Case Interview Math: Complete Guide, Formulas & Practice
Master all the math you need for consulting case interviews at McKinsey, BCG, Bain, and other top firms. This comprehensive guide covers every formula, mental math shortcut, and technique—plus free practice tools to build your speed.
1. What is Case Interview Math?
Case interview math refers to the quantitative calculations you'll need to perform during consulting case interviews. Unlike academic math tests, case interview math focuses on real-world business problems: calculating profit margins, estimating market sizes, analyzing breakeven points, and evaluating investment returns.
The challenge isn't the complexity of the math itself—most calculations involve basic arithmetic, percentages, and simple formulas. The difficulty comes from performing these calculations quickly and accurately under time pressure, often without a calculator, while maintaining clear communication with your interviewer.
Key insight: Interviewers aren't just testing your math skills—they're evaluating how you think under pressure, structure problems, and communicate your reasoning clearly.
2. The 6 Core Math Areas in Consulting Interviews
Virtually every quantitative question in a case interview falls into one of these six categories. Master these, and you'll be prepared for anything.
1. Profitability & Margins
The most common case math topic. You'll calculate revenues, costs, gross margins, operating margins, and net profit. Know the profit equation cold: Profit = Revenue - Costs.
2. Breakeven Analysis
Calculate how many units or how much revenue a business needs to cover its costs. Essential for "should we launch this product?" and pricing questions.
3. Growth & CAGR
Calculate year-over-year growth rates and compound annual growth rates (CAGR). Useful for market sizing, forecasting, and evaluating historical performance.
4. ROI & Payback Period
Evaluate investments by calculating return on investment and how long it takes to recoup initial costs. Critical for "should we invest in X?" cases.
5. Market Sizing & Estimation
Estimate unknown quantities using logical assumptions and basic multiplication. "How many coffee cups are sold in NYC daily?" requires structured estimation skills.
6. Mental Math Fundamentals
Quick arithmetic, percentage calculations, and division shortcuts. These skills underpin everything else—speed here saves time for strategic thinking.
3. Must-Know Case Interview Math Formulas
Memorize these formulas until they're automatic. In interviews, you'll need to recall and apply them instantly.
Profitability Formulas
Profit = Revenue - Total Costs
Revenue = Price × Quantity
Total Costs = Fixed Costs + Variable Costs
Gross Margin = (Revenue - COGS) / Revenue × 100%
Operating Margin = Operating Income / Revenue × 100%
Net Margin = Net Income / Revenue × 100%
Breakeven Formulas
Contribution Margin = Price - Variable Cost per Unit
Breakeven Units = Fixed Costs / Contribution Margin
Breakeven Revenue = Fixed Costs / Contribution Margin %
Growth & CAGR Formulas
Growth Rate = (New - Old) / Old × 100%
CAGR = (End Value / Start Value)^(1/n) - 1
Rule of 72: Years to double ≈ 72 / Growth Rate
ROI & Investment Formulas
ROI = (Gain - Cost) / Cost × 100%
Payback Period = Investment / Annual Cash Flow
Pro tip: Download our formula cheat sheet and review it daily until you can recall every formula without hesitation.
4. Worked Case Math Examples (Step-by-Step)
Example 1: Profitability Analysis
Question: A company sells products at $50 each. Variable cost is $30 per unit. Fixed costs are $200,000/year. They sell 15,000 units. What's their annual profit and profit margin?
Step 1: Revenue = $50 × 15,000 = $750,000
Step 2: Variable Costs = $30 × 15,000 = $450,000
Step 3: Total Costs = $450,000 + $200,000 = $650,000
Step 4: Profit = $750,000 - $650,000 = $100,000
Step 5: Profit Margin = $100,000 / $750,000 = 13.3%
Example 2: Breakeven Analysis
Question: A coffee shop has fixed costs of $10,000/month. Each coffee sells for $5 with a variable cost of $2. How many cups must they sell to breakeven?
Step 1: Contribution Margin = $5 - $2 = $3 per cup
Step 2: Breakeven = $10,000 / $3 = 3,333 cups per month
Step 3: Per day = 3,333 / 30 ≈ 111 cups per day
Example 3: Growth Rate Calculation
Question: Revenue grew from $100M to $150M over 5 years. What's the CAGR?
Step 1: Total growth = 150/100 = 1.5x (50% total)
Step 2: Using Rule of 72: 50% growth in 5 years
Step 3: Approximate CAGR ≈ 8-9% per year
Exact: (1.5)^(1/5) - 1 = 8.4%
5. Mental Math vs. Written Math in Interviews
Both have their place in case interviews. Knowing when to use each approach shows interview savvy.
Use Mental Math For:
- ✓Quick estimations and sanity checks
- ✓Simple percentage calculations
- ✓Rounding numbers for approximation
- ✓On-the-fly calculations while talking
Use Written Math For:
- ✓Multi-step calculations
- ✓Complex multiplication/division
- ✓When precision matters
- ✓Showing your work to the interviewer
Interview tip: Always verbalize your calculations. Say "Let me calculate that..." and walk through your steps out loud. This shows your thinking process and lets the interviewer catch any errors early.
6. Common Mistakes and How to Avoid Them
Mistake 1: Rushing Without Structure
Fix: Before calculating, write down what you're solving for and the formula you'll use. Take 5 seconds to plan.
Mistake 2: Decimal and Zero Errors
Fix: Keep track of units (thousands, millions, percentages). Write them down and do a sanity check: "Does $500M profit for a $100M revenue company make sense?"
Mistake 3: Over-Precision
Fix: Round early and often. 47 × 23 ≈ 50 × 23 = 1,150 is usually fine. Interviewers care more about your approach than exact answers.
Mistake 4: Silent Calculations
Fix: Think out loud. "Revenue is price times quantity, so $50 times 10,000 units is $500,000." This builds rapport and shows your reasoning.
Mistake 5: Not Checking Your Answer
Fix: Always sanity-check. "We calculated a 200% profit margin—that seems too high for retail, let me verify..."
7. Free Tools to Practice Case Math
Theory is important, but practice makes permanent. Use these free tools daily to build speed and confidence.
Mental Math Sprint
60-second timed drills to build raw calculation speed. Addition, subtraction, multiplication, division, percentages.
Start practicing →Case Math Drills
3-minute sessions with realistic business scenarios. Profitability, breakeven, growth, and ROI questions.
Start practicing →Brain Teasers
Classic consulting interview puzzles to sharpen logical thinking. Includes hints and full explanations.
Start practicing →8. Case Interview Math Study Plans
Follow a structured plan to systematically improve your case math skills. We offer plans for different timelines.
7-Day Crash Course
For candidates with interviews next week. Focus on mental math fundamentals and the most common case math scenarios.
- • Days 1-2: Mental math foundations (30 min/day)
- • Days 3-4: Profitability and breakeven (30 min/day)
- • Days 5-6: Growth, ROI, and estimation (30 min/day)
- • Day 7: Mixed practice and review
14-Day Foundation Builder
Our recommended plan for most candidates. Builds strong fundamentals with time for reinforcement.
- • Week 1: Mental math mastery + profitability basics
- • Week 2: Advanced topics + mixed practice
- • Daily commitment: 20-30 minutes
30-Day Complete Prep
For candidates starting from scratch or those who want thorough preparation. Covers everything with ample practice time.
- • Weeks 1-2: Mental math + core formulas
- • Weeks 3-4: All case math topics + brain teasers
- • Includes weekly assessments and targeted practice
9. Frequently Asked Questions
What math is tested in consulting case interviews?
Most consulting case interviews test basic arithmetic, percentages, ratios, breakeven analysis, profitability calculations, growth rates (including CAGR), and ROI. The difficulty comes from doing these calculations under time pressure, often without a calculator, and in realistic business contexts.
How can I practice case interview math for free?
You can use free web tools like Case Math Practice to run timed mental math sprints, case math drills covering profitability and breakeven, and brain teasers. Combine tool practice with casebooks from target firms and mock interviews with peers.
Do I need to be good at math to pass a case interview?
You don't need advanced math skills. Case interview math is about basic arithmetic done quickly and accurately under pressure. With consistent practice, anyone can improve. The key is mastering mental shortcuts and being comfortable verbalizing your calculations.
How long should I practice case interview math before my interview?
We recommend at least 2-4 weeks of daily practice (15-30 minutes per day) to build speed and confidence. If you're starting from scratch or haven't done math in a while, consider 4-6 weeks. Use our 14-day or 30-day study plans as a guide.
What's the difference between mental math and case math?
Mental math focuses on raw arithmetic speed—adding, subtracting, multiplying, dividing, and calculating percentages quickly in your head. Case math applies these skills to business scenarios like calculating profit margins, breakeven points, growth rates, and ROI. You need both for case interviews.
Can I use a calculator in case interviews?
No. Almost all consulting firms (McKinsey, BCG, Bain, and others) require you to do math mentally or on paper. This tests your ability to work under pressure and shows interviewers how you think through problems. That's why practicing mental math is essential.
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