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Get to a defensible number with nothing but assumptions
How many coffees does this city sell a day? How big is the market? How many support agents will we need next year? A guesstimate turns an unanswerable question into arithmetic you can show, argue with, and correct. The structure is the answer, not the number.
Ready?
1
What a Guesstimate Actually Tests
You are asked, in an interview: how many petrol stations are there in this country? You have no idea. That is the point.
A guesstimate is a structured estimate of a number nobody in the room knows, built from things you do know. It appears in interviews because it is a compressed version of a large part of the job — sizing a market, forecasting load, deciding whether an opportunity is worth a quarter — where the data does not exist and a decision is required anyway.
What is being assessed is not arithmetic. It is whether you can decompose an unfamiliar problem, state your assumptions where others can challenge them, and stay comfortable being approximately right.
That last part is the hardest for people who are good at exact answers. A guesstimate that is 40% out but built from named assumptions is a strong answer, because every assumption is a place where somebody can say “I think that number is wrong” and the estimate can be repaired.
A remembered figure, however accurate, is unrepeatable and uncorrectable — and the next question will be about something nobody has published a figure for at all.
Two candidates estimated the same figure; the one who was 40% out got the offer. Every line in the right-hand panel is a place someone can say “I think that number is wrong” — the left-hand answer has no such place, which is why being closer did not help.
The Fermi principle
Enrico Fermi famously estimated the yield of a nuclear test by dropping scraps of paper
and watching how far the blast wave carried them. His answer was within a factor of two
of the instrumented measurement. The trick isn't clairvoyance, it's decomposition: break
an impossible number into factors you can each approximate, and let the errors, which
point in both directions, partly cancel.
Judged badly
"About two million."
No structure. Can't be checked, corrected, or reused. Being close by luck teaches nobody anything.
Judged well
An equation you can argue with
Every assumption visible and separately challengeable, so a listener can replace one input instead of rejecting the whole answer.
That sets the accuracy bar: you are aiming for the right
order of magnitude, not the right number. Two significant figures on an
estimate assembled from assumptions is false precision, and it signals that you've
forgotten what kind of object you're holding.
What the interviewer was watching
Two candidates estimated the number of petrol stations in a country. One produced a number close to the published figure by recalling something they had read. The other was 40% out but built the estimate from population, car ownership, tank size and refuelling frequency, and said which assumption they were least sure of. The second candidate got the offer, because only one of those methods works on a question nobody has published an answer to.
Quick check
Asked how many coffee cups a city sells per day, a candidate answers "about two million" and stops. What's missing?
2
The Five-Step Method
The method is five steps, and doing them in order is most of the skill.
One — clarify. What exactly is being asked? Petrol stations in the whole country, or just the mainland? Currently operating, or ever built? Thirty seconds here prevents answering a different question well.
Two — structure. Break the number into things you can estimate. Petrol stations ≈ total fuel demand ÷ fuel sold per station. Fuel demand ≈ cars × annual mileage ÷ efficiency. This is the step being marked.
Three — assume, out loud. Put a number on each piece and say where it came from. “Call it 30 million cars, because the population is roughly 65 million and I will assume one car per two people.” Naming the source is what makes the estimate correctable.
Four — calculate, and round hard. Use round numbers. Precision here is false comfort and it slows you down; being out by 15% will not change the conclusion.
Five — sanity check. Compare the answer to something you already know the size of.
A grocery bill works the same way in four seconds: roughly fifteen items, roughly three pounds each, plus the two expensive ones. Structure, assumption, arithmetic, check. The interviewer is watching steps two and three — a clean structure with wrong numbers scores better than a lucky total with no reasoning, because only one of those is repeatable.
1
Scope the question
Units, population, geography, time period. "Piano tuners" means full-time professionals or anyone who tunes? Thirty seconds here saves the whole answer.
2
Pick top-down or bottom-up
Top-down starts from a big known total and filters. Bottom-up starts from one observable unit and multiplies up.
3
Write the equation first
Build the assumption tree with empty boxes before any numbers go in, so the logic is visible and each input is separable.
4
Populate and state each assumption
Say every number out loud as you use it. An assumption spoken can be corrected; an assumption hidden invalidates everything downstream.
5
Compute, then sanity check
Round hard, keep the arithmetic simple, and test the result against reality before presenting it.
Top-down
Population → filters → answer
Fast when a credible headline total exists. Risk: one sloppy penetration rate swings the whole result.
Bottom-up
One unit → multiply up
Revenue per store per day × stores × open days. Slower, but every input is concrete and challengeable.
Where you can, run both. Two independent paths that land close together is real
corroboration. Two that diverge by 7× have told you something valuable: somewhere
there's a bad penetration rate, a wrong frequency, or a double count. That divergence is
usually worth more than either number.
Step four is the one candidates rehearse and the one nobody is marking. Steps two and three are the whole assessment — they are where an unfamiliar problem gets taken apart and where each piece is put somewhere a stranger can argue with it, and neither of those improves by being faster at arithmetic.
Everyday example
Estimating a grocery bill before the till: not by recalling the total, but by counting roughly fifteen items at roughly three pounds each and adjusting for the two expensive ones. Structure, assumption, arithmetic, sanity check — in that order, in about four seconds.
The step that gets skipped
A candidate jumped straight to multiplying numbers and produced an answer in ninety seconds. Asked where one of the figures came from, they could not say. The arithmetic had been fine and the interview was over, because an estimate whose assumptions cannot be named cannot be corrected when one of them turns out to be wrong.
Quick check
Sizing a coffee chain's annual revenue, a candidate computes revenue per store per day, then multiplies by store count and days open. What approach is this, and what's its strength?
3
Anchor Facts and Fast Arithmetic
Estimates are built from anchors — facts you already carry that let you start. The useful discovery is how few you need.
A small set covers most questions: roughly how many people live in your country, roughly how many households that implies, an average salary, an average rent, how many hours are in a working year. Five or six numbers, known approximately and confidently, will get you into range on a surprising share of problems.
The arithmetic deserves the same treatment. Work in round numbers and powers of ten. 65 million becomes “call it 60”. Multiply the leading digits and count the zeros separately. If a step needs a calculator, your structure is too fine-grained — simplify it rather than pushing through.
And keep a running sense of the order of magnitude rather than the digits. Being out by 20% is invisible in a guesstimate; being out by a factor of ten is the only error that actually matters, and it almost always comes from a misplaced zero rather than a bad assumption.
Population
Your country to one significant figure, and your two or three largest cities. World ~8 billion.
Households
Population ÷ household size, roughly 2–4 people depending on the country. Most consumer questions are really household questions.
Average salary
The root of anything costed in people — headcount, service pricing, willingness to pay.
Average rent
And the root of anything costed in space — retail sites, offices, warehousing.
Hours in a working year
365 days, ~250 working days, ~2,000 working hours. Enough for most capacity and utilisation questions.
On the arithmetic: round to one significant figure and work in powers of
ten. 312,457 × 6.8 becomes 300,000 × 7 ≈ 2.1 million, computed in your
head, with the rounding stated. Precision you didn't have going in doesn't appear coming
out, and chasing it is the fastest way to lose the thread of your own argument.
Five numbers, and the second one is derived from the first — so it is really four. Knowing these cold is worth more than knowing fifty approximately, because hesitation eats the minutes that should have gone into structure, and structure is the part being marked.
The double-count trap
Estimating daily ride-hailing trips from the driver side and the rider side, then
adding them, counts every trip twice. Supply-side and demand-side views of the same
quantity are a cross-check against each other, never two components to be summed.
A handful of anchors goes a long way
Most market-sizing questions can be built from a very small set of remembered figures: roughly how many people live in the country, roughly how many households that is, roughly what an average salary looks like. A candidate who knows five anchors cold and rounds aggressively will beat one who knows fifty approximately and tries to be precise with all of them.
Quick check
A candidate needs the number of households in a country of 300 million people, with no data available. What's the best move?
4
Sanity Checks, and How to Present the Answer
Reaching a number is not finishing. The last two minutes carry a surprising share of the marks, and they are the ones most candidates skip in their relief at having an answer.
First, sanity check. Compare the result against something whose size you already know. Then ask whether it implies anything absurd — does it mean every household owns four of these, or that each site serves eleven customers a day? An answer that survives that test is worth presenting; one that does not needs no arithmetic review.
Second, present a range rather than a point. A single figure invites a challenge and implies a precision the method cannot support. A range invites a conversation, and is a more honest description of what you actually know.
Third, name your weakest assumption and say how much it matters. Something like: this figure moves the answer by half if I am wrong about it. This is the sentence that separates strong candidates from adequate ones, because it shows you know where your own estimate is fragile.
The underlying point applies well beyond interviews. An estimate whose uncertainty cannot be described cannot be built on by anybody else — they have no way to know which parts to trust, so they will either accept all of it or none.
Per-capita implication
Divide back down to one person. "This implies every adult buys 40 pizzas a day" is an error, not a finding.
Benchmark comparison
Hold it next to something you know. Is your market estimate larger than the company's entire industry?
Second method
Redo it the other way round. Agreement corroborates; divergence points at the broken assumption.
Three steps, none of which touches the arithmetic, and all three are usually skipped in the relief of having an answer. The third is the one that separates candidates: naming the assumption you are least sure of, and by how much it would move the total, is how somebody else learns which half of your estimate to trust.
Everyday example
If your estimate of the weight of a car comes out at 60 kilograms, you do not need to check the arithmetic to know something is wrong. A sanity check is comparing the answer to something you already know the size of, and it takes five seconds.
Presenting it well
Give a range, not a point. Name the two or three assumptions the answer
is most sensitive to, and say which one you'd spend real money to verify
first. If someone challenges an input, take their number, recompute, and show how much
the answer moves, that sensitivity read is more useful than either version of the input.
A guesstimate screens options and sizes a prize. Before a large commitment, go buy data
on the one assumption the whole answer is resting on.
Market sizing has a standard vocabulary worth reusing: TAM is everyone who
could conceivably buy, SAM is the slice your product and geography can
serve, and SOM is what you could realistically win in a few years. Most
credibility is lost by quoting TAM as if it were SOM.
Presenting the range, not the number
A candidate finished with "about 4.2 million". Asked how confident they were, they had no answer. The stronger version is "between three and six million, most likely around four — the number I am least sure of is how often people replace them". The second answer invites a correction; the first invites a challenge.
Quick check
Two methods size the same market: top-down gives $4B, bottom-up gives $600M. What should happen next?
Drill what you learned
Scenario 1
easy
Asked to estimate the number of coffee cups sold in a city per day, a candidate immediately answers "about two million" and stops.
What's missing?
Scenario 2
easy
A candidate is asked to size the market for electric scooters and starts by writing total national population, then narrowing to cities, then to adults, then to likely buyers.
Which approach is this?
Scenario 3
easy
Midway through an estimate a candidate multiplies 312,457 by 6.8 in their head and loses the thread.
What should they have done?
Scenario 4
easy
A candidate is asked "how many piano tuners are in this city?" and asks whether the question means professional full-time tuners or anyone who tunes pianos.
Is this a good move?
Scenario 5
easy
An estimate of annual pizza consumption in a country produces a number implying each person eats 40 pizzas a day.
What should the candidate do?
Scenario 6
medium
Estimating annual revenue for a coffee chain, a candidate computes revenue per store per day and multiplies by store count and days open.
What approach is this, and what's its main strength?
Scenario 7
medium
A candidate needs the number of households in a country of 300 million people and has no data available.
What's the most reasonable move?
Scenario 8
medium
Two methods are used for the same market size question. Top-down gives $4B; bottom-up gives $600M.
How should the candidate handle the gap?
Scenario 9
medium
An estimate of a country's smartphone users needs an age split, and the candidate assumes population is evenly distributed across ages 0–80.
Is that assumption acceptable?
Scenario 10
medium
A PM presents a market estimate as "$1.2B" with no range and no assumptions listed.
What's the problem with this presentation?
Scenario 11
hard
A candidate sizes a B2B SaaS opportunity by taking the total number of companies in a country and multiplying by an average contract value.
What's the biggest weakness?
Scenario 12
hard
In an estimate of daily ride-hailing trips, a candidate multiplies drivers × trips per driver per day, then separately adds riders × trips per rider per day.
What error has been introduced?
Scenario 13
hard
A guesstimate chain multiplies six assumptions together, each of which the candidate believes could be off by 2× in either direction.
What should the candidate say about the result?
Scenario 14
hard
An interviewer pushes back hard on a candidate's assumption that 60% of adults own a car, saying it feels high.
What's the strongest response?
Scenario 15
hard
A team uses a guesstimate to justify a two-year, multi-million investment decision, with no plan to validate any input.
What's the appropriate role for the estimate here?
Drilled it. Now apply it to a real situation.
Put it to work
From lesson 1
How many piano tuners are there in Chicago?
Enrico Fermi
Fermi set his physics students problems with no lookup-able answer —
the number of piano tuners in Chicago being the famous one. The point
was never the number. It was that a chain of defensible estimates lands
far closer to the truth than most people expect, and that being able to
build the chain is a skill separate from knowing any of the facts.
He is also said to have estimated the yield of the Trinity test by
dropping scraps of paper and measuring how far the blast wave carried
them. He got within a factor of two of the instrumented answer.
An interviewer asks you to size a market you know nothing about. What are they actually testing?
Select all that apply — there are 3 to find.
What actually happened
The canonical chain: Chicago's population, people per household,
the share of households with a piano, how often a piano is tuned, how
many a tuner can do in a day, and working days in a year. Every one of
those is a guess, and the errors partly cancel.
You are being marked on the chain, not the number. State each link so
someone can disagree with exactly one of them.
From lesson 2
Two candidates, same question
An interview panel
The question: how many electric-vehicle charging points does the UK
need by 2030? Two candidates answer.
A says: "Roughly 300,000. I read something like that in
a government report." B works through it out loud for
four minutes and arrives at 480,000.
The published target at the time was around 300,000. Who did better?
What actually happened
Asked where the difference lay, B's chain showed it immediately: they
had assumed 8 cars per public charger where the official model assumed
closer to 12. One number, one conversation, and the estimate reconciled.
The five steps exist so the answer can be argued with. Clarify, break it
down, assume out loud, calculate, sanity-check.
From lesson 3
Sizing a feature in ninety seconds
A grocery delivery app
In a planning meeting someone proposes a "reorder my last basket" button
and asks whether it is worth a sprint. You have these figures to hand,
and about ninety seconds.
Anchor facts everyone in the room already knows
Fact
Value
Monthly active customers
400,000
Orders per customer per month
2.5
Average order value
£52
Share of orders that repeat a previous basket
~30%
Current checkout time for a repeat basket
~4 minutes
Order the steps of the estimate, from the first thing you would say out loud to the last.
Drag the rows, or use the arrows, then check.
"Only repeat baskets can benefit — that is 30% of 1m monthly orders, so 300,000."First: narrow to the population the change can possibly affect. Estimating against all one million orders would overstate the prize threefold before any other reasoning happens.
"Say the button saves three of those four minutes, and lifts completion of repeat orders a little."Second: state the mechanism and the assumption in the same breath, so the number that follows is inspectable rather than asserted.
"If it converts 2% more of those 300,000, that is 6,000 extra orders a month."Third: the arithmetic, deliberately rounded. Precision here is false comfort — the 2% is a guess and carries all the uncertainty.
"At £52 that is about £310,000 a month, so a sprint is obviously worth it unless I am wrong by a factor of ten."Last: convert to the unit the decision is made in, and say how wrong you would have to be for the conclusion to flip. That is what makes a rough number safe to act on.
What actually happened
The team shipped it. Actual lift was 1.3%, not 2% — well inside the
margin the estimate had already declared, and the decision would have
been identical at half the number.
Anchor on figures the room already accepts, round hard, and finish by
saying how wrong you would need to be to change the decision.
From lesson 4
An estimate that failed its own sanity check
A pet-supplies subscription
An analyst presents the UK market for monthly dog-food subscriptions at
£4.1 billion a year. The chain: 12 million dogs, £28 a
month each, twelve months.
The arithmetic is right. The number is not.
In four or five sentences: name the check that catches this, say what it reveals, and give a corrected estimate with the assumption you changed.
One strong answer
The check is to compare the answer against a number we already know.
Total UK spend on all pet food across every species is on the order of
£3 billion a year, so an estimate of £4.1 billion for dog-food
subscriptions alone is larger than the entire market it sits inside.
That is a contradiction, not a rounding problem.
The chain assumes every dog in the country is on a £28 monthly
subscription. The real constraint is not how many dogs exist but how
many owners buy this way — subscription is a small share of a market
still dominated by supermarkets.
At perhaps 5% of dogs on a subscription, the estimate becomes 12m ×
0.05 × £28 × 12, roughly £200 million. Still worth building for, and
twenty times smaller than the figure on the slide.
Tick every point your own answer actually made.
Total pet-food spend, or household spend, or the revenue of the largest player. Any figure that bounds the answer from outside the chain.
Every dog is treated as a subscriber. The chain sized the population, not the market.
How many could buy versus how many buy this way. Conflating them is the single most common sizing error.
Not just "it is too high" — a new figure and the one input that moved, so the room can argue about that input.
£200m is still a market worth entering. A sanity check that only demolishes is half a contribution.
What actually happened
The corrected figure survived contact with reality: the category was
later reported in the low hundreds of millions. The original estimate
would have justified a sales team the business could never have paid for.
Before presenting any estimate, find one number outside your own chain
and check you have not exceeded it. Population is not market.