Calculation desk / interest & growth
CAGR Calculator
Calculate the constant annualized growth rate between a beginning and ending value.
CAGR Calculator: Find the constant annual growth rate that would turn a beginning value into an ending value over a stated number of years. CAGR summarises the two endpoints as one compounded rate, even when the actual path was uneven. Use it for a value series with comparable endpoints and no intervening cash flows. Runs 100% locally in your browser with zero server file uploads.
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CAGR
8.45%
- Growth multiple
- 1.5
CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1- This is an educational/planning estimate only, not personalized financial advice.
- Actual products, taxes, fees, contribution dates, and returns differ; confirm terms with the relevant provider.
- Inputs follow common calculator conventions such as initial amount, recurring contribution, time, estimated annual rate, and compounding frequency described by Investor.gov: https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
- CAGR describes a smoothed annualized rate; it does not imply that returns were steady each year or include cash-flow timing.
Formula and worked example
CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1
A worked example with sample values:
| Inputs | |
|---|---|
| Beginning value | $10,000.00 |
| Ending value | $15,000.00 |
| Time | 5 years |
| Results | |
|---|---|
| CAGR | 8.45% |
| Growth multiple | 1.5 |
Annualising the endpoint ratio
Let B be beginning value, E ending value and t elapsed years. Growth multiple = E ÷ B. CAGR as a decimal = (E ÷ B)^(1 ÷ t) − 1; multiply by 100 for a percentage. B and E must use the same currency or measurement unit, and t must represent the actual interval between them.
Starting at $10,000 and ending at $15,000 over 5 years gives a multiple of 1.5. CAGR = (1.5^(1 ÷ 5) − 1) × 100 = 8.447177%, displayed as 8.45%. Substituting the unrounded rate into $10,000 × (1 + 0.0844717712)^5 recovers $15,000. It does not mean each year actually earned 8.45%.
Compounded growth and purchasing power
OpenStax's compound-interest chapter (https://openstax.org/books/contemporary-mathematics/pages/6-4-compound-interest) explains repeated growth factors. CAGR reverses that relationship to solve for an annual factor. For a quick doubling-time estimate at a positive constant rate, compare the rule of 72; it is approximate and cannot forecast market returns.
A nominal dollar CAGR does not remove inflation. The Bureau of Labor Statistics explains constant-dollar comparisons (https://www.bls.gov/cpi/factsheets/purchasing-power-constant-dollars.htm). Adjust the endpoints to a common price basis before calculating a real growth rate. Equivalently, with nominal annual growth g and annualised inflation j as decimals, real annual growth = (1 + g) ÷ (1 + j) − 1. A deposit APY includes within-year compounding, while a loan APR measures credit cost; neither should be substituted for an observed endpoint return.
How to use it
- Enter the amounts, rate and duration shown in the worked example or your own scenario.
- Calculate to update the result and review the assumptions.
- Compare the formula and example before using the result for planning.
Privacy & limitations
Inputs and calculations stay in your browser. No values are uploaded.
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Frequently asked questions
Why is CAGR different from the average of yearly returns?
CAGR uses a geometric growth factor. A 50% gain followed by a 50% loss leaves 75% of the starting value, despite an arithmetic average return of zero. The endpoint calculation captures that overall change without describing the year-by-year volatility.
Can I calculate investment CAGR after adding deposits?
Not as an investment return from endpoints alone. Added money raises the ending value without necessarily reflecting growth. For dated contributions and withdrawals, use a cash-flow return calculation such as XIRR; CAGR cannot separate contributions from performance.
What happens if the ending value is lower or zero?
A positive ending value below the positive beginning value produces a negative CAGR. This calculator requires both endpoints to be greater than zero and the duration to be positive. A zero or negative endpoint is outside its supported comparison, rather than a usable input for every fractional root.
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