Fermi Estimation Game
Guess the order of magnitude. Scoring is logarithmic, so being ten times out costs the same whether the answer is forty or forty billion.
Your answers so far
A factor of ten costs the same at any scale
Scoring is on a logarithmic scale, which is the whole point. Being out by a factor of ten costs exactly one point whether the answer is forty or forty billion — and that is right, because getting within a factor of ten of the number of cells in a human body is a real achievement while getting within a factor of ten of your own height is not an achievement at all. Being ten times over and ten times under score identically, which linear scoring cannot manage.
If you scored absolute error instead, a single astronomical question would swamp every other answer put together and the game would measure nothing except whether you happened to know that one fact. The log scale is what makes a twenty-question round comparable across wildly different magnitudes — and it tends to reveal something people do not expect about themselves, which is that estimates get much worse above about a million, where intuition about "a lot" stops discriminating.
How to use
- Read the question and type a number — any number.
- Aim for the right order of magnitude rather than the exact figure.
- Scoring is logarithmic, so ten times over and ten times under cost the same.
- Watch where your estimates get worse; for most people it is the large ones.
Frequently asked questions
What is a Fermi estimate?
A rough calculation that gets the order of magnitude right using assumptions you can defend, rather than data you have looked up. Enrico Fermi was famous for them — he estimated the yield of the first atomic test by dropping scraps of paper and watching how far the blast wave carried them, and got within a factor of two.
Why is the scoring logarithmic?
Because it makes questions of wildly different sizes comparable. Being out by a factor of ten costs one point whether the answer is forty or forty billion, which is right — getting within a factor of ten of the number of cells in a body is a genuine achievement, and getting within a factor of ten of your own height is not.
What would linear scoring do instead?
Ruin the game. If you scored absolute error, one astronomical question would swamp every other answer combined and the round would measure nothing except whether you happened to know that single fact. On a log scale, twenty questions spanning fifteen orders of magnitude all count equally.
Is being over as bad as being under?
Exactly as bad, and that is deliberate. A guess ten times too large and one ten times too small are both one order out and score identically. Linear scoring cannot do this — it treats overestimates as unboundedly worse than underestimates, which does not match how estimation actually works.
What is a good score?
Consistently landing within one order of magnitude is a genuinely good result and better than most people manage cold. Within a factor of two is very good. If you are regularly three orders out, the useful move is to decompose the question into smaller quantities you know rather than guessing the total directly.
How do you actually make a Fermi estimate?
Break the question into pieces you can bound, then multiply. For piano tuners in Chicago: population, households per person, share with pianos, tunings per year, tunings a tuner does per day, working days. Each factor is only roughly right, and the errors partly cancel — which is why the method works far better than intuition.
Why do errors cancel out?
Because in a product of independent rough estimates, some factors are too high and others too low, and on a log scale those cancel rather than compound. That is the mathematical reason Fermi estimation is more reliable than guessing the answer directly, and the reason breaking a problem down usually beats intuition even when every step is shaky.
Why are large numbers harder to estimate?
Because intuition about quantity stops discriminating somewhere around a million. Most people can feel the difference between a hundred and a thousand, but a billion and a trillion both register simply as "enormous" — which is why estimates get much worse above that threshold, and why the history table here is worth looking at.
Are the answers here exact?
Some are and most are not, and each one says which. Seconds in a year is exact by definition; cells in the human body is a research estimate with real uncertainty; grains of sand in a teaspoon is an order-of-magnitude figure and nothing more. Since the game is about orders of magnitude, that imprecision does not matter much — but it should be stated rather than hidden.
Who was Fermi?
Enrico Fermi, the physicist who built the first nuclear reactor and won the 1938 Nobel Prize. He was renowned for extracting useful numbers from almost no data, and set his students problems like the piano tuner question to teach the habit — which is why this style of estimate carries his name.
What is this useful for outside a quiz?
Sanity-checking, mostly. Knowing roughly what an answer should be catches misplaced decimal points, wrong units and impossible claims before they cause trouble, and it is the fastest way to tell whether a project, a bill or a statistic is plausible. It is a habit rather than a technique.
Does the game save my progress?
No. Everything runs in your browser, nothing is stored or uploaded, and closing the tab loses the current round and history. Questions are shuffled fresh each round.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.