CAGR Explained: Compound Annual Growth Rate

If one investment returned 60% over four years and another returned 45% over three, which grew faster? You can't tell at a glance — the time periods differ. Compound annual growth rate (CAGR) solves this by expressing any total return as a single, steady yearly rate, so investments held for different lengths of time can be compared on a level footing.

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The formula

CAGR is the constant rate that, compounded annually, grows your starting value into your ending value:

CAGR = (Ending value / Starting value)^(1 / Years) − 1

Ending value = what the investment is worth now
Starting value = what it was worth at the beginning
Years = the length of the holding period

The exponent 1 / Years is what turns a total multiple into a per-year rate. It's the same maths as compound interest, run in reverse: instead of growing a balance forward at a known rate, you solve for the rate that connects two known balances.

Worked example

You invest $10,000 and it grows to $25,000 over 5 years.

Total return: ($25,000 − $10,000) / $10,000 = 150%
CAGR: (25,000 / 10,000)^(1/5) − 1 = (2.5)^0.2 − 1 = 20.1% per year

Both numbers are correct and describe the same outcome. The 150% is dramatic but says nothing about pace; the 20.1% is what lets you compare this investment against a savings account, an index fund, or a property.

Why CAGR beats a simple average

A common mistake is to average the yearly returns. That ignores compounding and overstates performance whenever returns vary. The classic example:

Year 1: +50%. $100 becomes $150.
Year 2: −50%. $150 becomes $75.

The simple average is (50% − 50%) / 2 = 0% — which implies you broke even. But you didn't: $100 became $75, a real loss. CAGR tells the truth: (75 / 100)^(1/2) − 1 = −13.4% per year. The bigger the swings, the wider the gap between the misleading simple average and the honest CAGR. This is sometimes called volatility drag.

CAGR can be negative

If the ending value is lower than the starting value, CAGR is simply negative — the steady annual rate of decline. $10,000 falling to $8,000 over 3 years is (8,000 / 10,000)^(1/3) − 1 ≈ −7.2% per year. The only values CAGR can't handle are zero or negative start/end values, because you can't take a fractional power of a negative number meaningfully.

Where CAGR misleads

CAGR is a summary, and like any summary it hides things. Use it knowing its blind spots:

It hides the path. Two investments can share a 10% CAGR while one rose smoothly and the other halved twice along the way. CAGR says nothing about the drawdowns you'd have had to stomach. Pair it with a sense of volatility before judging an investment.
It assumes a single lump sum. CAGR compares two endpoints and ignores anything in between. If you added money monthly or took withdrawals, CAGR on the start and end balances will be wrong. For cash flows in and out, you need a money-weighted return (IRR).
It's nominal, not real. A 7% CAGR during a period of 3% inflation is closer to 4% in purchasing power. For long-horizon planning, subtract inflation.
It's backward-looking. A high historical CAGR is not a forecast. Past growth, especially over a cherry-picked period, tells you little about the future.

The rule of 72 cross-check

For a quick sanity check, the rule of 72 estimates how long it takes money to double: divide 72 by the CAGR. A 20% CAGR doubles money in about 3.6 years, so $10,000 growing to $25,000 (2.5×) in 5 years is in the right ballpark — it more than doubled once. If your calculated CAGR fails this kind of gut check, re-enter your figures.

CAGR vs ROI vs IRR

ROI (return on investment) is the simple total gain as a percentage of what you put in — no time dimension. Good for a single before-and-after comparison.
CAGR adds the time dimension, turning total return into an annual rate. Best for lump-sum investments held over a known period.
IRR (internal rate of return) is CAGR's big sibling — it handles multiple cash flows in and out at different times. Use it when you've been contributing or withdrawing.