Check units and scales for consistency
Catch order-of-magnitude errors by ensuring your units are consistent across the estimate.
Why it works
Most large estimation errors are unit or scale errors: confusing thousands with millions, minutes with hours, or individuals with households. Units act as an error-detection system — when the units of the product do not match the units of the answer, something is wrong. Tracking units explicitly throughout the decomposition catches these errors before they produce a wildly wrong answer.
How to do it
- Label every sub-estimate with its units (people/household, minutes/day, dollars/unit).
- Verify that the units of each product combine to give the units of the quantity you want.
- If units do not work out, find the step where they went wrong.
- As a sanity check, compute whether the order of magnitude seems consistent with an everyday anchor.
Evidence
Dimensional analysis is a foundational technique in physics and engineering for catching errors in calculations. Its application to estimation is mechanistically straightforward and widely taught in quantitative reasoning curricula. (mechanistic)
Unit-checking catches scale errors but not errors in the values themselves; correct units with wrong numbers still produces a wrong answer.
Common mistake
Carrying units in your head rather than writing them down — unit errors are almost universally caught by writing them and almost universally missed when they are implicit.
Practice this with IX Coach
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More practices for Fermi Estimation
- Decompose the unknown into knowable sub-problems
Break the question you cannot answer directly into smaller questions you can.
- Anchor on what you know and scale from there
Start from a number you are confident about, then reason to the unknown.
- Estimate in ranges, not point estimates
Instead of "my estimate is 500," say "I think it is between 200 and 2000."
- Sanity-check against known extremes
Test your estimate against the clearly too-high and too-low bounds to calibrate your range.
- Track your estimates and calibrate
Compare your Fermi estimates to actual figures when you can, and use the gap to improve future estimates.
Related concepts
- Thinking in Bets
Probabilistic thinking, separating luck from skill, and building a better decision process
- Thinking, Fast and Slow, Made Usable
Two systems, the biases they create, and when to slow down
- Circle of Competence
Know what you know, know what you do not know, and act accordingly
- First-Principles Thinking, Made Usable
Reasoning up from fundamentals, with the mechanism behind why it beats analogy