Fermi Estimation

A Fermi estimate is a rough calculation used to answer a question that seems impossible to know exactly (e.g. ‘how many piano tuners are there in London?’), by breaking it into smaller pieces that are much easier to estimate sensibly.

Identify the separate facts/quantities you'd need to combine to reach an answer. For example, ‘how many football supporters could Wembley stadium fit?’ could break into: capacity of the stadium × the proportion who are genuine supporters (rather than corporate guests).

For each stage, choose a reasonable round-number estimate — you won't know exact figures, so state clear, sensible assumptions (e.g. ‘assume the average UK adult drinks 2 cups of tea a day’). The exam rewards clearly stated, realistic assumptions, not necessarily a ‘correct’ final answer.

Multiply/combine your estimates to reach a final answer, then sanity check it: does the order of magnitude feel reasonable? Fermi estimation is about getting roughly right (the right order of magnitude), not precisely right.

Example approach: assume the library has about 40 shelving units, each with 6 shelves, each shelf holding about 25 books.

Estimate = 40 × 6 × 25 = 6,000 books.

Any similarly structured estimate with clearly stated, reasonable assumptions and a correct combination of the assumed figures would gain full marks — the exact final number matters less than a sensible method and realistic assumptions.

1. Any three sensible, distinct assumptions, e.g.: (i) number of cars per minute during peak times, (ii) how many hours count as ‘busy’ vs ‘quiet’, (iii) whether the pattern is similar on weekdays vs weekends.
2. 80 years × 365 days × 24 hours × 60 minutes × 60 seconds ≈ 2.5 billion seconds. Accept any reasonable method reaching a similar order of magnitude.
3. Breaking the problem into stages means each individual assumption is easier to make sensibly and can be checked/adjusted separately, whereas guessing a single overall number has no clear reasoning behind it and is far more likely to be wildly wrong; breaking it down also makes errors easier to spot.
4. Example: classroom floor ≈ 8m × 6m = 48 m². One A4 sheet ≈ 0.06 m². Number of sheets ≈ 48 ÷ 0.06 = 800 sheets. Accept any similar reasonable method/assumptions.
5. Getting the ‘right order of magnitude’ means your estimate is roughly the correct size/scale (e.g. thousands rather than millions), even if not exact — e.g. estimating a stadium holds ‘about 50,000’ when it actually holds 60,000 is the right order of magnitude, but estimating ‘500’ would not be.