CAGR formula
The CAGR formula is (ending value ÷ starting value)1/n − 1, where n is the number of years. It is the growth-rate version of the compound interest formula, solved for the rate.[1][3]
Worked example: (25,000 ÷ 10,000)1/7 − 1 = 2.50.142857 − 1 = 13.985%. Check: 10,000 × 1.139857 = $25,000.
CAGR vs average annual return
The simple average of yearly returns overstates growth whenever returns vary. An investment that gains 50% and then loses 50% has an average return of 0%, yet $10,000 ends at $7,500: its CAGR is -13.4% a year. CAGR reflects what actually happened to the money. In the example above, total growth of 150% spread evenly is 21.4% a year, against a true compound rate of 13.99%.
CAGR table
The CAGR needed for common multiples over common periods:
| Value | 3 years | 5 years | 10 years | 20 years |
|---|---|---|---|---|
| up 50% | 14.47% | 8.45% | 4.14% | 2.05% |
| doubled | 25.99% | 14.87% | 7.18% | 3.53% |
| tripled | 44.22% | 24.57% | 11.61% | 5.65% |
| grew 5× | 71.00% | 37.97% | 17.46% | 8.38% |
Doubling in 10 years is a 7.18% CAGR; the rule of 72 estimates 7.2%.[2]
What CAGR is used for
- Investments: the annualized return of a fund, stock or portfolio between two dates, before deposits and withdrawals. With deposits, the interest rate calculator finds the rate that fits.
- Business metrics: revenue, users or costs growing over several years.
- Prices: how fast home values, tuition or inflation rose on average per year.
What CAGR hidesIt smooths the path: two investments with the same CAGR can have very different ups and downs along the way. It also assumes nothing was added or taken out. Use it to compare, not to predict.
Using CAGR to project forward
Switch to "Ending value" to grow a starting amount at a chosen rate. A past CAGR is not a forecast: investment returns vary, and a savings rate can change. For fixed-rate growth with monthly deposits, use the compound interest calculator or the future value calculator.
Related calculators
- Interest rate calculatorThe rate behind a growth figure or a loan payment
- Rule of 72 calculatorDoubling time, and how far off the shortcut is
- Future value calculatorA lump sum and a series of payments, grown forward
- DRIP calculatorDividends reinvested vs taken as cash, side by side
Frequently asked questions
How do you calculate CAGR?
Divide the ending value by the starting value, raise it to 1 ÷ years and subtract 1. $10,000 to $25,000 in 7 years: 2.51/7 − 1 = 13.99%.
What is a good CAGR?
It depends on what is growing and the risk taken. Compare a CAGR with alternatives over the same period, such as a savings rate or a broad market index.
Is CAGR the same as average annual return?
No. The arithmetic average of yearly returns is higher than CAGR whenever returns vary; CAGR is the single steady rate that produces the actual ending value.
Can CAGR be negative?
Yes. If the ending value is below the starting value, CAGR is negative: falling from $10,000 to $8,000 over 3 years is about −7.2% a year.