CAGR Calculator
With starting value 10000 USD, ending value 18000 USD, years 5, cagr comes to 12.47 % — cagr. It is reached in 6 steps, the last of which is (pow(1.8, 1 / 5) - 1) * 100, and each one is printed on the page with its numbers filled in. The formula is the one published by CFA Institute, not an approximation fitted to it.
Compound annual growth rate from a start, an end and a span — the one rate that would have produced the same result, beside the average that would not.
Formula and sources checked · How we check
Starting value 10000, Ending value 18000, Years 5
12.47 %
CAGR for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Total multiple
18000 / 100001.8- Compound annual growth rate
(pow(1.8, 1 / 5) - 1) * 10012.475 %- Total growth over the period
(1.8 - 1) * 10080 %- Total growth divided by the years
80 / 516 %- Years to double at this rate
log(2) / log(1 + 12.474611 / 100)5.896 yr- What the starting value becomes in ten years at this rate
10000 * pow(1 + 12.474611 / 100, 10)32,400 USD
Worked example
$10,000 growing to $18,000 in five years is 12.47% a year compounded, not the 16% a naive average gives. The gap widens with the rate: at 400% total growth the two answers differ by more than a factor of two.
How to work it out yourself
- 1.Enter the value at the start and the value at the end, with nothing added or withdrawn in between. CAGR describes a single lump left alone; contributions need a money-weighted return instead.
- 2.Use the exact span in years. Fractional years work — 18 months is 1.5 — and using 2 instead understates the rate.
- 3.Compare it to the naive average line. The two agree only for very small rates, and CAGR is always the smaller of the two.
- 4.CAGR hides everything that happened in between. Two investments with the same CAGR can differ completely in how rough the ride was, which is what standard deviation is for.
CAGR from $10,000, five years, ending value varied
| Ending value (USD) | CAGR | Total growth over the period | Total growth divided by the years |
|---|---|---|---|
| 8000 | -4.36 % | -20 % | -4 % |
| 10000 | 0.00 % | 0 % | 0 % |
| 12000 | 3.71 % | 20 % | 4 % |
| 14000 | 6.96 % | 40 % | 8 % |
| 16000 | 9.86 % | 60 % | 12 % |
| 18000 | 12.47 % | 80 % | 16 % |
| 20000 | 14.87 % | 100 % | 20 % |
| 25000 | 20.11 % | 150 % | 30 % |
| 30000 | 24.57 % | 200 % | 40 % |
| 40000 | 31.95 % | 300 % | 60 % |
| 50000 | 37.97 % | 400 % | 80 % |
The last two columns are why CAGR exists. Growing $10,000 to $50,000 is 400% total, which divided by five years reads as 80% a year — but 80% compounded for five years reaches $188,957, not $50,000. The true rate is 38%.
The formula
- Total multiple
18000 / 10000 - Compound annual growth rate
(pow(1.8, 1 / 5) - 1) * 100 - Total growth over the period
(1.8 - 1) * 100 - Total growth divided by the years
80 / 5 - Years to double at this rate
log(2) / log(1 + 12.474611 / 100) - What the starting value becomes in ten years at this rate
10000 * pow(1 + 12.474611 / 100, 10)
Source: CFA Institute — time-weighted and money-weighted return measurement, SEC Investor.gov — compound interest and rate of return, CFA Institute — professional learning on return measurement and annualisation
Questions people actually ask
- What is CAGR?
- The single annual rate that would take the starting value to the ending value if it compounded evenly. It is a description, not a prediction: nothing has to have actually grown at that rate in any individual year.
- What is the CAGR formula?
- (ending ÷ starting)^(1 ÷ years) − 1. For $10,000 to $18,000 over five years: 1.8^0.2 − 1 = 0.1247, so 12.47%.
- Why not just divide the total growth by the years?
- Because growth compounds. 80% total over five years is not 16% a year — 16% compounded for five years reaches 210% of the start, not 180%. The simple average always overstates, and it overstates more the larger the growth.
- Is a good CAGR 10%?
- For equities that is roughly the long-run US market average before inflation — the S&P 500 has run near 10% nominal and about 7% real over long periods. For a business, growth rates are judged against the sector; for a savings account 10% would be extraordinary.
- Can CAGR be negative?
- Yes, whenever the ending value is lower than the starting one. $10,000 falling to $8,000 over five years is −4.36% a year. The formula needs both values positive; it says nothing useful about a position that went to zero.
- What does CAGR not tell me?
- Volatility, drawdowns, and the effect of anything paid in or taken out. Two funds with identical CAGRs can have wildly different worst years, and a CAGR computed on an account you contributed to is not a return at all — it is a mixture of your deposits and the growth.
Related
- Compound Interest CalculatorFuture value of a starting balance plus monthly contributions, separating what you put in from what the interest earned.
- Doubling TimeHow long a quantity growing at a fixed rate takes to double, with the Rule of 72 shortcut beside the exact figure and the error between them.
- APY CalculatorAnnual percentage yield from a rate and its compounding frequency, and what it earns on a balance in dollars.
- Savings Goal CalculatorThe monthly contribution needed to reach a target by a date, given what you have saved already.
- ROI CalculatorReturn on investment as a total percentage and as an annualised rate, so holdings of different lengths compare fairly.
- Interest CalculatorWhat a balance grows to under simple and compound interest, with the gap between the two shown as its own figure.
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