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Fermi Estimation
Fermi estimation is a way to get surprisingly close to an unknown quantity by decomposing it into simple, defensible assumptions.
The method
- Break the question into factors. Ask what smaller quantities would determine the answer.
- Choose round numbers. Use assumptions you can defend, not made-up precision.
- Calculate with units. Multiply or divide the factors and check that the units cancel correctly.
- Check the order of magnitude. Compare the result with something familiar and revise if it feels implausible.
A worked example
Suppose you want to estimate the distance from Earth to the Sun. You can use the time sunlight takes to arrive and the speed of light:
- Light travel time: about 500 seconds.
- Speed of light: about 300,000 kilometers per second.
- Estimate: 500 × 300,000 ≈ 150 million kilometers.
Try this Earth–Sun question yourself
Why logarithmic error matters
If the answer is 100, guesses of 50 and 200 should be treated equally: both are off by a factor of two. Guesscale scores this symmetry on a logarithmic scale, which rewards getting the scale right rather than recalling an exact fact.
Common mistakes
- Starting with an exact-looking number without explaining where it came from.
- Forgetting to convert between days, years, hours, or seconds.
- Multiplying when the question requires a rate or a division.
- Stopping after one assumption instead of checking the result against reality.
Practice the method
The fastest way to improve is to make many estimates, see the multiplicative error, and notice your recurring bias.