Case 1
- Beginning value
- 1000
- Ending value
- 1331
- Number of years
- 3
10.0%
Open with these valuesCAGR Calculator
10.0%
Result: 10.0 %CAGR is the single steady rate that would have taken the beginning value to the ending value. It is a geometric rate, not the average of yearly returns, so volatility never flatters it. Only the two endpoints and the number of years count — deposits in between are invisible to it.
Worked examples
Case 2
- Beginning value
- 10000
- Ending value
- 20000
- Number of years
- 7
10.4%
Open with these valuesCase 3
- Beginning value
- 50000
- Ending value
- 40000
- Number of years
- 5
-4.4%
Open with these valuesHow it's calculated
CAGR = (Ending ÷ Beginning)^(1 ÷ Years) − 1
- StepDivide the ending value by the beginning value to get the growth multiple.
- StepRaise that multiple to the power of one divided by the number of years.
- ResultSubtract one and multiply by 100 to read the yearly rate.
What this number means
CAGR runs the compound interest equation the other way round. Instead of a rate producing a final balance, two balances produce the rate — and that is the interesting number, because periods of different lengths cannot be compared as multiples but can be compared as annual rates. The defaults are picked so the arithmetic can be checked by hand: 1000 growing to 1331 over three years is a multiple of 1.331, and since 1.1 × 1.1 × 1.1 is exactly 1.331, the answer is 10.0 % a year. Now take 10000 to 20000 over seven years. Twice the money sounds far bigger than a third more, yet it annualises to 10.41 %, almost the same rate — which is precisely the comparison the raw multiples cannot make. What the rate does not carry is any account of how it was earned: not the risk taken, not the worst point along the way, and not inflation, so a nominal 10.4 % is not 10.4 % of purchasing power. The limitation that bites most often is a short horizon. The years field goes down to a quarter, and annualising three months raises whatever happened in them, noise included, to the fourth power. The single decimal place in the output is there for the same reason: past a tenth of a percentage point, this figure's precision would be invented rather than measured.
Only the two endpoints count
CAGR reads the beginning value, the ending value and the number of years, and nothing in between. An uneven path and a straight line to the same endpoint give exactly the same figure.
Geometric, not the average of yearly returns
Because compounding punishes volatility, CAGR is always at most the simple average, and the gap widens as returns swing. A year of plus 50 % then minus 50 % averages zero but has a CAGR of about minus 13.4 %.
It can be negative
If the ending value is below the beginning value, the growth multiple falls under one and the rate turns negative. It then shows the annualised rate of decline.
Commonly misread
CAGR is the average of the yearly returns.
It is the geometric rate that actually reconciles the start and end values. The arithmetic mean is a different number, and it is never the lower of the two.
CAGR fits an account I paid into every month.
Deposits or withdrawals during the period distort it, because only the endpoints are read. When money flows in and out, the internal rate of return is the right measure.
Reference table
| Beginning, ending, years | Multiple | CAGR |
|---|---|---|
| 1000, 1100, 1 | 1.10 | 10.0 |
| 1000, 1331, 3 | 1.33 | 10.0 |
| 1000, 2000, 10 | 2.00 | 7.2 |
| 1000, 500, 10 | 0.50 | -6.7 |
| 1000, 1000, 5 | 1.00 | 0.0 |
| 1000, 10000, 20 | 10.00 | 12.2 |
Questions
What is CAGR?
CAGR, the compound annual growth rate, is the constant yearly rate that takes a beginning value to an ending value through compounding. It turns an uneven multi-year change into one annualised figure, which makes investments of different lengths comparable. It is a geometric rate, not the simple average of yearly returns.
How do I calculate CAGR?
Divide the ending value by the beginning value, raise the result to the power of one divided by the number of years, and subtract one. For 10000 growing to 20000 over seven years that is 2 to the power of one seventh minus one, about 10.41 % a year.
Why is CAGR different from the average annual return?
The average annual return is the arithmetic mean of each year's return; CAGR is the geometric rate that actually reconciles the start and end values. Because compounding punishes volatility, CAGR is always at most the simple average, and the gap widens as returns swing. A year of plus 50 % then minus 50 % averages zero but has a CAGR of about minus 13.4 %.
Can CAGR be negative?
Yes. If the ending value is lower than the beginning value the growth multiple is below one and the rate is negative, showing the annualised rate of decline. Enter an ending value below the beginning value and the calculator returns it directly.
Does CAGR work if I added money along the way?
No. CAGR looks only at the two endpoints, so deposits or withdrawals during the period distort it. When money flows in and out, the internal rate of return is the right measure; use CAGR for a single lump sum left to grow.
Sources and last check
Information, not financial advice.