CAGR: The Compound Annual Growth Rate Formula With Worked Examples
October 29, 2026
The compound annual growth rate (CAGR) is the constant yearly rate that would take a starting value to an ending value over a number of years. The formula is CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1. If an investment grows from $10,000 to $25,000 in 8 years, the ratio is 2.5, the eighth root of 2.5 is 1.1214, and the CAGR is 12.14%.
CAGR smooths out the ups and downs of actual returns into a single rate, which makes it easy to compare investments, track the growth of sales or users, and project the future. It is the geometric mean of annual growth rates.
Skip the math and get your answer instantly:
Open the Compound Interest Calculator →Worked Examples
Investment: $10,000 grows to $25,000 over 8 years, CAGR = 12.14%. Doubling in 10 years requires a CAGR of 2^(0.1) − 1 = 7.18%. A company's revenue grows from $2.0 million to $3.5 million in 5 years: (3.5 ÷ 2.0)^(0.2) − 1 = 11.8%. A user base grows from 50,000 to 410,000 in 4 years: 8.2^(0.25) − 1 = 69.2% per year. A stock falls from $80 to $50 over 3 years: (50 ÷ 80)^(1/3) − 1 = −14.4% a year.
Use the calculator's power function or a spreadsheet formula such as =(end/start)^(1/years)-1, or =RRI(years, start, end).
| Start | End | Years | CAGR |
|---|---|---|---|
| $10,000 | $25,000 | 8 | 12.14% |
| $10,000 | $20,000 | 10 | 7.18% |
| $2.0M revenue | $3.5M revenue | 5 | 11.84% |
| 50,000 users | 410,000 users | 4 | 69.2% |
| $80 stock | $50 stock | 3 | -14.4% |
CAGR vs. Average Annual Return
The arithmetic average of yearly returns overstates growth when returns vary. Suppose an investment goes up 50% in year 1 and down 50% in year 2. The average is 0%, but $100 becomes $150 and then $75, a loss of 25% overall, and the CAGR is −13.4%. CAGR reflects what you actually earned. When comparing funds, use CAGR over the same period, and be cautious about marketing that quotes averages. Also, CAGR ignores the path: two investments with the same CAGR can have very different volatility along the way.
Solving for Time or Future Value
Rearrange the formula to find years: n = ln(end ÷ start) ÷ ln(1 + CAGR). To grow $10,000 to $50,000 at 9%: ln 5 ÷ ln 1.09 = 18.7 years. To project a future value: end = start × (1 + CAGR)^years. A business growing 20% a year from $1 million reaches $1 × 1.2^5 = $2.49 million in five years. If you need $500,000 in 15 years from $100,000, the required CAGR is 5^(1/15) − 1 = 11.3%, which may be unrealistic, a signal to raise contributions.
Limitations
CAGR requires only the start and end values, ignoring contributions and withdrawals in between. For an investor adding money regularly, use the internal rate of return (IRR) or money-weighted return. Start and end dates can cherry-pick results: a CAGR measured from a market low looks great. Past CAGR does not guarantee future performance, and extrapolating a high growth rate indefinitely produces implausible results: 69% a year for 10 years is a 200-fold increase. Always check the period and the context.
Frequently Asked Questions
What is the CAGR formula?
(Ending value ÷ starting value)^(1 ÷ years) − 1.
How is CAGR different from the average return?
CAGR accounts for compounding and gives the actual constant growth rate, while the arithmetic average overstates it when returns vary.
What CAGR doubles money in 10 years?
About 7.2%.
Can CAGR be negative?
Yes, if the ending value is less than the starting value.
What is the Excel function for CAGR?
RRI(years, start, end), or the formula (end/start)^(1/years)-1.