CAGR Explained: What It Is, the Formula, and How to Use It
June 10, 2026 · 4 min read
CAGR Explained: What It Is, the Formula, and How to Use It
CAGR — Compound Annual Growth Rate — is the most honest way to measure how an investment, business metric, or any value has grown over time. It answers the question: "If growth had been perfectly smooth and compounding, what annual rate would produce the same result?" That single number lets you compare a choppy, volatile multi-year journey against any benchmark on equal terms.
The CAGR Formula
CAGR = (End Value / Start Value)^(1 / Years) − 1
Example: An investment grows from $10,000 to $18,000 over 5 years.
CAGR = (18,000 / 10,000)^(1/5) − 1
= 1.8^0.2 − 1
= 1.1247 − 1
= 0.1247
= 12.47% per year
That 12.47% is the smoothed annual rate that, compounded for 5 years, turns $10,000 into $18,000.
Why CAGR Differs from Average Annual Return
This is the most common source of confusion. Consider an investment that:
- Year 1: +50%
- Year 2: −50%
Simple average: (50% − 50%) / 2 = 0% (sounds breakeven)
Actual result: $10,000 × 1.50 × 0.50 = $7,500 (a 25% loss)
CAGR: (7,500 / 10,000)^(1/2) − 1 = −13.4% per year
The arithmetic average of returns is almost always higher than CAGR. CAGR is the geometrically compounded rate — the number that reflects what actually happened to your money.
Calculating CAGR from Start, End, and Time
| Start Value | End Value | Years | CAGR |
|---|---|---|---|
| $5,000 | $10,000 | 7 | 10.41% |
| $100,000 | $250,000 | 10 | 9.60% |
| $50,000 | $45,000 | 3 | −3.42% |
Negative CAGR is valid — it means the value declined, and the same formula applies.
Solving for Other Variables
The CAGR formula can be rearranged to solve for any unknown:
Find end value given start, rate, years:
End = Start × (1 + CAGR)^Years
Find start value given end, rate, years:
Start = End / (1 + CAGR)^Years
Find years given start, end, rate:
Years = log(End / Start) / log(1 + CAGR)
When to Use CAGR (and When Not To)
Use CAGR when:
- Comparing investments over different time periods
- Reporting growth to stakeholders (it's the expected format in finance)
- Smoothing out volatile year-to-year fluctuations to see the trend
- Projecting future values from historical growth
Don't rely on CAGR when:
- The time period is very short (1–2 years) — single-period returns are clearer
- Intermediate cash flows exist (dividends reinvested, capital contributions) — use IRR instead
- You need to understand volatility — CAGR says nothing about the bumpy road taken
- You're comparing CAGR to average return without noting the difference
CAGR vs IRR
CAGR assumes a single lump sum invested at the start and no cash flows in between.
IRR (Internal Rate of Return) accounts for cash flows at different points in time — regular contributions, withdrawals, dividends. It answers the same "what effective annual rate?" question but for irregular cash flow streams.
If you invested $10,000 today and added $1,000 per year for 5 years, your IRR on total returns would differ from the CAGR on the ending balance, because CAGR ignores when the extra $1,000 contributions arrived.
For simple start-to-end analysis with no intermediate flows: use CAGR. For anything more complex: use IRR.
Rule of 72
A quick mental shortcut: divide 72 by the annual growth rate (in percent) to estimate how many years it takes to double.
At 12% CAGR: 72 / 12 = 6 years to double
At 8% CAGR: 72 / 8 = 9 years to double
At 3% CAGR: 72 / 3 = 24 years to double
It's an approximation (accurate to within ~1–2% for rates between 2% and 30%), but it's fast enough to do in your head during any discussion.
Tools
Calculate CAGR, or solve for any variable given the others, with the CAGR Calculator. To project how a present sum grows at a given rate, use the Future Value Calculator. To find what a future amount is worth today, use the Present Value Calculator. For a full payment schedule including principal and interest breakdowns, the Loan Amortization Calculator handles multi-period finance math.