A parking garage can disappear into garbage math

A city can produce volumes of trash that sound impossible until you break the estimate into people, bags, and space.

A Fermi estimate is a rough, step-by-step calculation that breaks one huge unknown into smaller guesses you can inspect and improve.

By the Math Says Yes editorial team

Human-reviewed under our source and correction standards.

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THE TRAP

Big quantities feel unknowable, so people either guess wildly or avoid estimating.

A multi-level parking garage with its decks packed full of garbage bags instead of cars.

What this shows

A Fermi estimate turns a question that feels unknowable into a chain of smaller estimates. You do not begin by knowing the exact amount of trash in a city. You begin with pieces you can inspect: , trash per person, bag volume, days, compaction, and the volume of a garage. The answer is rough, but the roughness is visible. Each assumption can be replaced if better information appears.

Why intuition fails

Big quantities feel like they require secret data. That feeling creates two bad reactions: people either refuse to estimate or throw out a number with no structure. Fermi thinking takes a middle path. It accepts uncertainty but forces the uncertainty into named variables. If the estimate is wrong, you can usually see where: the trash per person, the air between bags, the garage dimensions, or the time period.

Worked example

Suppose a city has one million residents and each person produces about 5 liters of loose trash per day. That is 5 million liters, or 5,000 cubic meters, each day. A simple parking-garage level might be sketched as 50 meters by 40 meters by 2.5 meters, also about 5,000 cubic meters. The point is not that those exact dimensions are universal — none of the inputs has to be perfect. If each is in the right ballpark, the estimate is good enough to say whether the city fills one garage level a day, or ten, or a hundred, and an absurd-sounding claim becomes testable once the units line up.

How to use it

Write the estimate as a multiplication and division chain. For garbage volume, that might be people times trash per person times days, divided by cubic meters per garage level. Then run a low and high version. If changing one assumption by a factor of two changes the conclusion, that assumption deserves attention. If the conclusion survives several rough versions, the scale is probably informative.

What people get wrong

'That's just a guess' is the reflex that dismisses every Fermi estimate — and it misses what the method does. A Fermi estimate is not a license to invent whatever number you like; it is a way to expose the assumptions behind a rough answer. The bad version hides the guesses. The good version shows them, checks the units, and makes it easy for someone else to improve the weakest link. The goal is not to be exactly right on the first pass — it is to avoid being absurdly wrong.

When it applies

Fermi estimation is useful for planning, sanity checks, market sizing, operations, and deciding whether a detailed model is worth building. It is weakest when a problem has hidden bottlenecks, threshold effects, or inputs that vary by many orders of magnitude. Use it first to orient, then replace rough inputs with measured ones where the decision needs precision.

Source note

Efthimiou and Llewellyn discuss Fermi problems as a general-education tool, which fits this page's practical framing: estimation is a disciplined way to expose assumptions and scale, not a claim that every input is known exactly.

Try It

Build a rough estimate

Change the two guesses. Every step of the calculation stays visible.

Population

1,000,000 people

Trash per person

5 liters per person per day

City trash per day

1,000,000 × 5 L

= 5,000,000 L = 5,000 m³

Example parking-garage level

50 × 40 × 2.5 m = 5,000 m³

garage levels filled per day

1,000,000 people × 5 liters gives 5,000 m³ of trash per day. Divide by 5,000 m³ per example level: 1 level per day.

Illustrative inputs, not measurements from a real city.

FAQ

What is a Fermi estimate?

A Fermi estimate is a rough calculation built from smaller assumptions. Instead of guessing one huge unknown directly, you break it into quantities you can reason about, convert the units, and check whether the final scale is plausible.

Why is a rough answer useful?

A rough answer can tell you whether a claim is off by a little or by orders of magnitude. It also shows which assumption matters most, so the next step is targeted instead of vague.

How do I make the estimate better?

Keep the chain visible and replace the weakest assumption first. For the garbage example, better city population, measured waste per person, compaction data, or garage dimensions would improve the result more than adding decimal places to a weak guess.