Author: Taylor Warfield, Former Bain Manager and interviewer

Last Updated: June 14, 2026

 

Case interview formulas are the 34 business equations you need to solve the quantitative parts of consulting interviews at McKinsey, BCG, Bain, and other top firms. This guide explains every formula with a worked example, shows you which ones come up most often, and walks through how to apply them in a real case.

 

Before reading on:

 

Most candidates struggle to land interviews and even fewer turn them into offers. Watch my free training to learn how to triple your chances of landing interviews and increase your chances of receiving an offer by 8x.

 

👉 Watch for free

 

Key Takeaways

 

You need 34 case interview formulas across seven categories, but about 10 of them, led by profit, profit margin, contribution margin, and breakeven quantity, drive the math in the vast majority of cases.

 

• Profit formulas (revenue, costs, profit, and margins) are the foundation and appear in nearly every case

 

• Breakeven quantity and breakeven price decide most investment and pricing recommendations

 

• Market size, market share, and growth rate formulas power market entry and growth cases

 

• Finance formulas like NPV, EBITDA, and price elasticity are rare but worth recognizing

 

• Memorize the top 10 formulas cold first, then drill the rest inside full practice calculations

 

What Changed in 2026?

 

This article has been expanded from 26 to 34 formulas, adding breakeven, market size, percent change, and pricing and customer formulas that interviewers now test regularly. It also adds a top 10 cheat sheet table, a frequency guide showing which formulas matter most, a worked case that chains formulas together, and a memorization plan. All examples have been reviewed for accuracy.

 

What Are Case Interview Formulas?

 

Case interview formulas are the basic business equations used to solve quantitative problems in consulting interviews. They cover seven areas: profit, breakeven, investment, market size and share, operations, pricing and customers, and finance. The most important are Profit = Revenue - Costs, Profit Margin = Profit / Revenue, and Breakeven Quantity = Fixed Costs / Contribution Margin.

 

None of these formulas require technical math or finance knowledge. They are the building blocks of case interview math, and the challenge is recalling and applying them quickly without a calculator.

 

According to McKinsey's own interviewing page, the problem solving interview tests how you deal with the implications of facts and data and formulate conclusions. Formulas are the tool that turns that data into conclusions.

 

Here are the 10 formulas that matter most. Memorize these before anything else.

 

Formula	Equation	When you use it
Profit	Revenue - Costs	Almost every case
Revenue	Quantity × Price	Revenue and profitability cases
Total Costs	Variable Costs + Fixed Costs	Cost reduction cases
Profit Margin	Profit / Revenue	Comparing profitability
Contribution Margin	Price - Variable Cost per Unit	Pricing and breakeven decisions
Breakeven Quantity	Fixed Costs / Contribution Margin	Investment and launch decisions
Percent Change	(New - Old) / Old	Growth and decline analysis
Market Size	Number of Customers × Average Spend	Market sizing and entry cases
Market Share	Company Revenue / Market Revenue	Competitive position
Payback Period	Investment / Annual Profit	Investment decisions

 

Now let's go through all 34 formulas one by one, with an example for each.

 

What Are the Profit Formulas for Case Interviews?

 

Profit formulas are the most heavily tested formulas in case interviews because most cases ultimately ask whether a decision makes the client more money. Master these eight before anything else, since they form the backbone of profitability case interviews, the most common case type.

 

1. Revenue = Quantity × Price

 

Revenue is the money a company brings in from selling its products. Multiply the number of units sold by the price per unit.

 

Example: Your client sells shirts for $20 each and sold 1,000 shirts last year. Revenue was 1,000 × $20 = $20,000.

 

2. Total Variable Costs = Quantity × Variable Cost per Unit

 

Variable costs increase with each additional unit produced, such as raw materials, packaging, and shipping. Multiply units sold by the variable cost per unit to get total variable costs.

 

Example: Each shirt costs $5 in materials. Selling 1,000 shirts means total variable costs of 1,000 × $5 = $5,000.

 

3. Total Costs = Total Variable Costs + Fixed Costs

 

Fixed costs do not change with production volume. They include rent, equipment leases, and salaried staff.

 

Example: Your client pays $10,000 in annual rent and $2,000 for equipment, so fixed costs are $12,000. Adding the $5,000 in variable costs gives total costs of $17,000.

 

4. Profit = Revenue - Costs

 

Profit is what the company keeps after paying for everything. This is the single most important formula in case interviews because nearly every case decision comes back to it.

 

Example: With $20,000 in revenue and $17,000 in costs, profit is $20,000 - $17,000 = $3,000.

 

5. Profit = (Price - Variable Cost) × Quantity - Fixed Costs

 

This expanded version combines the first four formulas into one equation. Use it when you need to see how a change in price, volume, or costs flows through to profit in a single step.

 

Example: ($20 - $5) × 1,000 - $12,000 = $15,000 - $12,000 = $3,000. Same answer, one calculation.

 

6. Contribution Margin = Price - Variable Cost per Unit

 

Contribution margin is how much each unit sold contributes toward covering fixed costs and generating profit. It is the key input for breakeven analysis and pricing decisions.

 

Example: Shirts sell for $20 with $5 in variable costs, so the contribution margin is $15 per shirt.

 

7. Profit Margin = Profit / Revenue

 

Profit margin is the percentage of revenue a company keeps as profit. It lets you compare profitability across products, companies, and time periods of different sizes.

 

Example: Profit of $3,000 on revenue of $20,000 gives a profit margin of $3,000 / $20,000 = 15%.

 

8. Percent Change = (New Value - Old Value) / Old Value

 

Percent change measures how much a metric grew or declined between two periods. Interviewers use it constantly, both in math problems and when discussing exhibits.

 

Example: Revenue fell from $20,000 to $16,000. The percent change is ($16,000 - $20,000) / $20,000 = -20%.

 

What Are the Breakeven Formulas for Case Interviews?

 

Breakeven formulas tell you how much a company needs to sell, or charge, for a decision to stop losing money. They show up constantly in breakeven analysis questions tied to new products, new factories, and pricing changes.

 

9. Breakeven Quantity = Fixed Costs / Contribution Margin

 

Breakeven quantity is the number of units a company must sell to cover all of its costs. Below this volume the company loses money, and above it the company earns profit.

 

Example: A product has $100,000 in fixed costs, sells for $50, and has variable costs of $30. Breakeven quantity is $100,000 / ($50 - $30) = 5,000 units.

 

10. Breakeven Price = Variable Cost per Unit + (Fixed Costs / Quantity)

 

Breakeven price is the minimum price a company can charge at a given volume without losing money. Interviewers use it to test pricing judgment.

 

Example: With $30 in variable costs, $100,000 in fixed costs, and expected sales of 10,000 units, the breakeven price is $30 + ($100,000 / 10,000) = $40.

 

What Are the Investment Formulas for Case Interviews?

 

Investment formulas help you decide whether a client should spend money on a project, acquisition, or expansion. The difference between recommending an investment and rejecting it usually comes down to one of these four calculations.

 

11. Return on Investment = Profit from Investment / Investment Cost

 

ROI measures how much additional profit an investment generates relative to its cost. A higher ROI means a better use of the client's money.

 

Example: Your client spends $5,000 on marketing and earns $6,000 in additional profit before that cost. The net gain is $1,000, so ROI is $1,000 / $5,000 = 20%.

 

12. Payback Period = Investment Cost / Annual Profit

 

Payback period is how many years it takes to recoup the money spent on an investment. Shorter payback periods mean lower risk.

 

Example: A $5,000 redesign increases annual profit by $1,000. The payback period is $5,000 / $1,000 = 5 years.

 

13. NPV = Cash Flow / (1 + Discount Rate)^(Time Period)

 

Net present value measures what future cash is worth today, because money received now can be invested and grown. Cases rarely make you calculate NPV by hand, but you should understand the concept since it anchors most NPV case interview questions.

 

Example: You expect $1,000 in five years and an 8% return on invested money. The NPV is $1,000 / (1.08)^5, which is roughly $680. Receiving $680 today equals receiving $1,000 in five years.

 

14. Perpetuity: Present Value = Annual Cash Flow / Discount Rate

 

A perpetuity is a stream of equal payments that lasts forever, and this formula gives its value today. Interviewers love it because it is the fast way to value a company or asset in valuation case interviews, often with a 10% discount rate to keep the math clean.

 

Example: A business generates $1,000 in annual profit and the discount rate is 10%. Its value is $1,000 / 0.10 = $10,000.

 

What Are the Market Size and Market Share Formulas?

 

Market formulas measure how big an opportunity is and how much of it a company owns. You will use these in growth cases, competitive analyses, and any case that opens with an unfamiliar industry.

 

15. Market Size = Number of Customers × Average Spend per Customer

 

Market size is the total annual revenue available in a market. Every market sizing question reduces to this formula, whether you build it top-down from population or bottom-up from a customer segment.

 

Example: Let's say 50 million households buy coffee and spend an average of $200 per year. The market size is 50M × $200 = $10B.

 

16. Market Share = Company Revenue / Total Market Revenue

 

Market share is the percentage of total market sales a company captures, from 0% to 100%. Interviewers lean on it heavily in market entry case interviews to judge whether a target position is realistic.

 

Example: Your client generates $100M in a $500M market, giving it a market share of $100M / $500M = 20%.

 

17. Relative Market Share = Company Market Share / Largest Competitor's Market Share

 

Relative market share compares a company against the market leader rather than the whole market. A value above 1 means the company is the leader.

 

Example: Your client holds 20% of the market and the largest competitor holds 50%. Relative market share is 20% / 50% = 0.4.

 

18. CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) - 1

 

Compound annual growth rate measures how fast something grows per year over multiple years. You will rarely compute fractional exponents by hand, but you should recognize the formula and reverse it for simple cases.

 

Example: Revenue grew from $100M to $144M over two years. CAGR is ($144M / $100M)^(1/2) - 1 = 20% per year.

 

19. Rule of 72: Years to Double = 72 / Annual Growth Rate

 

The Rule of 72 is a shortcut for estimating how long a market or company takes to double in size. Divide 72 by the growth rate as a whole number.

 

Example: A market growing at 9% per year doubles in roughly 72 / 9 = 8 years.

 

What Are the Operations Formulas for Case Interviews?

 

Operations formulas measure how efficiently a company produces its output. They appear in cases about factories, capacity decisions, and cost reduction.

 

20. Output = Rate × Time

 

Output is the production rate multiplied by the time the process runs. It is the starting point for any capacity question.

 

Example: A machine produces 5 shirts per hour and runs for 12 hours, so output is 5 × 12 = 60 shirts.

 

21. Utilization = Actual Output / Maximum Output

 

Utilization measures how much of a factory's or machine's capacity is actually being used. Low utilization signals wasted fixed costs, and very high utilization signals a capacity constraint.

 

Example: A machine can produce 120 shirts per day but only produces 60. Utilization is 60 / 120 = 50%.

 

Two related metrics occasionally appear in operations cases. Inventory turnover (Cost of Goods Sold / Average Inventory) measures how quickly inventory sells, and labor productivity (Output / Number of Workers) measures output per employee.

 

What Are the Pricing and Customer Formulas?

 

Pricing and customer formulas evaluate how a company charges for its product and how much each customer is worth. These show up in pricing cases, subscription businesses, and new product launches.

 

22. Markup = (Price - Cost) / Cost

 

Markup measures price relative to cost, which is different from margin, which measures profit relative to price. Confusing the two is one of the most common math errors in pricing case interviews.

 

Example: A jacket costs $40 and sells for $70. The markup is ($70 - $40) / $40 = 75%, but the margin is $30 / $70, roughly 43%.

 

23. Customer Lifetime Value = Average Purchase Value × Purchase Frequency × Customer Lifespan

 

Customer lifetime value, or CLV, estimates the total revenue one customer generates over their entire relationship with the company. It matters most in subscription and repeat-purchase businesses.

 

Example: A gym charges $50 per month and the average member stays 24 months. CLV is $50 × 24 = $1,200.

 

24. Customer Acquisition Cost = Total Sales and Marketing Spend / New Customers Acquired

 

Customer acquisition cost, or CAC, is what a company spends to win one new customer. A healthy business keeps CLV well above CAC.

 

Example: A startup spends $100,000 on marketing and acquires 2,500 customers. CAC is $100,000 / 2,500 = $40.

 

25. Cannibalization Rate = Lost Sales of Existing Product / Sales of New Product

 

Cannibalization measures how much a new product eats into sales of a company's existing products. It comes up in new product launches and in M&A case interviews where overlapping product lines compete with each other.

 

Example: A new drink generates 1,000 sales, but sales of the original drink fall by 300. The cannibalization rate is 300 / 1,000 = 30%.

 

What Finance and Economics Formulas Should You Know?

 

These nine formulas appear far less often than the previous ones because they require more technical accounting and economics knowledge. You should still recognize each one so a rare case does not rattle you.

 

26. Gross Profit = Revenue - Cost of Goods Sold

 

Gross profit is revenue minus only the direct costs of making the product. It is always higher than net profit because it ignores overhead.

 

Example: $20,000 in shirt sales with $5,000 in production costs gives gross profit of $15,000.

 

27. Gross Profit Margin = Gross Profit / Revenue

 

Gross profit margin shows how profitable the core product is before overhead. A falling gross margin usually points to rising input costs or pricing pressure.

 

Example: Gross profit of $15,000 on $20,000 of revenue gives a gross margin of 75%.

 

28. Operating Profit = Gross Profit - Operating Expenses - Depreciation - Amortization

 

Operating profit subtracts overhead like rent, salaries, and marketing, plus depreciation and amortization. Depreciation spreads a physical asset's cost over its useful life, and amortization does the same for intangible assets like patents.

 

Example: Gross profit of $15,000 minus $10,000 in operating expenses, $2,000 in depreciation, and $500 in amortization gives operating profit of $2,500.

 

29. Operating Profit Margin = Operating Profit / Revenue

 

Operating profit margin measures profitability after the full cost of running the business. Comparing gross margin and operating margin tells you whether a profit problem sits in production or in overhead.

 

Example: Operating profit of $2,500 on $20,000 of revenue gives an operating margin of 12.5%.

 

30. EBITDA = Operating Profit + Depreciation + Amortization

 

EBITDA stands for earnings before interest, taxes, depreciation, and amortization, and it approximates the cash a business generates. Private equity cases use it constantly as a valuation base.

 

Example: Operating profit of $2,500 plus $2,000 in depreciation and $500 in amortization gives EBITDA of $5,000.

 

31. Return on Equity = Profit / Shareholder Equity

 

ROE measures how effectively a company turns its net worth into profit. Shareholder equity equals total assets minus total liabilities.

 

Example: Profit of $100M against $1B in shareholder equity gives an ROE of 10%.

 

32. Return on Assets = Profit / Total Assets

 

ROA measures how efficiently a company uses everything it owns, including cash, property, equipment, and inventory, to generate profit.

 

Example: Profit of $100M against $400M in assets gives an ROA of 25%.

 

33. Price Elasticity of Demand = % Change in Quantity / % Change in Price

 

Price elasticity measures how much demand changes when price changes. Since higher prices almost always reduce demand, elasticity is usually negative, and an absolute value above 1 means customers are price sensitive.

 

Example: A 10% price cut increases units sold by 20%. Elasticity is 20% / -10% = -2, so demand is elastic.

 

34. Cross Elasticity of Demand = % Change in Quantity for Good 1 / % Change in Price for Good 2

 

Cross elasticity measures how demand for one product responds to a price change in another. Positive values mean the products are substitutes, and negative values mean they are complements.

 

Example: A competitor cuts its price by 20% and demand for your product falls by 10%. Cross elasticity is -10% / -20% = 0.5, so the products are substitutes.

 

Which Case Interview Formulas Come Up Most Often?

 

The profit, breakeven, and market formulas come up most often, while finance and economics formulas are rare. In my time interviewing candidates at Bain, almost every quantitative question I gave could be solved with the first 10 formulas on this list.

 

Treat the 34 formulas as three tiers and prepare them in order. Formulas tell you how to calculate, while case interview frameworks tell you what to calculate, so the two skills reinforce each other.

 

Priority	Formulas	Standard to hit
Tier 1: Memorize cold	Revenue, costs, profit, profit margin, contribution margin, breakeven quantity, percent change, market size, market share, payback period	Recall instantly, with zero hesitation
Tier 2: Know well	ROI, breakeven price, CAGR, Rule of 72, relative market share, output, utilization, markup	Set up correctly within a few seconds
Tier 3: Recognize	NPV, perpetuity, gross and operating profit, EBITDA, ROE, ROA, elasticities, CLV, CAC, cannibalization	Understand the concept and apply it with a hint

 

How Do You Apply Case Interview Formulas in a Real Case?

 

You apply case interview formulas by chaining them together: state the formula out loud, plug in the numbers, calculate, and then say what the answer means for the client. Interviewers grade the setup and the interpretation as much as the arithmetic.

 

Here's an example of how a single case can chain six formulas together.

 

Let's say your client makes office chairs that sell for $100 with $60 in variable costs, carries $1.2M in annual fixed costs, and sells 40,000 chairs per year.

 

First, establish the baseline. Revenue is 40,000 × $100 = $4M, total costs are (40,000 × $60) + $1.2M = $3.6M, and profit is $400K. That gives a profit margin of $400K / $4M = 10%.

 

Next, the interviewer asks how many chairs the client must sell to break even. The contribution margin is $100 - $60 = $40, so breakeven quantity is $1.2M / $40 = 30,000 chairs. The client sells 40,000, which gives a 25% cushion above breakeven.

 

Finally, the interviewer proposes a $200K machine that cuts variable costs by $5 per chair. Annual savings are 40,000 × $5 = $200K, so the payback period is exactly 1 year and profit rises 50% to $600K. That is a strong investment, and saying so clearly is what earns the points.

 

Notice that the hard part was never the arithmetic. The skill is picking the right formula at each step and translating the output into a recommendation, which is exactly what case interview mental math practice builds.

 

If you want to learn how to handle case math and every other part of the case quickly, my case interview course walks you through proven strategies in as little as 7 days.

 

How Should You Memorize Case Interview Formulas?

 

Memorize case interview formulas by learning the logic behind each one, then drilling them inside full calculations until recall is automatic. Most candidates can lock in the core formulas in 2 to 3 days and reach interview fluency within 1 to 2 weeks.

 

Tip #1: Learn the logic, not the string of symbols

 

Every formula on this list describes something intuitive about how a business works. If you understand that profit is what's left after costs, you can rebuild half the formulas on this list from scratch.

 

Candidates who memorize by rote freeze when an interviewer phrases a question in an unexpected way. Candidates who learn the logic adapt.

 

Tip #2: Drill formulas inside full calculations

 

Flashcards alone build recognition, not speed. Timed case interview math drills force you to recall the formula, plug in numbers, and compute under pressure, which is the actual skill being tested.

 

Aim for 15 to 20 minutes of drills per day during your prep. Daily repetition beats occasional marathon sessions.

 

Tip #3: Keep a one-page reference while you practice

 

Condense all 34 formulas onto a single page and keep it next to you during early practice cases. A good consulting math cheat sheet also includes key fractions and percentages, like 1/8 = 12.5%, that speed up your arithmetic.

 

Wean yourself off the sheet after the first week. By your first mock interview, you should not need it at all.

 

Tip #4: Practice with full cases, not just isolated math

 

Formulas behave differently when buried inside a 30-minute case with an interviewer watching. Working through complete case interview examples teaches you to spot which formula a question is really asking for.

 

Bain's official case prep page publishes practice cases in the firm's own style, which makes them a reliable source for realistic quantitative questions.

 

Tip #5: Say the formula out loud before you calculate

 

In every practice session, state the formula before touching the numbers: "Profit equals revenue minus costs, so I'll calculate revenue first." This habit slows you down by three seconds and saves you from setup errors that cost minutes.

 

It also shows the interviewer your structure even when you make an arithmetic slip. In my experience as an interviewer, a clean setup with a small calculation error scores far better than a correct answer with no visible logic.

 

What Are the Most Common Formula Mistakes in Case Interviews?

 

The most common formula mistakes are setup errors, not arithmetic errors. Having coached hundreds of candidates 1-on-1, I see the same five mistakes derail otherwise strong performers.

 

• Diving into numbers before stating the formula: you lose structure points and make setup errors the interviewer can't follow

 

• Confusing margin with markup: margin divides by price while markup divides by cost, and mixing them up changes the answer significantly

 

• Mixing time units: combining monthly revenue with annual costs is the most frequent error I saw as an interviewer

 

• Dropping zeros between millions and billions: write out the units on paper and convert everything to the same scale before calculating

 

• Pulling the wrong number from an exhibit: misreading case interview graphs feeds a correct formula with incorrect inputs

 

The fix for all five is the same: slow down for the setup, then speed through the arithmetic. If you want targeted feedback on your specific math habits, my case interview coaching gives you 1-on-1 practice with a former Bain interviewer.

 

Mastering case interview formulas comes down to memorizing the top 10 cold, recognizing the rest, and drilling them inside full calculations until the setup is automatic. Start today by writing out the cheat sheet table from this article by hand, since that single exercise will lock in more formulas than an hour of passive reading.

 

Frequently Asked Questions

 

What formulas do you need to know for case interviews?

 

You need 34 formulas across seven categories: profit, breakeven, investment, market size and share, operations, pricing and customers, and finance. The most important are profit, profit margin, contribution margin, breakeven quantity, percent change, market size, and market share. These core formulas drive the math in the vast majority of cases.

 

Do you need to memorize formulas for case interviews?

 

Yes, you need the core formulas memorized cold because interviewers will not give them to you. Pausing to reconstruct a formula mid-case costs time and signals weak business fundamentals. Focus on understanding the logic behind each formula so recall becomes automatic rather than rote.

 

Can you use a calculator in a case interview?

 

No, calculators are not allowed in case interviews at McKinsey, BCG, Bain, or almost any other consulting firm. You are expected to do all calculations with pen and paper or in your head. This is why fluency with formulas and mental math is so important.

 

What is the most important case interview formula?

 

Profit = Revenue - Costs is the most important case interview formula. Most cases ultimately come back to whether a decision increases or decreases profit. Nearly every other formula, from contribution margin to breakeven to ROI, is a way of breaking this one equation into smaller pieces.

 

How hard is the math in case interviews?

 

The math itself is not hard. It is arithmetic, percentages, and basic business formulas, nothing beyond what you learned in high school. The difficulty comes from doing it quickly and accurately under pressure without a calculator while talking through your logic out loud.

 

How long does it take to learn case interview formulas?

 

Most candidates can memorize the core formulas in 2 to 3 days. Becoming fluent enough to apply them instantly under interview pressure takes 1 to 2 weeks of daily drills and full practice cases. Build the formulas into complete calculations rather than reviewing them as flashcards alone.

 

Everything You Need to Land a Consulting Offer

 

Need help passing your interviews?

• Case Interview Course: Become a top 10% case interview candidate in 7 days while saving yourself 100+ hours
  
  
• Fit Interview Course: Master 98% of consulting fit interview questions in a few hours
  
  
• Interview Coaching: Accelerate your prep with 1-on-1 coaching with Taylor Warfield, former Bain interviewer and best-selling author

 

Need help landing interviews?

• Resume Review & Editing: Craft the perfect resume with unlimited revisions and 24-hour turnaround

 

Need help with everything?

• Consulting Offer Program: Go from zero to offer-ready with a complete system

 

Not sure where to start?

• Free 40-Minute Training: Triple your chances of landing consulting interviews and 8x your chances of passing them