CAGR calculator: compound annual growth rate, ending value and years needed
CAGR is the steady yearly rate that would take a beginning value to an ending value: (ending ÷ beginning)^(1 ÷ years) − 1. Enter the two values and the years or the two dates, or switch the calculator to find the ending value for a rate you enter, or the years it takes. It describes growth between two numbers; it is not a forecast, and it ignores taxes and fees. To compare it with the effect of regular deposits, see the dollar cost averaging calculator.
CAGR calculator
Compound annual growth rate:
7.18%
Total change: 100.00% over 10.00 years.
Assumptions
- CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1: a steady yearly rate between two values, not the path in between.
- With two dates, years = actual days ÷ 365.25. The beginning value must be above zero.
- The reverse modes assume the rate you enter holds every year; they are estimates, not forecasts. No taxes, fees or inflation are applied.
Worked examples
These results come from the same code as the calculator. They are FedRateCalc arithmetic, not examples printed by the SEC or Investor.gov.
| Case | Years used | CAGR |
|---|---|---|
| $10,000 grows to $20,000 over 10 years | 10.00 | 7.18% |
| $100 falls to $81 over 2 years | 2.00 | -10.00% |
| +100% in one year, then −50% the next: $100 → $200 → $100 over 2 years | 2.00 | 0.00% |
| $100 to $200 from 2024-01-01 to 2025-01-01 (366 days ÷ 365.25) | 1.0021 | 99.72% |
The third case shows why CAGR and an average of yearly returns differ: a simple (arithmetic) average of the yearly returns of +100% and −50% is +25%, yet the value ends where it began, so the CAGR is 0.00%. For a savings account, the high-yield savings calculator and the I bond calculator start from a stated rate instead of solving for one.
CAGR and the annual return the SEC describes
Investor.gov, the SEC's investor education site, defines an annual return in its glossary:
“An annual rate of return is the profit or loss on an investment over a one-year period. There are many ways of calculating the annual rate of return. If the rate of return is calculated on a monthly basis, multiplying it by 12 expresses an annual rate of return. This is often called the annual percentage rate (A.P.R.).”
The SEC's Rate of Return Definition page says:
“The annual rate of return is the percentage change in the value of an investment.”
Investor.gov defines compound interest:
“Interest paid on principal and on accumulated interest.”
For funds other than money market funds, prospectus performance is set by another SEC document, Form N-1A. Its Item 26(b)(1), read from an Internet Archive capture, says that a fund's “average annual total return” is a compound rate, not a simple average of yearly returns:
“For the 1-, 5-, and 10-year periods ended on the date of the most recent balance sheet included in the registration statement (or for the periods the Fund has been in operation), calculate the Fund’s average annual total return by finding the average annual compounded rates of return over the 1-, 5-, and 10-year periods (or for the periods of the Fund’s operations) that would equate the initial amount invested to the ending redeemable value, according to the following formula:
- P(1+T)n = ERV
- Where:
- P= a hypothetical initial payment of $1,000.
- T= average annual total return.
- n= number of years.
- ERV = ending redeemable value of a hypothetical $1,000 payment made at the beginning of the 1-, 5-, or 10-year periods at the end of the 1-, 5-, or 10-year periods (or fractional portion).
”
In that formula n is the number of years (it is an exponent in the form). The form may have been revised since the capture.
When we checked on November 6, 2026, we did not find an SEC or Investor.gov page that defines “CAGR” or “compound annual growth rate” by name, so the formula above is stated as FedRateCalc's arithmetic and not attributed to the SEC. Because there are many ways of calculating an annual rate of return, a figure from a fund, broker or report may use a different method than this calculator.
What the calculator assumes
- The beginning value must be greater than zero, and the ending value cannot be negative. A fall in value gives a negative CAGR, and an ending value of zero gives −100%.
- With two dates, the years are the actual days between them divided by 365.25. A period from 2024-01-01 to 2025-01-01 is 366 days, or 1.00205 years.
- The ending value and years-needed modes assume the rate holds every year; they are estimates if that assumption holds. A rate of −100% or lower and a rate of zero (for years needed) are rejected, and results too large to show are reported as an error, not as Infinity.
- Periods are limited to 1,000 years. Taxes, fees, inflation, deposits and withdrawals are not included.
Frequently asked questions
What is CAGR and how is it calculated?
CAGR is the constant yearly rate that takes a beginning value to an ending value: (ending value ÷ beginning value)^(1 ÷ years) − 1. For example, $10,000 growing to $20,000 in 10 years is 7.18% a year. The formula is FedRateCalc arithmetic; Investor.gov (SEC) describes an annual rate of return as the profit or loss on an investment over a one-year period and says there are many ways of calculating it.
How is CAGR different from an average annual return?
A simple (arithmetic) average of yearly returns adds the percentages and divides by the number of years, while CAGR compounds them. If a value rises 100% in one year and falls 50% in the next, the yearly figures average 25%, but $100 becomes $200 and then $100 again, so the CAGR is 0%. This comparison is FedRateCalc arithmetic. Investor.gov (SEC) notes that there are many ways of calculating an annual rate of return, and the SEC's Form N-1A (Item 26(b)(1), Internet Archive capture of September 22, 2023) has a fund calculate its "average annual total return" by finding "the average annual compounded rates of return", which is a compound (geometric) rate rather than a simple average.
How does the calculator count years between two dates?
FedRateCalc counts the actual days between the two dates and divides by 365.25, so 2024-01-01 to 2025-01-01 is 366 days, or 1.00205 years. The end date must be after the start date. This is a convention of the calculator, not a rule from the SEC or Investor.gov; other tools may count years by months or by 365 days and give slightly different rates.
What happens if the beginning value is zero, negative or a loss?
A beginning value of zero or less is rejected, because the formula divides by it. A fall in value gives a negative CAGR: $100 becoming $81 in 2 years is −10% a year, and an ending value of zero is −100%. These are FedRateCalc calculator rules based on the formula; they are not SEC or Investor.gov guidance.
Does a CAGR predict future growth?
No. CAGR only describes the steady rate between two values. The SEC's Rate of Return Definition page uses a rate as an assumption: "If you assume you earn a 10% annual rate of return, then you are assuming that the value of your investment will increase by 10% every year." The reverse modes on FedRateCalc work the same way, from a rate you enter, and the results are estimates if that assumption holds, not forecasts.
How are the ending value and the years needed worked out?
The ending value is the beginning value × (1 + CAGR)^years. The years needed are ln(ending value ÷ beginning value) ÷ ln(1 + CAGR), which needs a growth rate greater than −100% and not zero. Both formulas are FedRateCalc arithmetic; Investor.gov (SEC) defines compound interest as interest paid on principal and on accumulated interest.
Related calculators and guides
Sources
Pages were read on November 6, 2026. The Investor.gov and SEC pages and the SEC form were read from Internet Archive captures taken on the dates shown, because those sites refused plain requests.
- Investor.gov (SEC): Annual Return, Internet Archive capture of August 11, 2026
- SEC: Form N-1A, Item 26(b)(1), Internet Archive capture of September 22, 2023
- Investor.gov (SEC): Compound Interest, Internet Archive capture of October 11, 2026
- SEC: Rate of Return Definition, Internet Archive capture of October 9, 2025
Reviewed November 6, 2026. FedRateCalc is not affiliated with the IRS, the SEC or FINRA; their sites are the official sources, and any later change they publish overrides this site. Results are estimates from the numbers you enter, not financial or tax advice.