Case interview math: the formulas, shortcuts and practice you need

Case interview math is the arithmetic inside a consulting case: percentages, growth rates, margins, breakeven, payback and the odd valuation, worked by hand on big round numbers while the interviewer watches. It is not hard maths. It is mental maths and pen-and-paper arithmetic under pressure, judged on accuracy, speed and how clearly you talk it through. This guide covers the formulas, the shortcuts, how to do maths out loud and a four-week practice plan built on our drills.

In live case interviews you are normally expected to work without a calculator, with squared paper and a pen. Interviewers forgive slow maths far more readily than wrong maths, and they forgive a slip you catch yourself far more readily than one they have to point out.

Estimation has its own method, covered in our guide to market sizing questions. This guide focuses on the arithmetic and formulas that sit underneath all four types.

About a dozen formulas cover nearly every calculation you will meet. Know them well enough that the question brings the formula to mind before you touch a number.

Listen for the family in the question. 'Will it pay for itself?' is payback. 'How many do we need to sell?' is breakeven. 'What is it worth?' is valuation. Naming the family out loud buys a few seconds of thinking time and shows the interviewer you have a method. The case maths essentials lesson works through each family with examples.

Nobody wants a human calculator. Interviewers want quick, reliable arithmetic with no lost zeros, and a handful of mental maths shortcuts gets you most of the way.

Learn the fractions by heart: 1/3 ≈ 33.3%, 1/6 ≈ 16.7%, 1/7 ≈ 14.3%, 1/8 = 12.5%, 1/9 ≈ 11.1%, 1/11 ≈ 9.1% and 1/12 ≈ 8.3%. Dividing by 12.5% is multiplying by 8; dividing by 8% is multiplying by 12.5. These come up constantly, and they turn a long division into one step.

Round on purpose, and say so. '340m, call it 350m to keep the maths clean' is good practice in an estimate. In a calculation where the interviewer gave you exact figures, keep them exact unless rounding clearly cannot change the answer.

The most expensive case interview math error is rarely a wrong digit. It is a wrong unit: a million read as a billion, a monthly figure treated as annual, dollars per kWh used where the price was per MWh. A few habits remove almost all of them.

• Write every number with its unit: '$m', 'k units', 'a year'.
• Convert to one unit before you multiply: everything in millions, or everything in thousands.
• For very large numbers, use powers of ten: 340m people × $250 = 3.4 × 10^8 × 2.5 × 10^2 = 8.5 × 10^10 = $85bn.
• Line the steps up vertically on the page and box the answer, so you can find any step again.
• Before you say a final number, test its size per person, per store or against the client's revenue.

The interviewer scores your process as much as your answer. Silent maths looks like panic, and a wrong answer with no visible working leaves them nothing to credit. Narrate the structure, not every carry.

Saying the approach first matters most. If your method is wrong, the interviewer can redirect you in five seconds rather than after two minutes of arithmetic. And ending with the so-what turns a sum into a business answer, which is what you are actually being hired to produce.

Ten to twenty minutes a day is enough, as long as it is every day. Short, timed sessions build the speed and confidence a long weekend cram cannot. Start each session with a warm-up, then one topic set, then redo yesterday's mistakes.

The quick maths and case maths sprint warm-ups are generated fresh each time, so you cannot memorise the answers. The topic sets, such as breakeven and payback, are authored drills in the sentences an interviewer actually says, with a worked solution after each one. Try a stretch question now:

In week 4, the maths has to survive a live case. Run full cases with the AI interviewer and score the maths in each review: approach stated, units labelled, answer checked, so-what given. Our guide on how to prepare for case interviews shows where this fits in a full preparation plan.

Drills build speed; cases build judgement about which number to calculate. Do both. The featured warehouse case has a capacity calculation at its heart, and the two below put profitability and deal maths inside a full case.

McKinseyNordwind Airlines: the vanishing marginProfitability · Medium

Nordwind Airlines: the vanishing margin

A profitability case where the numbers, not the framework, find the answer.

Interviewer

Our client is Nordwind Airlines, a short-haul carrier operating out of northern Europe. Over the past three years passenger numbers have grown 18%, but operating profit has fallen by roughly 40%. The CEO wants to understand what is driving this and what to do about it. How would you approach the problem?

Start the caseGuided, step by step

McKinseyAtlas Logistics eyes a last-mile acquisitionM&A · Hard

Atlas Logistics eyes a last-mile acquisition

Deal maths: multiples before and after synergies, and whether the price clears.

Interviewer

Our client, Atlas Logistics, is a regional freight and warehousing operator. They are considering acquiring Kestrel, a last-mile delivery company, for $340m. Their CFO thinks the price is high. Should they proceed?

Start the caseGuided, step by step