Consulting Math Cheat Sheet: Every Formula You Need

Author: Taylor Warfield, Former Bain Manager and interviewer

Last Updated: May 6, 2026

 

Consulting math cheat sheet formulas are the single fastest thing you can memorize to improve your case interview performance. About 85% of all case interviews at McKinsey, BCG, and Bain include at least one math problem, and getting these wrong is the quickest way to get rejected.

 

This cheat sheet gives you every formula, mental math shortcut, and key statistic you need, all in one place. Print it, bookmark it, and review it before every practice session.

 

But first, a quick heads up:

 

McKinsey, BCG, Bain, and other top firms accept less than 1% of applicants every year. If you want to triple your chances of landing interviews and 8x your chances of passing them, watch my free 40-minute training.

 

What Math Do You Need for Consulting Interviews?

 

You need basic arithmetic plus about 10 business formulas. No calculus, no statistics, no advanced math of any kind. If you passed 8th grade math, you already know how to do every calculation that shows up in a case interview.

 

The catch is that you need to do it fast, under pressure, and without a calculator. According to McKinsey's interviewer guidelines, clear communication of quantitative reasoning is weighted as heavily as getting the right answer. So consulting math is really about three things: knowing the formulas, doing mental math quickly, and explaining your work out loud.

 

The math expectations also vary slightly by firm. McKinsey tends to expect more precise calculations with less rounding. BCG and Bain generally allow more rounding and estimation. But at all three firms, you will be doing math in every single case interview. Having coached hundreds of candidates through their interviews, I can tell you that math mistakes are the number one reason otherwise strong candidates get rejected.

 

What Are the Essential Consulting Math Formulas?

 

Below are all the formulas you need, organized by category. If you want a deep dive into each formula with additional practice problems, check out my full case interview math guide.

 

Formula

Equation

When to Use

Revenue

Price x Quantity

Any case involving sales or income

Total Cost

Fixed Costs + (Variable Cost x Quantity)

Profitability, pricing, cost reduction

Profit

Revenue – Total Cost

Profitability cases (most common)

Profit Margin

Profit ÷ Revenue

Comparing profitability across companies

Gross Margin

(Revenue – COGS) ÷ Revenue

Product-level profitability

Contribution Margin

Price – Variable Cost per Unit

Breakeven analysis, pricing decisions

Breakeven Quantity

Fixed Costs ÷ Contribution Margin

New product, market entry, investment

ROI

Annual Profit ÷ Initial Investment

Investment and acquisition cases

Payback Period

Initial Investment ÷ Annual Profit

How long to recoup an investment

Market Share

Company Revenue ÷ Total Market Revenue

Competitive positioning

Growth Rate

(New – Old) ÷ Old

Revenue or market trends

Rule of 72

72 ÷ Growth Rate = Years to Double

Quick compounding estimates

Output

Rate x Time

Operations and capacity cases

Utilization

Actual Output ÷ Maximum Capacity

Efficiency and operations cases

 

What Are the Profit Formulas?

 

Profit formulas are the most frequently tested math in case interviews. In my experience at Bain, roughly 60% of all case interviews involve some form of profitability calculation. You need to know four formulas that build on each other.

 

  • Revenue = Price x Quantity

 

  • Total Cost = Fixed Costs + (Variable Cost per Unit x Quantity)

 

  • Profit = Revenue – Total Cost

 

  • Profit Margin = Profit ÷ Revenue

 

Worked example: A coffee shop sells 200,000 cups per year at $5 each. Each cup costs $1.50 in variable costs. Rent and salaries total $400,000 per year.

 

Revenue = 200,000 x $5 = $1,000,000. Total cost = $400,000 + ($1.50 x 200,000) = $700,000. Profit = $1,000,000 – $700,000 = $300,000. Profit margin = $300,000 ÷ $1,000,000 = 30%.

 

For a complete list of all 26 formulas with examples, see my case interview formulas guide.

 

What Is the Difference Between Margin Formulas?

 

There are three margin formulas that come up in case interviews, and candidates confuse them constantly. Here is exactly how they differ.

 

Margin Type

Formula

What It Measures

Profit Margin

Profit ÷ Revenue

Overall company profitability after ALL costs

Gross Margin

(Revenue – COGS) ÷ Revenue

Profitability after direct production costs only

Contribution Margin

Price – Variable Cost per Unit

How much each unit contributes to covering fixed costs

 

The key distinction: profit margin is always lower than gross margin because it includes all costs (rent, salaries, marketing), not just the cost of making the product. Contribution margin is a dollar amount per unit, not a percentage. It tells you how much each additional sale contributes to covering your fixed costs and generating profit.

 

What Are the Investment Formulas?

 

Investment formulas show up in market entry, acquisition, and new product cases. The three you need are ROI, payback period, and breakeven.

 

ROI = Annual Profit ÷ Initial Investment. If a company invests $2M in a new factory that generates $400K per year in profit, the ROI is 20%. A higher ROI means a better investment.

 

Payback Period = Initial Investment ÷ Annual Profit. Using the same example, the payback period is $2M ÷ $400K = 5 years. This tells you how long until the investment pays for itself.

 

Breakeven Quantity = Fixed Costs ÷ Contribution Margin. If fixed costs are $500,000 and each unit contributes $10, you need to sell 50,000 units to break even. For a detailed walkthrough with practice problems, check out my breakeven analysis guide.

 

A common mistake is confusing breakeven with payback period. Breakeven tells you the number of units you need to sell. Payback period tells you how many years it takes to recover your investment. According to Glassdoor data, about 1 in 5 candidates mix these up during interviews.

 

What Are the Growth and Market Formulas?

 

These formulas come up in market sizing, competitive analysis, and growth strategy cases.

 

Market Share = Company Revenue ÷ Total Market Revenue. If the total market is $500M and your client generates $75M, they hold 15% market share.

 

Growth Rate = (New Value – Old Value) ÷ Old Value. If revenue grew from $80M to $100M, the growth rate is ($100M – $80M) ÷ $80M = 25%.

 

Rule of 72: Divide 72 by the annual growth rate to estimate how many years it takes for something to double. At 8% growth, a market will double in about 9 years (72 ÷ 8 = 9). This is a powerful shortcut for quickly evaluating compound growth during an interview.

 

What Are the Operations Formulas?

 

Operations formulas show up in cases about manufacturing, logistics, and efficiency improvements.

 

Output = Rate x Time. If a machine produces 50 units per hour and runs for 8 hours, output is 400 units.

 

Utilization = Actual Output ÷ Maximum Capacity. If the machine produces 400 units but could produce 600, utilization is 67%. Low utilization signals an opportunity to cut costs by reducing excess capacity or increase revenue by ramping production.

 

Which Formula Should You Use?

 

One of the biggest mistakes candidates make is picking the wrong formula. Use this quick decision guide to match the interview question to the right formula.

 

If the Interviewer Asks...

Use This Formula

"Is this company profitable?"

Profit = Revenue – Cost

"How does profitability compare?"

Profit Margin = Profit ÷ Revenue

"How many units to break even?"

Breakeven = Fixed Costs ÷ Contribution Margin

"How long to recoup the investment?"

Payback = Investment ÷ Annual Profit

"Is this a good investment?"

ROI = Annual Profit ÷ Investment

"What is the market size?"

Market Size = # of Customers x Purchase Frequency x Price

"How fast is the market growing?"

Growth Rate = (New – Old) ÷ Old

"How efficient is the factory?"

Utilization = Actual Output ÷ Max Capacity

 

When in doubt, ask the interviewer to clarify what they want you to solve for. Asking a good clarifying question is always better than using the wrong formula. For a broader look at how to structure your entire case approach, see my complete case interview guide.

 

What Mental Math Shortcuts Should You Memorize?

 

Fast mental math separates good candidates from great ones. These shortcuts will save you time in every case interview. For a deeper dive into mental math strategies, see my case interview mental math guide.

 

What Are the Best Percentage Shortcuts?

 

The fastest way to calculate any percentage is to build from easy anchors. Start with 10% (just move the decimal point one place left), then combine.

 

To Find...

Do This

Example (Base: 4,800)

10%

Move decimal left one place

480

5%

Take half of 10%

240

1%

Move decimal left two places

48

15%

10% + 5%

480 + 240 = 720

20%

10% x 2

960

25%

Divide by 4

1,200

33%

Divide by 3

1,600

75%

Subtract 25% from 100%

4,800 – 1,200 = 3,600

 

This building-block method lets you calculate any percentage in seconds. In my coaching experience, candidates who practice this technique for just 15 minutes a day see a noticeable improvement within one week.

 

What Fraction and Decimal Conversions Should You Know?

 

Memorize these common conversions. They come up constantly in case interviews when you need to quickly convert between fractions, decimals, and percentages.

 

Fraction

Decimal

Percentage

1/2

0.50

50%

1/3

0.33

33.3%

1/4

0.25

25%

1/5

0.20

20%

1/6

0.167

16.7%

1/7

0.143

14.3%

1/8

0.125

12.5%

1/9

0.111

11.1%

1/10

0.10

10%

2/3

0.667

66.7%

3/4

0.75

75%

3/8

0.375

37.5%

 

What Are the Best Multiplication and Division Shortcuts?

 

The divide and conquer method is the single most useful mental math technique. Break hard calculations into easier parts.

 

Example: 36 x 25. Split 25 into (100 ÷ 4). So 36 x 25 = 36 x 100 ÷ 4 = 3,600 ÷ 4 = 900. Much faster than multiplying 36 x 25 directly.

 

Zeroes management is also critical. Use K for thousands, M for millions, B for billions. Write $4.5M instead of $4,500,000. According to BCG interviewers, dropping or adding a zero is the most common math error in case interviews. Abbreviating large numbers eliminates this problem entirely.

 

When rounding, a good rule of thumb is to round to within 5% of the actual number. Rounding $487M to $500M is fine. Rounding $487M to $400M changes the answer too much and signals that you are uncomfortable with the math.

 

What Numbers Should You Have Memorized?

 

You do not need specialized knowledge for case interviews, but memorizing a few key statistics helps enormously with market sizing questions and sanity checks. Here is a reference table of the most useful numbers.

 

Statistic

Value

World population

~8.1 billion

United States population

~335 million

US households

~130 million

US average household size

~2.5 people

US median household income

~$80,000

US average life expectancy

~78 years

China population

~1.4 billion

India population

~1.45 billion

EU population

~450 million

Japan population

~124 million

UK population

~68 million

Germany population

~84 million

Brazil population

~215 million

Canada population

~41 million

Australia population

~27 million

Global GDP

~$105 trillion

US GDP

~$29 trillion

 

These numbers are approximate and are fine to use for estimation purposes. For your own market sizing practice, you should also memorize the population of the city and country where you are applying. A candidate interviewing at McKinsey's Chicago office should know that Chicago has about 2.7 million people and the greater metro area has about 9.5 million.

 

What Are the Most Common Consulting Math Mistakes?

 

Having coached hundreds of candidates, I see the same five mistakes over and over. Avoiding these will instantly put you ahead of most applicants.

 

1. Dropping or adding zeroes. This is by far the most common error. A $50 million answer turns into $500 million with one extra zero. The fix: write K, M, and B instead of writing out full numbers, and double check your zeroes at each step.

 

2. Forgetting to convert units. If the interviewer gives you monthly costs but asks for annual profit, you need to multiply by 12. About 15% of math errors I see in coaching are unit conversion mistakes.

 

3. Rounding too aggressively. Rounding every number in a multi-step calculation compounds the error. By the final answer, you could be off by 20% or more. Round only once or twice, and choose the step where it simplifies the math the most.

 

4. Calculating the number but not interpreting it. Saying "the breakeven is 50,000 units" is not enough. You need to answer "so what?" Is 50,000 units achievable given the market size? Is that more or less than the client currently sells? Always connect the number to the business decision.

 

5. Doing math silently. Many candidates go quiet when they calculate. This is a missed opportunity. Talking through your math shows the interviewer your thought process, reduces errors, and allows the interviewer to redirect you if you are headed in the wrong direction.

 

How Should You Communicate Math During a Case Interview?

 

Strong consulting math is not just about getting the right number. It is about walking the interviewer through your thinking in a clear, structured way. Here is the four step process that works.

 

Step 1: State the formula. Before you calculate anything, say which formula you are going to use. For example: "To find out whether this investment makes sense, I'm going to calculate the payback period using Initial Investment divided by Annual Profit."

 

Step 2: Walk through each calculation out loud. Narrate as you go: "Revenue is 500,000 units times $20 per unit, which gives us $10 million." This makes it easy for the interviewer to follow and catch any mistakes early.

 

Step 3: Sanity check the result. Ask yourself if the number makes sense. A $90 billion toothbrush market would be almost as big as the entire US GDP. A 0.1% profit margin for a SaaS company would be unusually low. If something looks off, recheck your work.

 

Step 4: Connect the number to the business decision. This is the "so what?" step. "The payback period is 5 years. Given that the client typically evaluates investments on a 3 year horizon, this investment may not meet their threshold. However, if there are strategic benefits beyond the financial return, it could still be worth pursuing."

 

If you want to master this process with guided practice, my case interview course walks you through every formula and calculation type with step-by-step drills.

 

Frequently Asked Questions

 

Do You Need a Math Degree for Consulting Interviews?

 

No. The math in consulting interviews is basic arithmetic: addition, subtraction, multiplication, division, and percentages. You do not need any advanced math background. Consulting firms like McKinsey, BCG, and Bain actively recruit from non-quantitative majors and expect candidates to learn the required business formulas during preparation, not during college.

 

Can You Use a Calculator in Case Interviews?

 

No, calculators are not allowed at McKinsey, BCG, Bain, or most other consulting firms. You are expected to do all math by hand or mentally. The one notable exception is Capital One, which does allow calculators in their case interviews, but gives you messier numbers to compensate.

 

How Long Should You Practice Consulting Math Before Interviews?

 

Most candidates need two to four weeks of daily practice to reach a comfortable level. Based on my coaching experience, 15 to 30 minutes per day of mental math drills produces the best results. Focus on speed and accuracy with the core formulas first, then move to timed practice with realistic case math problems.

 

What Is the Hardest Math You Will See in a Case Interview?

 

The hardest math is usually a multi-step calculation where you need to chain several formulas together. For example, calculating market size, then market share, then revenue, then profit, then payback period. Each individual step is simple, but keeping track of all the numbers without making an error requires practice and clear notation.

 

How Do You Get Faster at Mental Math for Consulting?

 

Practice with timed drills daily. Start with basic arithmetic (two digit multiplication and division), then progress to percentage calculations and formula application. Use the shortcut techniques in this cheat sheet, especially the percentage building blocks and the divide and conquer method. For a full set of mental math strategies, see my case interview mental math guide.

 

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