Case interview maths without a calculator

Most case interviews don't allow a calculator, and the maths isn't hard. It's percentages, multiplication with lots of zeros, a growth rate, maybe a break-even. People get it wrong because they're nervous and trying to talk at the same time. The fix is a small set of shortcuts you've practised so often that they don't need your full attention.

Say the set-up before any arithmetic

Before you multiply anything, say what you're calculating and how. “To get annual revenue I'll multiply customers by average spend per year.” This gives the interviewer the chance to correct your approach before you spend a minute on the wrong sum, and if your arithmetic slips, they can see your logic was right.

Handle zeros with powers of ten

Big numbers are where most errors happen. Split each number into a simple figure and a count of zeros.

Write units next to every number. “£420m” is much harder to misread than “420”.

Percentages: build them from 10% and 5%

1. 15% of 360 = 36 (10%) + 18 (5%) = 54
2. 35% of 4.2m ≈ a third of 4.2m (1.4m) plus a bit = 1.47m
3. 48 × 25 = 48 × 100 ÷ 4 = 1,200
4. Percentage change is always relative to the starting point. 80 to 92 is +15%. 92 back to 80 is about −13%, not −15%.

Fractions worth knowing by heart

These come up constantly when you're asked for a margin or a market share. If profit is £1.5m on revenue of £12.5m, recognising 1.5/12.5 as 12/100 gives you a 12% margin in a second.

Growth and compounding

For small rates over a few years, compound growth is a bit more than simple growth. 5% a year for three years is 15% simple, about 15.8% compounded. For an interview, “just under 16%” is fine.

For bigger rates or longer periods, the gap matters. 10% a year for five years is about 61%, not 50%. And the rule of 72 tells you how long doubling takes: at 8% a year, about 72 ÷ 8 = 9 years.

Break-even, the one formula you'll use most

Break-even volume = fixed costs ÷ contribution per unit, where contribution is price minus variable cost per unit.

Then give the so-what. “So they need 200,000 units a year. If the market is about a million, that's a 20% share, which seems ambitious for a new entrant.” The number alone gets you half the credit.

Round sensibly, and say so

Rounding is allowed, often encouraged. UK population of about 67 million? Call it 70 and say so. Just keep the direction of your rounding in mind. If you round several numbers up in a row, your answer will drift high, so round one up and the next down where you can.

“I'll round 67 million to 70 to keep it simple, so this will be a slight overestimate.”

Weighted averages come up more than you'd think

Whenever a case has customer segments, product tiers or regions, you'll need a weighted average. Multiply each value by its share, then add. Don't average the prices directly unless the shares are equal.

Check the order of magnitude before you move on

After any big calculation, turn the answer into something you can picture. Say you've estimated a coffee chain's revenue at £420m across 500 shops. That's £840,000 a shop, or roughly £2,300 a day. At under £4 a drink, that's about 600 drinks a day per shop. Busy, but plausible for a city chain. If you'd got 6,000 drinks a day, you'd know you'd slipped a zero somewhere.

Doing this out loud takes ten seconds and interviewers notice it. It shows you treat numbers as facts about a business, not just sums on a page.

When the interviewer says “are you sure?”

Sometimes this means you're wrong. Sometimes they're testing whether you'll fold. Don't guess which. Re-check quickly and out loud: “Let me check. 2.4 million divided by 12, that's 200,000. Yes, I'm confident in that.” If you find a mistake, correct it plainly and keep going. A fixed error costs far less than a defended one.

Being challenged on maths is a big part of what makes a real case feel different from a casebook. If you want practice with an interviewer who checks your numbers against the case script and asks you to redo them when they're off, try the consulting track.

A 15-minute daily drill

1. 01Five multiplications with large numbers (millions times hundreds).
2. 02Five percentages of awkward numbers (17% of 340, 35% of 8.6m).
3. 03Two percentage changes in both directions.
4. 04One break-even with a so-what sentence.
5. 05One compound growth question.

Say every one out loud, including the set-up. Two weeks of this makes a visible difference, mostly because the arithmetic stops competing with your thinking for attention.