TL;DR:
Size a market twice, once top-down from the population and once bottom-up from a small sample you count, then compare.
Write every assumption on its own line with a label, because the assumptions are the real answer.
If the two methods land within about a factor of two, report a range. If they do not, one assumption is wrong and is worth finding.
Someone asks how many bike shops there are in your city, and a search gives you a list that is clearly out of date. You do not need an exact count. You need a number you can defend in a sentence, with the reasoning visible so that anyone can change an input and see what happens. That is what a back-of-the-envelope estimate is.
When a rough number is the right tool
Use an estimate when the decision does not change between 18 and 24, but would change between 2 and 200. Is a city big enough to support a second repair business? Is a niche worth a week of work? You are checking the order of magnitude, not auditing a ledger.
Do not use it when someone needs a number to sign, file or pay against. Then you need a real source, and the estimate becomes a sanity check on whatever number the source gives you.
What to open before you start
You need three things: a blank spreadsheet, a map or search app for one quick sample, and a note with the question written as one sentence. The question must name the thing, the place and the time, for example: "How many shops that sell and repair bicycles operate in our city today?" A vague question gives a vague answer.
Decide the definition now. Does a department store that sells a few bikes count? Does a repair stand at a market? Write the rule down, because the two methods below will only agree if they count the same thing.
The two ways to build the number
Top-down starts with a large known quantity and narrows it with percentages: population, then households, then households that buy the product, then the money they spend, then how many businesses that money supports. Bottom-up starts small: count what you can see in a sample, then scale it up by how many samples fit in the whole.
Top-down is quick but every step is a guess. Bottom-up is grounded in something you actually counted, but the sample can be unrepresentative. Doing both is the point: they fail in different ways, so agreement between them means something.
Step by step in a spreadsheet
Write the question and the definition: Put them at the top of the sheet. Add the date, so the estimate can be re-run later.
List each assumption in its own row: Column A is the label, column B the value, column C the reason. Anything you looked up gets a source in column C; anything you guessed says "guess".
Build the top-down chain with formulas: Each row multiplies or divides the row above, so changing one assumption updates everything below it.
Take a small real sample for bottom-up: Search a map for the thing in two or three areas of the city and count. Write down the counts, not just the average.
Scale the sample and compare: Multiply the average by the number of areas. Put the two results side by side and note the gap.
Report a range and the weakest assumption: Say what you would check first if the number mattered more.
Worked example: bike shops in a city
All numbers below are made-up inputs for illustration. Swap in your own city and the method stays the same. The question: how many bike shops (selling and repairing bicycles) are in a city of 600,000 people?
Top-down
Row | Assumption | Value | How it is used |
|---|---|---|---|
1 | Population | 600,000 | Starting point (guess, check the city website) |
2 | People per household | 2.5 | 600,000 ÷ 2.5 = 240,000 households |
3 | Share of households with a regular bike rider |
| 240,000 × 0.30 = 72,000 households |
4 | Yearly spend at shops per such household | $150 | 72,000 × 150 = $10,800,000 |
5 | Yearly revenue of one typical shop | $600,000 | 10,800,000 ÷ 600,000 = 18 shops |
The same chain as spreadsheet formulas, with the assumptions in column B:
B1: 600000 (population)
B2: 2.5 (people per household)
B3: 0.30 (share with a regular rider)
B4: 150 (yearly shop spend per such household)
B5: 600000 (revenue of one typical shop)
B6: =B1/B2*B3*B4/B5 (shops, top-down)Check the arithmetic: 600,000 ÷ 2.5 = 240,000. Then 240,000 × 0.30 = 72,000. Then 72,000 × 150 = 10,800,000. Then 10,800,000 ÷ 600,000 = 18. The formula in B6 returns 18.
Bottom-up
The city has 24 neighborhoods of similar size (say you read that off the city map). You search a map app for "bicycle shop" in three of them that look typical and count 2, 1 and 0. That is 3 shops in 3 neighborhoods, an average of 3 ÷ 3 = 1 per neighborhood. Scaled up: 1 × 24 = 24 shops.
Compare
Top-down says 18 and bottom-up says 24. A gap of 6 on numbers this size is a good result: the two methods are within a factor of 2 of each other. The honest statement is "roughly 20, plausibly 15 to 30". If the answer had been 18 against 180, you would stop and look for the broken assumption instead of averaging them.
Notice which assumption moves the answer most. If the average shop earns $400,000 instead of $600,000, the top-down count becomes 10,800,000 ÷ 400,000 = 27. One input changed the result by half, so that is the one to verify first.
Mistakes that make an estimate useless
Hidden assumptions. If a number appears without a label, nobody can challenge it. State every assumption, even the ones that feel obvious.
Fake precision. Reporting 21.6 shops claims a precision the inputs do not have. Round to one or two significant figures.
A sample of one. Counting a single neighborhood, especially the busiest, biases the scaling. Use at least three and keep the individual counts.
Mixing definitions. If the top-down chain counts only specialist shops but your map search also finds department stores, the methods disagree for a boring reason.
Not showing the arithmetic. Write the multiplication out, as in the table. A reader who can follow it can also correct it.
Doing it faster
Keep one reusable sheet with the assumption rows and a formula column, and copy it for each new question. If you want help talking through whether an assumption is reasonable while you work, DuckyHelper is always there: press one key in any app and ask out loud, and it answers out loud while you keep working. The judgment about the inputs is still yours.
Frequently asked questions
Which method should I trust more?
Neither alone. Trust the pair. The bottom-up count rests on something you observed, and the top-down chain shows what scale to expect. When they agree within about a factor of two, report a range.
How many assumptions is too many?
If the chain is longer than about six steps, errors compound and the estimate is hard to defend. Look for a shorter route or replace a guessed step with something you can look up.
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