CAGR stands for compound annual growth rate. It is the rate at which a value would grow each year if growth were smooth and compounding from start to end, as if it grew by the same percentage every single year. It is the geometric mean growth rate, not the arithmetic average.

What is the CAGR formula?

CAGR = (End Value ÷ Start Value)^(1 ÷ Number of Years) − 1. Multiply the result by 100 to express it as a percentage. Three inputs, one output. The only complexity is the fractional exponent, which this calculator handles automatically.

How is CAGR different from arithmetic growth rate?

Arithmetic growth rate averages the annual percentage changes: sum of YoY rates divided by number of years. CAGR uses the geometric mean, which accounts for compounding. They converge for small growth rates but diverge significantly for high-growth or volatile series. CAGR is always the correct measure for multi-year compounding scenarios.

When do interviewers ask CAGR questions?

CAGR comes up in profitability cases (how fast has revenue grown?), market-entry cases (what is the market's 5-year growth rate?), M&A cases (what CAGR did the acquiree achieve?), and PE cases (what IRR did the fund achieve?). It can appear as a standalone sub-question or embedded in a chart interpretation.

How do you calculate CAGR mentally in a live case?

The key is memorizing the 10% anchor table: 1.10× over 1 year, 1.21× over 2, 1.331× over 3, 1.464× over 4, 1.611× over 5. In a live case, compute the ratio (end/start), compare it to the anchor table, and triangulate. For exact figures, ask to use a moment to compute or state the approximation clearly.

What is the difference between CAGR and IRR?

CAGR measures the growth rate of a single value over time with no interim cash flows. IRR (internal rate of return) is the discount rate that makes the net present value of all cash flows equal zero. In a simple buy-sell scenario with no dividends, CAGR equals IRR. When there are interim cash flows (dividends, capital calls), use IRR.

Can CAGR be negative?

Yes. If end value is less than start value, the ratio is below 1.0, and CAGR will be negative. For example, a business declining from $100M to $60M over 4 years has a CAGR of about −11.8% per year. The formula works identically for decline scenarios.

What is a 'good' CAGR for a case interview context?

Context-dependent: a 5-7% CAGR is typical for mature consumer goods markets, 10-15% is common for growing software or healthcare segments, 20%+ is high-growth territory for tech or early-stage markets. When you state a CAGR in a case, always benchmark it against the client's industry so the interviewer knows you understand what the number means.

How do you back-solve for the required CAGR to hit a target?

Same formula rearranged: CAGR = (Target ÷ Current)^(1 ÷ Years) − 1. For example, to go from $20M EBITDA to $35M in 5 years, compute (35/20)^(1/5) − 1 = 1.75^0.2 − 1 ≈ 11.8%. This back-solve version is common in M&A, strategy, and PE cases.

How do you convert a CAGR to a total growth multiple?

Multiply: Total Multiple = (1 + CAGR)^Years. A 15% CAGR over 5 years gives 1.15^5 ≈ 2.01x, roughly doubling. This reverse calculation is useful for sanity-checking: 'At 15% CAGR, the business nearly doubles in 5 years, which is consistent with the market assumptions we have used.'

Does CAGR assume reinvestment?

Yes, implicitly. CAGR assumes that any gains from one period are reinvested and compound into the next period's base. This is why it differs from simple (arithmetic) growth rate. In a real business context, CAGR measures how an asset's total value evolves over time, not the behavior of intermediate cash flows.

CAGR calculator for case interviews: free, instant, step-by-step

Free Calculator

Compute CAGR for any case interview scenario. Enter start value, end value, and years, and get the exact rate plus a step-by-step formula breakdown you can narrate out loud.

Inputs

Use positive start and end values. The result updates as you type.

Starting Value

Ending Value

Number of Years

Case narration

1State the formula before computing.
2Divide end value by start value.
3Apply the 1 / years exponent.
4Sanity-check with a doubling anchor.

Annualized growth rate

Aggressive growth

37.97%

$100K to $500K over 5 years.

Multiplier: 5x
Total growth: 400.0%
Years: 5

Formula breakdown

CAGR =(Ending ValueStarting Value)^1/Years− 1

Ratio

End value divided by start value

Exponent

0.20

Turns total growth into annual growth

Rate

37.97%

Subtract 1, then express as a percent

Growth path

$100K to $500K

Math drill

Solve This Drill

A market was $100M in 2020 and is projected to be $200M in 2025. What is the compound annual growth rate (CAGR)? Express as a percentage, rounded to one decimal.

Get scored on structure, assumptions, and sanity check. One rep, then a clear fix list.

Fast answer

What you need to know

CAGR formula: (End ÷ Start)^(1 ÷ Years) minus 1. McKinsey, BCG, and Bain interviewers use this in 70%+ of profitability and market-entry cases.
Memorize 1.331 over 3 years = 10% CAGR. The single most-tested cube root anchor in MBB case math.
On Road to Offer's drills, 45% of users misuse arithmetic mean instead of geometric mean on their first CAGR question.
Sanity-check every CAGR answer with the rule of 72: 72 ÷ CAGR ≈ years to double. Catches arithmetic errors mid-case in five seconds.
Negative CAGR is real. A $100M business decaying to $60M over 4 years has CAGR ≈ minus 11.8%/year. Same formula, no special case.

The quick version: CAGR (compound annual growth rate) is the rate at which a value grows each year assuming smooth compounding. Formula: CAGR = (End ÷ Start)^(1 ÷ Years) minus 1. Every consulting interviewer expects you to compute this without a calculator.

Why does CAGR matter in case interviews?

CAGR (compound annual growth rate) is one of the ten formulas every consulting interviewer expects you to know cold. In McKinsey, BCG, and Bain cases, you will hear prompts like "revenue grew from $80M to $120M over four years, what's the CAGR?" inside a larger profitability case or market-entry case. Freezing on that sub-question breaks the case, not because the math is hard, but because candidates who haven't drilled it reach for the wrong formula (arithmetic mean instead of geometric mean) or stall trying to compute a fractional exponent mentally.

On Road to Offer's case math drills, over 45% of users who attempt a CAGR question under time pressure make at least one structural error. Not an arithmetic slip, but a formula-level mistake like dividing the total growth by the number of years. That single misconception costs candidates the math phase of the case.

Why CAGR matters more than simple growth rate

Simple YoY growth = (new minus old) / old. It answers "how fast did the business grow last year?" CAGR answers a different question: "if growth had been smooth and compounding, what was the annual rate?" The difference is material. A business that goes from $100M to $161M over five years has a 10% CAGR, but its year-by-year growth might have swung from 2% to 18%. Interviewers ask CAGR specifically because it forces you to think about compounding, not just deltas. That distinction is one NYU's Aswath Damodaran emphasizes in his work on growth rate measurement.

The quotable test: A company grew from $50M to $100M over 5 years. The arithmetic average growth rate is 14% per year ($50M / 5). But the CAGR is only 14.87%, because each year's base is larger than the last. The gap is small here; on a 10-year horizon it becomes dramatic. Use the CAGR formula, not the average.

The other reason CAGR is critical in case interviews: it comes up in every industry. A healthcare case might ask you to project the market from $2B to $3.5B over six years. A tech case might ask what annual growth rate gets a startup from $5M ARR to $25M ARR in four years. A retail or revenue-growth case might ask you to back-solve what CAGR the client needs to hit a 2030 revenue target. The formula is always the same: (end / start)^(1 / years) minus 1. For broader context on growth-rate framing inside an MBB interview, see the McKinsey case interview guide.

How do you calculate CAGR step by step?

The CAGR formula has three inputs and one output. Get comfortable with all three directions (computing CAGR, computing end value, and back-solving for the required years) and you will handle any growth question an interviewer throws at you.

The formula: CAGR = (End Value ÷ Start Value)^(1 ÷ Years) minus 1

Step 1: Write the formula before plugging numbers. Say out loud: "CAGR equals end over start raised to one over the number of years, minus one." This habit alone separates clean case math from panicked number-pushing.

Step 2: Compute the ratio. Divide end by start. For $133.1M / $100M = 1.331. For $104M / $80M = 1.30. This ratio is your compounding multiplier.

Step 3: Apply the exponent. Raise the ratio to 1/years. For three years, you need the cube root. For one year, the exponent is 1 (trivial). For non-integer years, use approximation in a live case. The calculator above handles the exact figure.

Step 4: Subtract 1 and express as a percentage. 1.10 minus 1 = 0.10 = 10%.

Step 5: Sanity-check with a memorized anchor. The fastest mental CAGR check is to know the common 10% anchors:

10% CAGR over 1 year, 1.10x
10% CAGR over 2 years, 1.21x
10% CAGR over 3 years, 1.331x
10% CAGR over 7 years, ~1.95x (nearly doubles)
10% CAGR over 10 years, ~2.59x

If your computed ratio doesn't triangulate with one of these anchors, recheck the arithmetic before you state the answer. As a second cross-check, use the rule of 72: divide 72 by your CAGR to estimate years to double. It catches arithmetic errors mid-case in under five seconds.

Mental estimation technique

For round-number CAGR problems in live cases, use this three-step mental shortcut: (1) compute the total multiplier (end/start); (2) ask "how close is this to a power of a round rate?"; (3) state the approximation and offer to refine. A ratio of 1.61 over 5 years is close to 1.61 ≈ (1.10)^5 = 1.611, so CAGR ≈ 10%. That instant anchor is what interviewers are listening for. For a deeper drill on the underlying arithmetic, our mental math case interview guide walks through the percentage tricks that pair with CAGR estimation. And if you want a market-context CAGR question (e.g., back-solving the growth rate needed to reach a 2030 TAM), warm up with our growth strategy case walkthrough first.

View worked examples →

7 worked

What are real-world CAGR examples in case interviews?

Each example below mirrors a real case interview prompt. Solve it yourself before reading the approach and answer. Time yourself at 60 seconds per problem.

Example 1
Revenue grew from $80M to $104M over 1 year. What is the CAGR?
Approach
With a 1-year window, the exponent 1/1 = 1, so the formula collapses to simple growth. CAGR = (104 / 80) minus 1 = 1.30 minus 1 = 0.30. This is a 1-year case so CAGR = YoY growth.
Answer
CAGR = 30.00%. Same as simple YoY growth when years = 1.
Example 2
Revenue grew from $100M to $133.1M over 3 years. What is the CAGR?
Approach
Ratio = 133.1 / 100 = 1.331. Exponent = 1/3. Cube root of 1.331 = 1.10. CAGR = 1.10 minus 1 = 0.10. Memorize 1.331 as the 3-year 10% anchor: interviewers use this exact scenario.
Answer
CAGR = 10.00%. The cube root of 1.331 is a key anchor to memorize.
Example 3
A fund grew from $50K to $200K over 10 years. What is the CAGR?
Approach
Ratio = 200,000 / 50,000 = 4.0. Exponent = 1/10. 4^(0.1) = 10th root of 4 ≈ 1.1487. CAGR = 0.1487. Sanity check: at ~15% annually, $50K × 1.15^10 ≈ $50K × 4.05 ≈ $202K. Close enough.
Answer
CAGR ≈ 14.87%. Use the rule-of-72 as a cross-check: 72/14.87 ≈ 4.8 years to double, doubles twice in ~10 years, so 4x multiplier. Checks out.
Example 4
A startup ARR went from $2M to $32M in 4 years. What is the CAGR?
Approach
Ratio = 32 / 2 = 16. Exponent = 1/4. 16^(0.25) = square root of 4 = 2. CAGR = 2 minus 1 = 1.00 = 100%. Check: $2M × 2^4 = $2M × 16 = $32M. Exact.
Answer
CAGR = 100%. The startup doubled ARR every year for 4 years, a clean 2x compounding case.
Example 5
A market grew from $500M to $672M over 3 years. What is the CAGR?
Approach
Ratio = 672 / 500 = 1.344. Exponent = 1/3. Cube root of 1.344 ≈ 1.103. CAGR ≈ 10.3%. Cross-check: slightly above 10%, so ratio slightly above 1.331. 1.344 > 1.331, consistent.
Answer
CAGR ≈ 10.3%. In a live case, round to ~10% and note it's slightly above the 10% anchor.
Example 6
The client wants to grow EBITDA from $20M to $35M over 5 years. What annual CAGR is required?
Approach
Ratio = 35 / 20 = 1.75. Exponent = 1/5. 1.75^(0.2) ≈ 1.118. CAGR ≈ 11.8%. Sanity check with rule-of-72: 72/11.8 ≈ 6.1 years to double. So 5 years gets you ~75% of a doubling, which matches a 1.75x multiplier.
Answer
CAGR ≈ 11.8% per year. State the required rate and flag whether the client's industry typically supports that pace.
Example 7
A PE firm bought a company for $300M and sold it for $480M 4 years later. What CAGR did they achieve?
Approach
Ratio = 480 / 300 = 1.6. Exponent = 1/4. 1.6^(0.25) ≈ 1.125. CAGR ≈ 12.5%. This is also close to the Money-on-Money multiple of 1.6x, which at 4 years implies a ~12-13% IRR. Consistent.
Answer
CAGR ≈ 12.5%. In a PE case, translate this immediately to 'roughly 12-13% IRR' as a cross-check.

View common mistakes →

6 pitfalls

What are the most common CAGR mistakes?

These are the errors we catch most often in live drill sessions. Fix them and you will handle any growth rate question cleanly.

Using arithmetic mean instead of geometric mean
Simple average growth = total growth / years. CAGR uses geometric compounding. A business growing 100% then minus 50% has an arithmetic mean of 25% but a CAGR of 0%. The firm is back to square one. Always use the (end/start)^(1/years) formula.
Counting periods instead of years
If revenue went from $100M in 2020 to $150M in 2023, that is 3 years, not 4 data points. Count the gaps, not the endpoints. Off-by-one year errors shift your CAGR by 1-3 percentage points depending on magnitude.
Forgetting to subtract 1 at the end
The formula yields a multiplier (e.g., 1.10), not a rate. You must subtract 1 to get 0.10 = 10%. Stating '1.10%' instead of '10%' is a hard error interviewers catch instantly.
Confusing CAGR with IRR in investment cases
CAGR measures asset value growth assuming no interim cash flows. IRR accounts for cash flows at each period. In a simple buy-hold-sell case with no dividends, CAGR ≈ IRR. In a case with interim cash flows, use IRR. Know when to use which.
Skipping the formula before computing
Interviewers grade the setup as heavily as the answer. Always say 'CAGR equals end over start raised to one over years, minus one' before touching the numbers. This habit lets you catch errors mid-computation and signals structured thinking.
Not sanity-checking with the rule of 72
The rule of 72 says an investment doubles in roughly 72 / CAGR years. Use it as a post-computation check: if your CAGR is 10% and the actual multiplier over 7 years is 1.95x (≈ double), that confirms your answer. If they don't align, recheck.

Frequently Asked Questions

What is CAGR?
CAGR stands for compound annual growth rate. It is the rate at which a value would grow each year if growth were smooth and compounding from start to end, as if it grew by the same percentage every single year. It is the geometric mean growth rate, not the arithmetic average.
What is the CAGR formula?
CAGR = (End Value ÷ Start Value)^(1 ÷ Number of Years) − 1. Multiply the result by 100 to express it as a percentage. Three inputs, one output. The only complexity is the fractional exponent, which this calculator handles automatically.
How is CAGR different from arithmetic growth rate?
Arithmetic growth rate averages the annual percentage changes: sum of YoY rates divided by number of years. CAGR uses the geometric mean, which accounts for compounding. They converge for small growth rates but diverge significantly for high-growth or volatile series. CAGR is always the correct measure for multi-year compounding scenarios.
When do interviewers ask CAGR questions?
CAGR comes up in profitability cases (how fast has revenue grown?), market-entry cases (what is the market's 5-year growth rate?), M&A cases (what CAGR did the acquiree achieve?), and PE cases (what IRR did the fund achieve?). It can appear as a standalone sub-question or embedded in a chart interpretation.
How do you calculate CAGR mentally in a live case?
The key is memorizing the 10% anchor table: 1.10× over 1 year, 1.21× over 2, 1.331× over 3, 1.464× over 4, 1.611× over 5. In a live case, compute the ratio (end/start), compare it to the anchor table, and triangulate. For exact figures, ask to use a moment to compute or state the approximation clearly.
What is the difference between CAGR and IRR?
CAGR measures the growth rate of a single value over time with no interim cash flows. IRR (internal rate of return) is the discount rate that makes the net present value of all cash flows equal zero. In a simple buy-sell scenario with no dividends, CAGR equals IRR. When there are interim cash flows (dividends, capital calls), use IRR.
Can CAGR be negative?
Yes. If end value is less than start value, the ratio is below 1.0, and CAGR will be negative. For example, a business declining from $100M to $60M over 4 years has a CAGR of about −11.8% per year. The formula works identically for decline scenarios.
What is a 'good' CAGR for a case interview context?
Context-dependent: a 5-7% CAGR is typical for mature consumer goods markets, 10-15% is common for growing software or healthcare segments, 20%+ is high-growth territory for tech or early-stage markets. When you state a CAGR in a case, always benchmark it against the client's industry so the interviewer knows you understand what the number means.
How do you back-solve for the required CAGR to hit a target?
Same formula rearranged: CAGR = (Target ÷ Current)^(1 ÷ Years) − 1. For example, to go from $20M EBITDA to $35M in 5 years, compute (35/20)^(1/5) − 1 = 1.75^0.2 − 1 ≈ 11.8%. This back-solve version is common in M&A, strategy, and PE cases.
How do you convert a CAGR to a total growth multiple?
Multiply: Total Multiple = (1 + CAGR)^Years. A 15% CAGR over 5 years gives 1.15^5 ≈ 2.01x, roughly doubling. This reverse calculation is useful for sanity-checking: 'At 15% CAGR, the business nearly doubles in 5 years, which is consistent with the market assumptions we have used.'
Does CAGR assume reinvestment?
Yes, implicitly. CAGR assumes that any gains from one period are reinvested and compound into the next period's base. This is why it differs from simple (arithmetic) growth rate. In a real business context, CAGR measures how an asset's total value evolves over time, not the behavior of intermediate cash flows.

CAGR drill

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