Foundations
Case interview math: the formulas and shortcuts you need
Updated 4 min readBy the MECE Editorial Team
Short answer
Case interview math is business arithmetic done out loud, usually without a calculator: percentages, margins, break-even, growth rates, and simple payback or NPV. You need about ten formulas, clean rounding, and the habit of saying what each result means for the client. Speed comes from daily practice, not advanced math.
Key takeaways
- About ten formulas cover most cases. Learn them until they are automatic.
- Round early, and say that you are rounding. Precision is rarely the point.
- Keep units attached to every number: thousands vs. millions is the most common slip.
- Percent change is not percentage points. 10% to 12% is +2 points, or +20%.
- Every result needs a "so what".
Which formulas come up most in case interviews?
| Concept | Formula | Example |
|---|---|---|
| Profit | Revenue − costs | $12M − $10M = $2M |
| Revenue | Price × volume | $4 × 500,000 = $2M |
| Gross margin | (Revenue − cost of goods) ÷ revenue | ($10 − $6) ÷ $10 = 40% |
| Contribution per unit | Price − variable cost per unit | $10 − $6 = $4 |
| Break-even volume | Fixed costs ÷ contribution per unit | $200,000 ÷ $4 = 50,000 units |
| Growth rate | (New − old) ÷ old | (120 − 100) ÷ 100 = 20% |
| CAGR | (End ÷ start)^(1 ÷ years) − 1 | $100M → $150M in 3 years ≈ 14.5% a year |
| Payback period | Up-front investment ÷ annual cash flow | $2M ÷ $0.5M = 4 years |
| Value of a perpetuity | Annual cash flow ÷ discount rate | $1M ÷ 10% = $10M |
| Simple customer lifetime value | Annual margin per customer ÷ annual churn rate | $120 ÷ 25% = $480 |
How do you calculate break-even in a case?
Break-even is the volume at which contribution covers fixed costs. Here it is for a fictional coffee cart in Denver.
- Price per drink $5.00 − variable cost $1.50 = $3.50 contribution per drink
- Fixed costs (permit, cart lease, wages): $7,000 a month
- Break-even: $7,000 ÷ $3.50 = 2,000 drinks a month
- Per day, over 30 days: 2,000 ÷ 30 ≈ 67 drinks
- Over a 10-hour day: 67 ÷ 10 ≈ 7 drinks an hour
So what: about seven drinks an hour is achievable in a busy spot and hard on a quiet corner. Location decides this business, which is the insight to say out loud.
What mental math shortcuts help in case interviews?
- Build percentages from 10% and 5%. 15% of 240 = 24 + 12 = 36.
- Flip percentages. 8% of 25 is the same as 25% of 8, which is 2.
- Rule of 72. Years to double ≈ 72 ÷ growth rate. At 8% a year, about 9 years.
- Count the zeros separately. 3 million × 40 thousand: 3 × 4 = 12, and 6 + 4 = 10 zeros, so 12 followed by 10 zeros = 120 billion.
- Round the divisor to a friendly number. 1,960 ÷ 49 is about 2,000 ÷ 50 = 40.
- Margin is not markup. Cost $6, price $10: margin is 40% of price, markup is 67% of cost.
How do NPV and payback show up in case interviews?
Investment questions ("should the plant buy this robot?") come down to whether the money you get back is worth more than the money you put in. Payback is the quick version; net present value (NPV) accounts for the time value of money. In live interviews you will more often use payback or the perpetuity shortcut than a full NPV table.
- Cost today: $4M. Savings: $1M a year for 6 years.
- Payback: $4M ÷ $1M = 4 years
- NPV at 8%: $1M × annuity factor (6 years, 8%) − $4M
- Annuity factor = (1 − 1.08^−6) ÷ 0.08 ≈ 4.62
- NPV ≈ $4.62M − $4M ≈ +$0.6M, so the project creates value at an 8% cost of capital
How should you read a chart or table in a case?
Read the frame first
Title, units, axes, time period, and whether numbers are absolute or percentages.
Find the biggest mover
Which bar, line or row changed most, or differs most from the others?
Compute one ratio
Growth, share or per-unit figures turn raw numbers into a comparison.
Say the so-what
Tie it back to the question: "This segment explains two-thirds of the decline."
How do you do math out loud without losing the interviewer?
- Announce the approach first: "I'll take revenue per store times stores, then subtract costs."
- Say when you round: "Call it 340 million to keep it simple."
- Write units next to every number on your paper.
- Check the order of magnitude before you announce a result.
- Finish with the implication, not the number.
Practice this with a live case
Reading builds recognition; solving builds skill. Each case below runs with MECE's AI interviewer, which answers your clarifying questions, pushes back and scores you out of 100.
Profitability · Beverages · easy
A craft brewery's profits fall despite record volume Practice livePricing · Real estate & mobility · easy
Should a Chicago parking operator switch to dynamic pricing? Practice liveProfitability · Automotive retail · easy
A Texas car-dealership group's profits dropped by half Practice live
Browse all 50 case interview examples and 50 market sizing questions.
Frequently asked questions
Is case interview math hard?
The math itself is middle-school arithmetic: multiplication, division and percentages. What makes it hard is doing it quickly, out loud and under pressure, which is why daily practice matters more than learning new formulas.
Do I need to know NPV for a case interview?
Know the idea and the shortcuts: payback period, and the perpetuity formula (cash flow ÷ discount rate). Full NPV calculations come up more in finance and corporate development interviews.
How do I get faster at mental math?
Ten minutes a day of drills (percentages, large-number multiplication, division) for two to three weeks, plus doing every case's math by hand rather than on a calculator.
Keep learning
- FoundationsMarket sizing questions: the method, US numbers and a worked exampleRead the guide
- Case frameworksThe profitability framework for case interviewsRead the guide
- Case frameworksPricing strategy framework: how to set a price in a caseRead the guide
- Role guidesFinance case interviews: variance analysis, business cases and valuationRead the guide
MECE (mece.in) is an AI practice platform for case interviews and business problem solving, named after the consulting principle Mutually Exclusive, Collectively Exhaustive. It is not affiliated with McKinsey or any other consulting firm. Companies in worked examples are fictional and their figures are illustrative.
