- The maths in a case is basic: percentages, growth, margins, break-even, payback and market sizing, plus reading charts. What makes it hard is choosing the right inputs and keeping track of units under pressure.
- Before you calculate, ask which result would change the answer. It tells you what to calculate and how precise you need to be.
- Set up the calculation aloud, round in a way you declare, keep units and zeros visible, and check whether the result is plausible.
- Each decision-relevant result should lead to a sentence about what it means for the client. A correct number with no "so what" is half an answer.
- A mistake you catch and correct is very different from one that silently leads to a wrong conclusion. Short daily drills, then full cases, build both accuracy and calm.
Many candidates fear the maths part of the case more than any other, and many prepare for it with speed drills alone. Speed helps a little. What helps much more is a reliable way of working: knowing why you are calculating, saying the set-up before the numbers, and turning the result into a conclusion. This guide shows that routine, then puts it to work on original exercises with simple numbers.
What maths comes up in a case, and why
Consultants use numbers to decide things: whether a price change pays, how big a market is, which option earns more. Case maths copies that. You will rarely meet anything harder than multiplication, division and percentages, but you will meet them in the middle of a business problem, with large numbers, mixed units and an interviewer waiting.
| Type of calculation | A typical question | What it tests |
|---|---|---|
| Percentages and shares | "Our share fell from 20% to 15%. How big is the drop?" | Percent versus percentage points |
| Growth | "What annual growth do we need to reach £60m?" | Compounding, sense of size |
| Margin and profit | "Revenue is £500m and costs £460m. What is the margin?" | Clean set-up |
| Break-even and payback | "How many units to cover the investment?" | Choosing the right inputs |
| Market sizing | "How big is this market?" | Assumptions and logic |
| Charts and tables | "What do you take from this exhibit?" | Finding the point fast |
Why interviewers include it
Interviewers want to know whether they could trust your numbers in front of a client. That breaks down into four questions: did you choose the right inputs, did you set the calculation up correctly, is the result right, and did you say what it means? Arithmetic speed sits inside the third question only. BCG's preparation page lists quick calculations among the things candidates do during the case, and Bain's case interview page asks candidates to share their reasoning and calculations as they go, even when unsure.
You usually work with pen and paper and no calculator. Some online case formats have their own rules, so check the instructions for your interview and ask your recruiter if they are unclear.
A routine for every calculation
The six steps below take a few seconds each once they are a habit. They prevent most errors candidates make, because most errors happen before or after the arithmetic, not during it.
- Ask which result would change the answer. Before calculating, say what you need to know and what result would make the client decide one way or the other.
- Set it up aloud. State the formula in words, then the inputs, before you touch the numbers.
- Round, and say so. Choose round numbers when precision does not change the decision, and tell the interviewer.
- Keep units and zeros visible. Write "£m", "units a year" or "%" next to every number.
- Check whether it makes sense. Compare the result with something you already know.
- Close with the "so what". One sentence on what the number means for the client and what you would do next.
1. Ask which result would change the answer
Suppose the client asks whether a new machine pays for itself. Before you calculate anything, say: "If the payback is under three years, which is the client's usual target, it's a yes; otherwise we need other benefits." Now you know what to compute, and you know that "about two and a half years" is precise enough. You also show the interviewer that you treat numbers as a means to a decision.
2. Set it up aloud
Say the formula in words first: "Break-even volume is fixed costs divided by the margin on each unit." Then name the inputs: "Fixed costs are £600k; the margin per unit is the price, £25, minus the variable cost, £10." Only then calculate. This lets the interviewer correct a wrong set-up before you spend a minute on arithmetic, and makes your reasoning easier to follow.
3. Round, and say so
Rounding is fine, and often wise, as long as it is declared and does not change the conclusion. "There are 52 weeks; I'll use 50 to keep it simple" is good practice. Round in directions that cancel out when you can, and be careful when the answer sits close to the decision threshold: then the precision matters.
4. Keep units and zeros visible
Write units next to every number and use k, m and bn instead of strings of zeros. "4.5m customers × £80 = £360m" is far harder to get wrong than 4,500,000 × 80. Be precise with percentages: a share moving from 6% to 10% has risen by 4 percentage points, which is a 67% increase. Mixing the two is one of the errors interviewers notice most.
5. Check whether it makes sense
Before you announce a result, compare it with something: today's revenue, the size of the market, the number of people in the country. If a regional bakery chain comes out with sales of £4bn, a zero has gone missing somewhere. Saying "that seems high compared with total revenue of £50m, let me check" is a strength, not a weakness.
6. Close with the "so what"
Finish every calculation with what it means: "So the machine pays back in two and a half years, inside the three-year target, which supports buying it. I'd like to check whether the savings are reliable." Many candidates stop at the number. The sentence after it is what makes the number useful.
"Okay, so 600 divided by 15... that's 40. 40,000."
"Break-even is fixed costs over margin per unit. Fixed costs are £600k, and each unit earns £25 minus £10, so £15. £600k divided by £15 is 40,000 units a year. They sell 55,000 today, so they're comfortably above break-even, by almost 40%. I'd look next at whether the volume is stable."
Both answers get 40,000. The stronger one shows the set-up, so an error would be easy to spot, keeps the units, and turns the number into a judgement with a next step.
Mental maths techniques worth having
You do not need tricks for everything, but a few techniques remove most of the effort.
Percentages by building blocks. To find 15% of 480, take 10% (48) and add half of it (24): 72. For 35%, take 10% three times and add 5%. One percent of a number moves the decimal point two places, which makes small percentages easy.
Large numbers with labels. Work in k, m and bn and handle the labels separately: thousands × thousands = millions; millions × thousands = billions. "3m × £20k" is 3 × 20 = 60, then m × k = bn, so £60bn.
Division by dropping zeros. Remove the same number of zeros from the top and the bottom first: £360m ÷ 4.5m becomes 360 ÷ 4.5, which is 80.
Growth that compounds. A rough rule: a quantity growing at r% a year doubles in about 72 ÷ r years, so 10% a year doubles in about seven years. For short periods, multiply step by step: 1.1 × 1.1 = 1.21, so two years at 10% is +21%.
Combined changes. If volume rises 20% and price falls 20%, revenue does not stay flat: 1.2 × 0.8 = 0.96, a fall of 4%. Multiply the factors instead of adding the percentages.
Common fractions are worth knowing by heart, because they turn divisions into percentages instantly:
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/6 | about 17% |
| 1/3 | about 33% | 1/7 | about 14% |
| 1/4 | 25% | 1/8 | 12.5% |
| 1/5 | 20% | 1/9 | about 11% |
Worked exercises
The exercises below are fictional and built for this guide. Each uses three or four numbers at most, because in a real case the difficulty lies in choosing what to calculate, not in the arithmetic. Try each one before reading the solution.
Exercise 1: percentages and percentage points
The question
A client's share of its national market fell from 20% to 15% in three years, while the market itself grew. The CEO says: "We only lost 5%." Is that right, and does it matter?
Solution
Separate the two measures before answering.
Change in share: 15% − 20% = −5 percentage points
Relative change: 5 ÷ 20 = −25% of the client's former share
The CEO is right about the points and wrong about the size: the client has lost a quarter of its position. Because the market grew, sales may still have risen, which can hide the problem. The "so what": the client is growing more slowly than its competitors, so I would ask which segments or competitors took the share.
Exercise 2: break-even
The question
A city bike-sharing operator is considering adding e-bikes. Each e-bike costs £1,500 a year to lease, charge and maintain. Each ride earns £2.50 after payment fees. Today's standard bikes average 2 rides a day. Should the operator go ahead?
Solution
First the threshold: the e-bike pays if it gets more rides than its break-even. Then compare with what bikes achieve today.
Break-even rides = yearly cost ÷ earnings per ride = £1,500 ÷ £2.50 = 600 rides a year
Per day: 600 ÷ 365 ≈ 1.6, call it under 2 rides a day (rounded)
At 2 rides a day: 730 rides × £2.50 ≈ £1,825, so about £325 a year profit per e-bike
E-bikes break even at fewer rides than standard bikes already achieve, so the case looks positive. But the margin is thin: at 2 rides a day the profit is about a fifth of the cost. The "so what": the decision depends on whether e-bike demand consistently clears the break-even of about 1.6 rides a day and whether all relevant costs are included, so I would ask for evidence from other cities or a small pilot before ordering a full fleet.
Exercise 3: growth
The question
A software client has revenue of £40m and wants £60m in four years. Its market grows about 4% a year. What growth does the target require, and what does it imply?
Solution
The target is +50% in four years. Find the annual rate by testing a round number.
Try 10% a year: 1.1 → 1.21 → 1.33 → 1.46, so £40m becomes about £58.5m
Slightly short of £60m, so the required growth is just over 10% a year
Check: four years at 10% without compounding would give +40%; compounding adds a little, so a rate just over 10% for +50% is plausible. The "so what": the client must grow more than twice as fast as its market, which means taking share from competitors or adding new products. I would look at where that extra growth could come from before accepting the target.
Exercise 4: market sizing, then an unknown to solve
Market sizing questions often come in two parts: first an estimate with no data, then a few numbers and something to solve for.
The question
A client is considering a mobile dog-grooming service, with vans that visit customers' homes, in a country of 20 million households. How big is the market for mobile grooming, in visits and in pounds?
Solution
Lay out the logic before any number, then state each assumption as an assumption.
- Households with a dog: assume 25%, and one dog each to keep it simple
- Dogs groomed professionally: assume 40%
- Groomings per dog per year: assume 4
- Share done by mobile groomers today: assume 10%
- Price per visit: assume £60
20m households × 25% = 5m dogs
5m × 40% = 2m dogs groomed professionally
2m × 4 = 8m groomings a year
8m × 10% = 0.8m mobile visits a year
0.8m × £60 = about £50m a year (exactly £48m, rounded)
A good candidate then says which assumption matters most. Here it is the mobile share: if it is 20% rather than 10%, the market doubles. That is the assumption to check first.
The question
The client wants £3m of revenue in year three. One van can do 5 visits a day on 240 working days, at £60 a visit. How many vans does it need, and is the plan realistic?
Solution
Work out revenue per van, then divide.
Visits per van: 5 × 240 = 1,200 a year
Revenue per van: 1,200 × £60 = £72k a year
Vans needed: £3m ÷ £72k ≈ 42, so about 40 to 45 vans
Share of the market: 42 × 1,200 ≈ 50k visits, out of 0.8m ≈ 6%
The "so what": the plan needs about 6% of the mobile market within three years. In a fragmented market that is ambitious but not absurd. The risk is the assumption that every van is fully booked; at four visits a day the client would need over 50 vans. I would test demand in one city before buying the fleet.
Exercise 5: reading a two-axis chart
Interviewers like charts with two axes because the story only appears when you combine the two series. The exercise below shows how to read one in three moves: orient yourself, find the main movement, then say what it means.
The question
Brightleaf, a bakery-café chain, has doubled its number of stores in three years. The CEO wants to open ten more next year. The interviewer hands you Exhibit 1: "What do you take from this?"
Solution
Orient. Two series: stores on the left axis, sales per store on the right. Treat year-end stores as trading all year, which is a simplification for this exercise.
Find the main movement. Stores doubled, from 20 to 40. Sales per store fell by 40%, from £2.0m to £1.2m. Multiply them to get total sales:
2022: 20 × £2.0m = £40m
2024: 30 × £1.6m = £48m
2025: 40 × £1.2m = £48m
Doubling the stores raised total sales by only 20%, and total chain sales did not grow last year despite ten openings.
Say what it means, and what to check. There are two possible explanations. New stores may simply be young and still building their customer base, or they may be taking customers from the existing stores. The answer decides whether to keep opening, so ask for the data that separates them: sales of the original 20 stores.
The interviewer tells you the original 20 stores now average £1.7m.
Original 20 stores: 20 × £1.7m = £34m, down from £40m, so £6m lost
The other 20 stores: £48m − £34m = £14m, about £0.7m each
The newer stores sell well under half of what the original ones sell, and the original stores have lost £6m. This is consistent with cannibalisation, but does not prove it: check store locations and other changes in local demand before attributing the decline to expansion.
"The number of stores went up from 20 to 40, which is very good growth. Sales per store went down from 2 to 1.2 million. So the company is growing but each store is selling less."
"Stores doubled but sales per store fell 40%, so total sales only rose from £40m to £48m, and total sales stayed flat last year despite ten openings. New stores may still be maturing, and the original stores lost £6m. That raises a concern about cannibalisation, but we should also check other causes of weaker demand. I'd pause the ten openings and look at how close the new stores are to the old ones."
The weaker answer describes each series and stops. The stronger one combines them, does two simple multiplications, tests an alternative explanation with one more number and ends with a recommendation.
Orient: read the title, the axes, the units, and which series belongs to which axis. Find the movement: say the one or two changes that matter, in a sentence. Say what it means: tie it to the client's question and propose the next step. Do the orientation aloud and briefly, so the interviewer hears your thinking rather than silence.
If you want an experienced interviewer to watch you work through exhibits like this one, 1:1 coaching with Franco runs each session as a realistic interview, with a written report afterwards.
From the number to the "so what"
The habit that separates good candidates most clearly is the sentence after the number. It has three parts: what the number means for the question, how sure you are, and what you would do next.
| The number | A sentence that adds the "so what" |
|---|---|
| Payback is 2.5 years | "That's inside the three-year target, so it supports the investment." |
| Share fell 5 points | "We've lost a quarter of our position while the market grew." |
| 42 vans needed | "That's 6% of the market in three years: ambitious, so I'd pilot first." |
| Margin is 8% | "That's below the 12% competitors report, so costs are worth a look." |
If you are not sure what the number means, say what would tell you: "That's 8%; I'd need competitors' margins to judge whether it's low."
What to do when you make a mistake
Everyone makes calculation slips under pressure, and interviewers know it. What matters is what happens next. An error you notice, say out loud and correct, with a sentence on what changes in the conclusion, usually costs little. An error that goes unnoticed and leads to a wrong recommendation is far more serious, because it is exactly what a client would see.
Three habits make recovery easy. Saying the set-up aloud lets the interviewer, or you, spot a wrong input early. The plausibility check catches most lost zeros. And if the interviewer asks "are you sure?", take it as an invitation to recheck, not as a trap: go back to the set-up calmly rather than defending the number.
"So the market is £4.8bn... and the client wants £3m, which is tiny, so it should be easy."
"I get £4.8bn, which feels too big for a niche like mobile grooming. Let me check: 0.8m visits times £60 is £48m, not £4.8bn; I added two zeros. So the market is about £50m, and the client's £3m target is 6% of it, which is more ambitious than I first said."
The weaker answer lets a lost-zero error drive the conclusion. The stronger one notices that the size is implausible, finds the slip, corrects it and updates the judgement.
Common case maths mistakes
The mistakes below come up repeatedly in practice sessions with candidates. Almost none of them are about arithmetic.
- Confusing percent and percentage points. A move from 6% to 10% is 4 points, or a 67% increase, not "4%".
- Losing zeros and units. Results given without saying whether they are pounds, millions or percentages, or a thousand times off.
- Using totals instead of changes. Multiplying all customers by a cost when only the extra customers add that cost.
- Losing track when an input must be derived first. Jumping into the final formula before working out the number it needs.
- Long silent mental maths. Calculating in your head without writing or speaking the steps, which hides errors and leaves the interviewer waiting.
- Taking the long way. Computing two full scenarios and subtracting them when you could calculate the difference directly.
- No plausibility check. Announcing a result without comparing it with anything you know.
- A number with no meaning. Stopping at the result instead of saying what it implies for the client.
- Describing a chart instead of interpreting it. Reading out every bar, or misreading how a metric is defined, instead of finding the two or three points that matter.
Drill set with answers
Ten quick questions, no calculator. Write your answer, then open the question to check it. Aim for the right set-up first and speed second.
1. What is 15% of 480?
72. 10% is 48, 5% is 24, so 48 + 24 = 72.
2. Revenue grows from £80m to £100m. What is the growth rate?
25%. The change is £20m on a base of £80m: 20 ÷ 80 = 25%. Saying 20% is the classic slip.
3. Market share falls from 12% to 9%. Give the change in points and in percent.
−3 percentage points, or −25%. 3 ÷ 12 = 0.25.
4. Fixed costs are £600k a year, the price is £25 and the variable cost is £10 per unit. What is the break-even volume?
40,000 units a year. The margin per unit is £15; £600k ÷ £15 = 40k.
5. An investment of £2.4m saves £0.8m a year. What is the payback?
3 years. £2.4m ÷ £0.8m = 3.
6. £360m of revenue comes from 4.5m customers. What is the revenue per customer?
£80. Drop the millions: 360 ÷ 4.5 = 80.
7. A £200m market grows 10% a year. How big is it after two years?
£242m. £200m × 1.1 = £220m; £220m × 1.1 = £242m.
8. Revenue is £500m and total costs are £460m. What is the profit margin?
8%. Profit is £40m; £40m ÷ £500m = 8%.
9. Volume rises 20% and price falls 20%. What happens to revenue?
It falls 4%. 1.2 × 0.8 = 0.96. Adding +20% and −20% to get zero is the trap.
10. A business wants to double in about seven years. What annual growth does that need?
About 10% a year. By the rule of 72, 72 ÷ 7 ≈ 10.
How to practise case maths
Maths improves fastest with short, regular practice, then with practice inside full cases, where you also have to choose inputs and explain results. The same applies to structuring, which decides which numbers you will need in the first place; the structuring guide has examples and practice prompts, and the complete case interview guide shows maths and structure working together in one fictional case. A simple weekly routine:
| When | What to do | What to check |
|---|---|---|
| Every day, 10 minutes | Mixed drills like the set above, no calculator | Set-up said first, units kept |
| Twice a week | One chart or table summarised aloud in three sentences | Main point found, "so what" stated |
| Twice a week | One market sizing, with assumptions written down | Most important assumption named |
| Every full case | Note each calculation error and why it happened | The same error does not repeat |
Practise saying everything aloud, even alone. The skill being tested is calculating while explaining, which is harder than calculating in silence. Recording yourself once a week shows quickly whether you announce results without a set-up or without a "so what".
When you practise with other candidates, ask your partner to give you numbers in awkward units, to interrupt with "are you sure?", and to hand you a chart with no explanation. Then compare notes on where your set-up was unclear, not only on whether the number was right.
Where feedback from an experienced interviewer helps
Drills tell you whether a result is right. They do not tell you whether an interviewer would have doubted your set-up, noticed a silent pause, or found your "so what" weak. In coaching sessions with Franco, analytical and quantitative skills are one of the five dimensions scored in the written report after each session, and the report names the exact slip and the correct path, so your next practice can target it. Coaching packages of three or more sessions also include targeted self-practice materials between sessions.
1:1 interview coaching
Practise case maths with a former BCG Principal
Franco Borgonovo spent ten years at BCG, from intern to Principal, has conducted more than 1,500 interviews, over 800 of them for MBB firms, and is currently an official BCG coach for new hires. Every session is a realistic interview with him, followed by a written report with your scores and priorities.
- Start with one session for a diagnosis and a plan (US$249)
- Packages of 3, 5 or 10 sessions add a progress dashboard, targeted self-practice materials and email support between sessions
- Money-back guarantee if the coaching does not meet your expectations
Not sure which option fits? Use the free call to tell Franco your target firms, interview dates and where you feel stuck.
Frequently asked questions
How hard is the maths in a case interview?
The operations are basic: multiplication, division, percentages and growth. The difficulty comes from large numbers, mixed units, deciding which inputs to use and explaining as you go, all under time pressure.
Can I use a calculator?
Usually not in a live case interview, where you work with pen and paper. Some online cases and tests allow one, so read the instructions for your format and ask your recruiter if they are unclear.
How precise do I need to be?
Precise enough for the decision. Rounding that you announce is normal; when the result sits close to a decision threshold, be more careful. Never round in a way that changes the conclusion.
Should I do speed drills?
Short daily drills help you stay accurate and calm, but speed matters less than set-up, units and interpretation. Most lost points come from choosing the wrong input or not saying what the result means.
What if I freeze on a calculation?
Go back to the set-up and say it aloud: what you are calculating and from which inputs. Breaking the calculation into smaller steps, and writing them down, usually unblocks it.
How do I get better at reading charts?
Practise with real charts from business news and annual reports: orient in one sentence, state the main movement in one sentence, and say what it means in one sentence. Two-axis charts are worth extra practice, because the point usually appears only when you combine the series.
Checklist for your next case
Your next step
Do the drill set above without looking at the answers, then try Exercise 5 aloud as if the interviewer were in front of you. If you want to know how your maths and chart reading come across to an experienced interviewer, and which habits to fix first, one coaching session gives you a diagnosis and a written plan to follow.
Coaching with Franco
Get precise feedback on your case maths
A realistic case interview, a debrief and a written report with your priorities. Start with one session, or talk it through for free first.
About Franco
Franco Borgonovo
Former BCG Principal · 10-year tenure · Official BCG coachFranco spent ten years at BCG, from intern to Principal, interviewing and selecting candidates as a global lead recruiter. He is still an official BCG coach for new hires, and today works one to one with candidates on applications, McKinsey Solve and interviews.
More about Franco →- BCG: Case interview preparation (careers page) · candidates are expected to perform quick calculations; read 2 November 2026
- Bain & Company: Case interview (careers page) · share your reasoning and calculations as you go; read 2 November 2026