - but they are meant to be better than random guesses. The process of making one usually helps remove bias from your answer, and should converge to a general ballpark which is close to the answer you're looking for.

Several PMs I've spoken with so far tell me that, when interviewing, while they don't expect a very accurate answer from a back of the envelope calculation for the interviewee, they do expect that the number won't be off by too much - that is, not more than one order of magnitude in either direction.

I was surprised to hear an answer so consistent - multiple PMs from multiple industries, citing exactly the one order of magnitude margin of error.

So, I'm wondering where that one order of magnitude number came from - is it some sort of industry-wide standard? Is there a methodology book or course that introduced it? Or is it just accidental anecdotal evidence from my social circle, and not spread much farther than that?

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The PMBOK-Guide knows five types of estimates. One of them is the Rough Order of Magnitude (ROM). It has a range of -50% to +50%. As it is literally the roughest estimate, I guess your colleagues are referring to it as the minimum criteria.

And just in case you are curious, the other four types are:

  • Preliminary Estimate: -15% to + 50%
  • Budget Estimate: -10% to +25%
  • Definitive Estimate: -5% to +10%
  • Final Estimate: 0%

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