Home / Estimation
3.3 · Paper 1 · Compulsory
Fermi estimation, sensible rounding and sanity-checking answers — a short unit, but easy marks if practised.
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A Fermi estimate answers a question you can't look up directly (e.g. "how many football fans watch Premier League games in a season?") by breaking it into smaller quantities you can reasonably estimate, then combining them.
The method: identify the quantities you need, make sensible assumptions for each (round numbers are fine — you're aiming for the right order of magnitude, not precision), then multiply/divide them together.
An estimate is only as good as its weakest assumption, so it should never be given to more decimal places than the data justifies. If your inputs are rounded to 1 significant figure, your answer shouldn't pretend to be accurate to the nearest whole number.
Upper and lower bounds: a rounded measurement like "80 m to the nearest 10 m" could really be anywhere from 75 m up to (but not including) 85 m. When quantities are combined, bounds can be used to find the largest and smallest possible values of a calculation.
Many estimation questions combine a real formula (area, volume, speed = distance ÷ time) with unit conversion. Always convert to consistent units before calculating, and check your final answer is a sensible size for the context — a common exam skill is spotting when an answer is out by a factor of 1000 because of a units slip.
Estimate the number of people who attend Premier League football matches in a single season.
Break it down: roughly 20 teams, each playing 19 home games in a season $\Rightarrow$ about $20\times19 = 380$ matches. A typical stadium holds around 40,000 people, and assume grounds are roughly 80\% full on average.
Estimate: $380 \times 40\,000 \times 0.8 \approx 12.2$ million attendances across the season.
(This counts attendances, not unique people — the same fan attending many matches is counted each time, which is worth stating as an assumption.)
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