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What Is CAGR and How Is It Calculated?

By ExpTool Editorial Team · Published Recently

What Is CAGR and How Is It Calculated?

CAGR stands for Compound Annual Growth Rate — it’s the steady yearly growth rate that would take an investment or business metric from its starting value to its ending value over a set number of years, assuming profits compound. The formula is CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Number of Years) − 1. For example, $10,000 growing to $14,000 over 3 years has a CAGR of (14,000 ÷ 10,000)^(1/3) − 1 = 11.9% per year.

Why CAGR Exists (And Why Simple Averages Lie)

Here’s a scenario. You invest $10,000. Year one, it jumps 40%. Year two, it crashes 30%. Year three, it climbs 25%. What’s your average annual return?

If you just average the three percentages — (40 − 30 + 25) ÷ 3 — you get 11.7% per year. Sounds decent, right?

But let’s check the actual money. After year one: $10,000 × 1.40 = $14,000. After year two: $14,000 × 0.70 = $9,800. After year three: $9,800 × 1.25 = $12,250.

You turned $10,000 into $12,250 over three years. The true annualized rate — the CAGR — is (12,250 ÷ 10,000)^(1/3) − 1 = 7.0%. Not 11.7%.

That gap between 11.7% and 7.0% is exactly why CAGR exists. Simple averages ignore compounding — the fact that each year’s growth (or loss) applies to a bigger or smaller base. CAGR accounts for it. It’s the financial world’s way of asking: “If growth had been perfectly smooth, what steady rate would have gotten us here?”

The Formula, Step by Step

CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Number of Years) − 1

Let’s break down each piece:

  • Ending Value ÷ Beginning Value — this gives you the total growth multiple. If you started with $10,000 and ended with $16,105, that’s 1.6105 — your money grew 1.61 times over.
  • ^(1 ÷ Number of Years) — this is the “annualizing” step. It takes the total growth and spreads it evenly across each year. The ^ symbol means “to the power of.” On most calculators, you’d use the x^y button.
  • − 1 — this converts the growth multiple back into a rate. If the result of step 2 is 1.119, subtracting 1 gives 0.119, which is 11.9%.

Multiply by 100 at the end to express it as a percentage.

Worked Example 1: A Stock Investment

You bought $8,000 worth of stock. Five years later it’s worth $13,200. What’s the CAGR?

  • Step 1: 13,200 ÷ 8,000 = 1.65.
  • Step 2: 1.65^(1/5) = 1.65^0.2 = 1.1053. (Use a calculator’s power function.)
  • Step 3: 1.1053 − 1 = 0.1053.
  • Step 4: 0.1053 × 100 = 10.53%.

Your investment compounded at about 10.5% per year. That’s a solid return — comfortably above long-term stock market averages.

Worked Example 2: Business Revenue Growth

A small business did $120,000 in revenue in 2021 and $210,000 in 2025. That’s 4 years of growth. What’s the CAGR?

  • Step 1: 210,000 ÷ 120,000 = 1.75.
  • Step 2: 1.75^(1/4) = 1.75^0.25 = 1.1502.
  • Step 3: 1.1502 − 1 = 0.1502.
  • Step 4: × 100 = 15.02%.

Revenue grew at roughly 15% per year, compounded. If you’re pitching investors, that’s the number that goes on the slide — not the raw dollar figures.

Worked Example 3: A Savings Account (Low Growth)

You put $5,000 in a high-yield savings account. Three years later you have $5,486.

  • Step 1: 5,486 ÷ 5,000 = 1.0972.
  • Step 2: 1.0972^(1/3) = 1.0314.
  • Step 3: 1.0314 − 1 = 0.0314 → 3.14%.

About 3.1% per year. Modest, but that’s savings accounts for you — safety over speed.

Worked Example 4: Checking Your Work Backwards

Let’s verify Example 1. If $8,000 really grew at 10.53% per year for 5 years:

8,000 × (1.1053)^5 = 8,000 × 1.65 = $13,200.

It checks out. This reverse calculation is a great habit — if the numbers don’t round-trip, you made an arithmetic slip somewhere.

When CAGR Is Useful

  • Comparing investments over different time periods. A 40% total gain over 2 years (18.3% CAGR) beats a 60% gain over 5 years (9.9% CAGR), even though 60 looks bigger.
  • Business planning. If your revenue CAGR is 15%, you can project next year’s revenue with reasonable confidence.
  • Evaluating fund managers. Anyone can cherry-pick a good year. CAGR over 5–10 years tells you who actually delivers.
  • Population, subscriber, or traffic growth. Anytime something compounds, CAGR is the honest way to describe the trend.

When CAGR Misleads (Read This Before You Trust It)

CAGR has a blind spot, and it’s a big one: it hides volatility. Remember our first example? The investment swung +40%, −30%, +25%. The CAGR was a smooth 7.0% — but the actual ride was anything but smooth. Two investments can have identical CAGRs and wildly different risk profiles.

CAGR also assumes reinvestment of all gains, which doesn’t always happen in real life (if you spent the dividends, your actual return is lower). And it tells you nothing about what happens *after* the measurement period — past compounding doesn’t guarantee future compounding.

Use CAGR as a summary statistic, not the whole story. Always ask: “What did the actual year-by-year path look like?”

CAGR vs. Simple Average Growth Rate

Quick comparison using our volatile investment (+40%, −30%, +25% over 3 years):

  • Simple average: (40 − 30 + 25) ÷ 3 = 11.7% — overstates reality.
  • CAGR: 7.0% — the true annualized compounding rate.

The simple average is almost always higher than the CAGR when returns bounce around, because it doesn’t account for the fact that losses shrink the base that future gains compound on. Losing 30% requires a 43% gain just to break even — the simple average pretends otherwise.

Frequently Asked Questions

What’s a good CAGR for investments?

It depends on the asset. For US stocks, the long-term historical CAGR is roughly 7–10% after inflation (about 10% nominal). A diversified portfolio doing 7–8% CAGR over a decade is solid. Anything consistently above 12% over long periods is exceptional — and worth scrutinizing for hidden risk.

Can CAGR be negative?

Yes. If your ending value is lower than your beginning value, the CAGR will be negative. For example, $10,000 shrinking to $7,500 over 3 years: (7,500 ÷ 10,000)^(1/3) − 1 = −9.1% per year. Painful, but at least the math is honest about it.

How is CAGR different from IRR?

CAGR assumes a single lump-sum investment at the start and measures growth to the end. IRR (Internal Rate of Return) handles messier real-world situations — multiple deposits and withdrawals at different times. If you invested once and never touched it, CAGR is all you need. If you added money along the way, use IRR.

Do I need the exact number of years, or can I use months?

You can use any time unit as long as you’re consistent. For 30 months, use n = 2.5 years (30 ÷ 12). The formula works the same: (End ÷ Start)^(1/2.5) − 1. Just make sure the result is interpreted as an *annual* rate.

Why do companies love quoting CAGR?

Because it makes growth look smooth and inevitable. “Our revenue grew at a 25% CAGR over five years” sounds better than “we had two flat years, one bad year, and two great ones.” It’s not dishonest — it’s just a summary. Always ask for the underlying yearly numbers before making decisions based on a CAGR figure.

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