back-of-the-envelope estimate
Also called: back of the envelope, quick estimate, rough estimate, Fermi estimate
A quick estimate from a short chain of round numbers you can defend, done in your head or on scrap paper. Its job is to get the order of magnitude right, not the exact value.
A back-of-the-envelope estimate answers "roughly how big?" in a minute, from a short chain of round numbers you can defend. Its job is to get the order of magnitude right, so you can sanity-check a report, size an idea or challenge a target before anyone builds a spreadsheet.
The method: break the question into a few links (users × actions per user × price, lessons ÷ lessons per learner), round each input to one significant figure, multiply the leading digits and count the zeros. Compare each link with something you know.
When a link is uncertain, push a low and a high value through the chain and report a range. A result built from guesses should look like one: "about 2 million, between 1.2 and 3 million" is honest; "1,982,437" is false precision.
Example
A CEO says an online school will deliver 50,000 lessons a month next September.
- Lessons per active learner today: 6.1 in September, 7.4 in the May peak.
- Learners needed: 50,000 ÷ 7.4 ≈ 6,800 to 50,000 ÷ 6.1 ≈ 8,200.
- Today: 1,300 at the peak, 820 last September. The claim needs 5–6 times the best month so far, about ten times last September.
- Verdict: a stretch at best; worth a growth plan and a milestone, not a promise.
Common mistakes
- Too many links. Each guess adds error; three or four links are usually enough.
- One number instead of a range. Show the low and high case when a link is uncertain.
- False precision. Round the result to match the inputs.
- Skipping the comparison. An estimate is useful only when you compare it with something real: last year, the peak month, the report you are checking.