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Fermi Lab

Fermi estimation practice for quant interviews

80 guesstimation problems scored on order of magnitude: get within 3x of the answer and you nailed it. Build the back-of-the-envelope reasoning that trading desks test constantly. Free, in your browser.

Named after physicist Enrico Fermi, who could estimate almost anything from a few sensible assumptions, these problems reward structure over precision. Quant interviewers use them to see whether you can break a vague question into factors you can defend, keep the arithmetic clean, and land in the right ballpark. The score here is based on log-distance to a hand-calibrated reference: within 3x is sharp, within 10x is good.

How to attack a Fermi problem

Decompose the target into a product of quantities you can each estimate, sanity-check every factor, and multiply. Optionally write out your decomposition and an AI examiner grades the method: was the factorization sound, were the sub-estimates defensible, was the arithmetic consistent? That is exactly what an interviewer listens for.

Example problems

How many human babies are born worldwide per day?
Roughly 380,000. World population about 8 billion, life expectancy about 73 years, so in steady state roughly 8e9 / 73 people are born per year, near 110 million, divided by 365 gives about 300,000 per day. The true figure is close, and within 3x either way counts as sharp.
How many seconds are there in a human lifetime?
About 2.5 billion. 80 years × 365 days × 24 hours × 3,600 seconds is roughly 2.5e9. A clean cascade of round factors, the template every Fermi answer should follow.
How many ATMs are there worldwide?
On the order of 3 million. Start from population, the fraction with bank access, and a plausible number of people served per machine, then cross-check against a big country you know. The point is a defensible chain, not a lucky guess.

The set spans finance and markets (daily FX notional, assets under management, options traded), demographics and the digital world (births and deaths, emails, hours of video), the great big-number classics (grains of sand, atoms in a body, stars in the galaxy), and physical infrastructure (power plants, cars produced, world electricity).

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