What case interview math formulas is really testing
Case formulas are compact statements of business relationships. They help translate a prompt into a calculation and expose the input that drives the result.
Memorization without interpretation creates common errors: the wrong denominator, mixed time periods, double-counted growth, or an answer that is mathematically correct but irrelevant to the client decision.
A step-by-step method for case interview math formulas
Group formulas by the business question they answer. For each one, practice naming the output, equation, unit, assumption, and interpretation before doing arithmetic.
Economics
Revenue = volume × price. Profit = revenue − variable cost − fixed cost. Contribution per unit = price − variable cost per unit.
Margins and growth
Margin = profit ÷ revenue. Percentage growth = (new − old) ÷ old. Percentage-point change = new rate − old rate.
Breakeven and capacity
Breakeven volume = fixed cost ÷ contribution per unit. Utilization = actual output ÷ available capacity.
Weighted values and market size
Weighted average = sum of value × weight. Market value = customers × penetration × frequency × price.
Investment returns
ROI = gain or profit ÷ investment. Payback = investment ÷ annual cash contribution. CAGR = (ending ÷ beginning)^(1 ÷ years) − 1.
Worked example: case interview math formulas
Follow the reasoning, then rebuild it for a different industry instead of memorizing the wording.
Contribution
$100 − $60 = $40
Selling price less product cost.
Contribution margin
$40 ÷ $100 = 40%
Contribution as a share of revenue.
Markup
$40 ÷ $60 ≈ 67%
Contribution as a share of cost.
Business check
40% ≠ 67%
Always name the denominator before stating the rate.
Calculation quality
- The equation appears before the numbers.
- The denominator is stated for every rate.
- Time periods and units match.
- The result is translated back into business language.
Case math formula reference table
Use this table as a recall check after you attempt the relationship from memory. Keep the business meaning beside the equation.
When a prompt varies, rebuild the equation from units rather than forcing a formula that almost fits.
| Question | Formula | Output check |
|---|---|---|
| How much revenue? | Volume × price | Currency per period |
| How profitable? | (Revenue − costs) ÷ revenue | Percentage of revenue |
| How many units to break even? | Fixed cost ÷ contribution per unit | Units per period |
| How fast did it grow? | (New − old) ÷ old | Percentage change |
| What is blended performance? | Σ(value × weight) | Weights sum to 100% |
| How long to recover investment? | Investment ÷ annual cash contribution | Years |
Formula mistakes
- Confusing margin and markup.
- Calculating percent change using the new value as denominator.
- Applying CAGR over the wrong number of periods.
- Using average values when a weighted average is required.
Practice the formulas
Write each formula from a verbal prompt rather than copying symbols.
Create one example with dollars, one with units, and one with percentages.
Explain what a higher or lower result means.
Mix formula families so recognition depends on the question, not drill order.
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Frequently asked questions
Do I need to memorize all case interview formulas?
Memorize the core relationships and understand how to derive them from units. Rare formulas can usually be rebuilt from business logic.
What is the most common case math error?
Using the wrong denominator or mixing units and time periods. Writing the equation and units first prevents many errors.
Should I use exact or rounded numbers?
Use the precision the decision requires. State rounding assumptions and check that they do not change the conclusion.
Sources and further reading
- Interviewing at McKinsey: McKinsey & CompanyPrimary source for McKinsey recruiting and interview guidance.
- Consulting interview process: Boston Consulting GroupPrimary source for BCG interview stages and evaluated capabilities.
- Interviewing at Bain: Bain & CompanyPrimary source for Bain case-interview expectations and sample cases.