Case maths is the mental arithmetic a case interview requires: estimation, percentages, growth rates, break-even points and the simple financial relationships behind a profit or investment decision, all done on paper and spoken aloud. It is not advanced mathematics, and the difficulty is not the operations. It is doing them accurately while explaining them, under time pressure, with an interviewer watching.
This guide covers the techniques that make that manageable, the relationships worth knowing without derivation, and how to practise them so they hold up on the day.
What is actually being assessed
Speed is the least of it. An interviewer watching you calculate is checking four things:
- Can you set the calculation up? Choosing what to compute is a harder skill than computing it, and it is where most errors originate.
- Is your working visible? A number that appears without an audible path cannot be checked, corrected or credited.
- Do you know when you are wrong? A candidate who says “that gives eighty per cent margin, which is too high for a grocer — let me check” has demonstrated more than one who reaches the right figure silently.
- Can you say what the number means? The arithmetic is only useful once it becomes a statement about the client.
Speed matters only because it leaves room for the other four.
Round deliberately, and say so
Rounding is not a shortcut you get away with; it is the technique. The rule is to round early, round to something that divides cleanly, and state what you did.
| Instead of | Use | Say |
|---|---|---|
| 48,700 | 50,000 | “Rounding to fifty thousand, slightly overstating” |
| 19.4% | 20% | “Call it twenty per cent, a touch high” |
| $3.87m | $4m | “Roughly four million, rounded up” |
| 3,150 ÷ 61 | 3,000 ÷ 60 | “About fifty, and both roundings pull down slightly, so a little over fifty” |
The last row is the one worth practising. When you round both numbers in a division you need to know whether the errors cancel or compound. Rounding the numerator down and the denominator down pushes in opposite directions and roughly cancels; rounding the numerator down and the denominator up understates twice.
Keeping approximations within about a tenth of the true value is usually close enough for a case, but the real test is different: would the recommendation change if the figure were ten per cent the other way? If not, the approximation is fine. If it would, you need the precision, and you should say so.
Handle large numbers by working in units
Most case arithmetic goes wrong in the zeros rather than the digits. Fix the unit before you start and write it at the top of the working.
Write 2.4 billion as 2,400 million, or as 2.4 with “billions” noted beside it. Then the arithmetic is on small numbers and only the label moves. When you multiply, add the labels: millions times thousands is billions. When you divide, subtract them.
A worked example. A client sells 18 million units at an average price of $34 and wants revenue in billions.
- 18 × 34 = 18 × 30 + 18 × 4 = 540 + 72 = 612
- Units are millions × dollars, so the answer is 612 million dollars
- In billions, $0.61bn
Splitting 34 into 30 and 4 is the second habit worth building. Any multiplication becomes two easier ones, and the intermediate figures are small enough to hold while you speak.
Percentages, growth and the relationships worth memorising
Percentage change trips candidates in one specific way: the base. A rise from 40 to 50 is a 25 per cent increase; a fall from 50 to 40 is a 20 per cent decrease. Same ten units, different denominators. State which base you are using every time.
The relationships worth knowing cold, because deriving them costs time you do not have:
| Relationship | Form | Where it appears |
|---|---|---|
| Profit | Revenue − Cost | Almost every profitability case |
| Revenue | Price × Volume | The first split in most revenue branches |
| Margin | Profit ÷ Revenue | Comparisons across products or competitors |
| Break-even volume | Fixed cost ÷ (Price − Variable cost) | Pricing, launch and investment cases |
| Payback period | Investment ÷ Annual cash benefit | Capital expenditure and technology cases |
| Market share | Client revenue ÷ Total market revenue | Market entry and growth cases |
Two growth approximations save real time. To compound a growth rate over several years, multiplying the rate by the number of years is close enough below about five per cent and short horizons — 3 per cent for four years is roughly 12.5 per cent, against a true 12.55. Above that, compounding runs ahead of the approximation and you should say so. To find how long a quantity takes to double, divide 72 by the growth rate: 8 per cent growth doubles in about nine years.
Set up before you calculate
Say what you are about to do before you do it.
“To get to break-even volume I need fixed costs divided by contribution per unit. Fixed costs are $2 million, price is $50, variable cost is $30, so contribution is $20. That gives 100,000 units.”
This costs five seconds and buys two things. The interviewer can stop you at the setup if the method is wrong, rather than after two minutes of correct arithmetic on the wrong quantity. And when you make a slip, it is visible as a slip rather than as confusion.
If the interviewer offers an exhibit, read the axis labels and units before extracting anything. Charts in case interviews frequently carry an index rather than an absolute, a log scale, or a unit that differs from the one in the prompt.
Sanity-check before you speak
Every number gets one check before it leaves your mouth. Three that catch most errors:
- Order of magnitude. Does a national market of $40 billion make sense for this product? Is a grocery chain plausibly earning a 45 per cent net margin? Grocery retail runs on low single-digit net margins, so 45 per cent means a slipped decimal or the wrong denominator.
- Direction. If costs rose and revenue was flat, profit fell. If your arithmetic says otherwise, the arithmetic is wrong.
- Reasonableness against the case. A market-sizing answer implying every household buys eleven units a year deserves a second look before you defend it.
Say the check out loud. “That is about four dollars per household per year, which seems plausible for a product at this price” is worth more than the number alone, because it demonstrates the judgement the number is supposed to support.
Turn the number into a statement
Finish every calculation with what it means.
“So break-even is 100,000 units. They are currently selling 60,000, which means the new line would need to grow volume by two-thirds before it covers its fixed costs — that is a large jump for a mature category, and it is the main risk in this option.”
The arithmetic is the input. The sentence is the answer. Candidates who stop at the figure leave the interviewer to do the interpretation, and interpretation is the part being assessed.
How to practise
Short and frequent beats long and occasional, because what needs training is recall under pressure rather than understanding.
- Ten minutes daily. Twenty multiplications and divisions of two- and three-digit numbers, written down, spoken aloud, timed.
- Practise out loud from the start. Silent arithmetic is a different skill, and it is not the one being tested. Talking while calculating roughly halves most people’s speed at first; that gap is the thing to close.
- Keep an error log. Write down every mistake and its type. Most people have two or three recurring errors — dropped zeros, percentage base, sign on a change — and fixing those is faster than general practice.
- Use real case exhibits. Arithmetic drills build fluency, but setting up the calculation is the harder half and only case material trains it. The worked case studies carry exhibits and full arithmetic, and the profitability walkthrough shows the setup, the calculation and the interpretation in sequence.
Timed digital assessments such as the McKinsey Solve and BCG Casey exercises test the same arithmetic under different conditions — screen-based, often with a calculator permitted, and against a clock. The guide to consulting digital assessments covers how that changes what to practise.
For where case maths sits in the rest of preparation, the case interview hub sets out the sequence, and market sizing is the format that leans on estimation arithmetic most heavily.
