How to Run a Back of the Envelope Calculation

A back of the envelope calculation is a fast, rough estimate that tests whether an idea makes sense before you commit money to it. Entrepreneurs, strategy consultants and investors use it to turn opinions into arithmetic, and the habit takes minutes to learn.

What Is a Back of the Envelope Calculation?

A back of the envelope calculation is a rough estimate that turns a debate into arithmetic using averages, stated assumptions and one or two divisions. Entrepreneurs use it to test whether a price, a profit number or an investment makes sense before building anything elaborate.

The technique is sometimes called napkin math or, in Brazilian Portuguese, a "conta de padeiro". The label matters: the output is an order-of-magnitude sanity check, not an audited figure. You pick defensible averages, write the assumptions down, and see whether the conclusion survives them.

The habit is common among people whose job is judgment under uncertainty. Strategy firms such as McKinsey & Company and the Boston Consulting Group are known for screening candidates on estimation questions, and venture investors run the same arithmetic on market sizes before writing a check.

Why Quick Estimates Beat Big Spreadsheets

Quick estimates beat elaborate spreadsheets because they expose the one assumption that actually decides the question. A 40-tab model hides that assumption behind formulas; a five-line calculation puts it in plain sight where you can argue with it.

There is a failure mode on the other side too. People who are data-driven often build spreadsheets so large that they can no longer run simple premise tests: change one input, see what breaks. A napkin calculation is the smallest tool that still produces a falsifiable answer.

The point is not precision. The point is to leave the conversation knowing whether the answer is "obviously yes", "obviously no" or "genuinely close", because those three cases demand completely different amounts of further work.

The Supermarket Profit Example

A single division showed whether a supermarket chain's profit could fund large wage increases. In April 2026, a public debate in Brazil followed news that the supermarket chain Assaí had reported R$86 million in net profit for the first quarter, alongside criticism of sector salaries below R$2,000 per month and the 6x1 work schedule.

The arithmetic went as follows: R$86 million per quarter is roughly R$28 million per month. The chain employs about 90,000 people, so profit per employee is about R$300 per month. Even if the company took its profit to zero, an unrealistic scenario that ignores the cost of capital needed to open stores and hold inventory, each worker's pay could rise by only about R$300, from R$2,000 to roughly R$2,300.

The conclusion the numbers support is modest and specific: the chain pays little partly because its profit per worker is small, and any larger raise becomes a labor-market question rather than a profit-redistribution question. That conclusion came from one estimate, not from a position on the politics of the 6x1 schedule.

Pricing Therapy Against a Patient's Income

A two-column estimate explained why therapy prices cluster where they do in Brazil. The question was whether R$100 to R$200 per session is expensive for the average Brazilian, and the answer fell out of comparing a psychologist's monthly capacity with a patient's monthly income.

On the supply side: assume 25 sessions per week, the average of about five per day that working psychologists report before emotional fatigue sets in, times 4 weeks, times R$200 per session. That is R$20,000 per month for the psychologist. On the demand side: a patient attending weekly pays 4 sessions per month, and R$3,560, roughly the average Brazilian income and also the per-person income of the top 10% of earners, carries R$800 of therapy. That is 22.5% of income, rent-level spending.

The model then explains the market's observed prices. At R$100 per session the patient still spends about 11% of income; at R$35, a common price on online therapy platforms, the psychologist earns about R$3,500 per month, close to the patient's own income, and the patient commits roughly 4% of it. A psychologist who wants to charge R$500 must serve clients earning around R$50,000 per month, for whom R$500 is also about 4% of income. High prices and high-income clients are two sides of one calculation.

How to Run a Back of the Envelope Calculation

Any useful estimate follows the same five moves, whether the subject is wages, session prices or a new store. Write each step down so the assumptions are visible and arguable.

1. State the question as a number. Not "is our profit too low?" but "what price increase doubles profit?"
2. Collect two or three averages. Headcount, sessions per week, ticket per client. Use figures you can defend if challenged.
3. Fix the constraint you cannot change. Four weeks in a month, 24 hours in a day, the client's income.
4. Do the arithmetic in one direction, then the reverse. Profit per employee, then the raise it could fund; income share, then the price that share implies.
5. Stress the assumption that decides it. Ask how many clients would have to leave, or how many sessions a day the model requires, before the conclusion flips.

A Price Increase Test at a Marketing Agency

One napkin model showed a small price increase could double profit, and a second showed the risk depends entirely on cost structure. An agency owner with about 150 clients charged roughly R$1,200 per client per month and kept about R$100 of profit per client.

The first calculation: raising the ticket from R$1,200 to R$1,300 adds R$100 of profit per client because costs do not move, taking monthly profit from R$15,000 to R$30,000. The second calculation changes with the cost assumption, which is the whole lesson.

Scenario	Cost assumption	Clients needed to beat R$15,000 profit
Ticket R$1,200 (baseline)	R$1,100 per client, variable	150 (R$15,000)
Ticket R$1,300, variable costs	R$1,200 per client	even losing half the clients still matches baseline
Ticket R$1,300, fixed costs	R$165,000 total, fixed	losing 10 of 150 clients still leaves about R$17,000

With fixed costs such as payroll, only about 10 clients out of 150 need to stay for the increase to win; if too many leave and staff cannot be cut, the increase barely clears the old profit. The same frame surfaces a third option: sell an optional R$1,000-per-month add-on, and if 10% of the base accepts, the average ticket rises by R$100 with no churn risk at all.

Using Estimates as a Simple Business Model

A small spreadsheet of averages is a working business model, not just a calculation. When the variables are colored by role, fixed inputs, adjustable inputs and outputs, the file becomes a simulator you can interrogate: raise the price, see income share; cut the session count, see the psychologist's income fall.

This is where tools matter less than structure. A few cells in Microsoft Excel or on paper are enough; the discipline is labeling which numbers are assumptions and which are constraints. The same five-line model works for a new machine, a new store, or the question of how many customers per day a location needs to pay for itself within three years.

Bruno Faggion, whose June 2026 video walks through these examples, built a similar simulator the previous year while thinking through his own business model, and the practice generalizes: most business dilemmas shrink to one or two divisions once someone is willing to write the assumptions down.

FAQ

• How accurate is a back of the envelope calculation? Accurate enough to rank options, not to set a final price. It uses averages and stated assumptions, so treat its output as an order-of-magnitude answer that tells you whether the question deserves a full model.

• What inputs do you need to start? Two or three defensible averages, such as headcount, sessions per week or ticket per client, plus one fixed constraint like weeks per month or the customer's income. Everything else follows from division.

• When should I not rely on napkin math? When the decision is large, irreversible, or sensitive to a variable the estimate cannot pin down, such as churn after a price increase. In those cases the calculation defines the hypothesis that a proper model must test.

• Is this the same as a financial model? No. A financial model tracks line items, timing and taxes; a back of the envelope calculation compresses all of that into the two or three numbers that drive the answer. The two complement each other.

• Why do consultants and investors practice this skill? Because their job is judging many opportunities quickly. An estimate that takes five minutes filters out weak ideas before anyone spends days modeling them.

Your Videos Hold This Kind of Arithmetic Too

A good napkin calculation is a small piece of teaching: three numbers, one constraint, one conclusion that changes how a reader sees a market. If you explain pricing, margins or decisions in your own videos, that reasoning is usually trapped in the recording.

Skala Blog turns a YouTube video into a written article: paste the URL, the video is transcribed, and the explanation becomes a structured, searchable piece your audience can read and quote. The estimate you worked through on camera becomes an article people can find.

Source video