Fermi estimation
Decompose an unknown quantity into factors you can bound, so that errors partly cancel and the result lands within an order of magnitude.
- Time cost
- 15 min
- Output
- A decomposition with a low, central and high estimate.
- Steps
- 5
Use when
- You need a number now and no data source will produce one.
- You want to size a branch before deciding whether to research it.
- Someone has quoted a figure and you want to know whether it is plausible.
Do not use when
- Precision matters. This gets the order of magnitude, not the number.
- Real data is available in less time than the estimate would take.
Inputs required
- The quantity, stated precisely
- Factors you can bound within a factor of three
Procedure
- 01
State the quantity exactly
Including units and period. Most Fermi errors are definition errors rather than arithmetic errors.
- 02
Decompose multiplicatively
Break it into factors that multiply. Population × rate × frequency × amount. Each factor should be one you can bracket.
- 03
Bound each factor
Give a low and a high that you would bet on, then take the geometric mean. Round aggressively — precision in a factor is wasted.
- 04
Multiply through
Carry the low path and the high path separately as well as the central one. The spread between them is the honest uncertainty.
- 05
Sanity-check against something known
Compare the result to a quantity you do know. If it implies something absurd, a factor is wrong by an order of magnitude — find it.
Characteristic failure mode
Worked example
How many hours a year does a mid-sized office spend in recurring meetings?
- 01120 staff × 60% who attend recurring meetings = 72 people.
- 02Roughly 4 recurring meetings a week × 45 minutes = 3 hours a week each.
- 033 × 46 working weeks × 72 people.
Result
About 10,000 hours a year, with a plausible range of 6,000 to 17,000. Enough to decide whether the question deserves real measurement.
Where to go next