One annual rate between two endpoints
Find the compound annual growth rate that connects a starting value to an ending value. Enter years or months, then compare the annual rate with the total change over the whole period.
Compound annual growth rate
Enter starting and ending values and a duration, then select Calculate.
≈ marks numerical approximation or display rounding. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
[(1,728 ÷ 1,000)1/3 − 1] × 100 = 20%
Growing by 20% each year gives 1,000 → 1,200 → 1,440 → 1,728. The total increase is 72.8%. The calculator marks the computed root with ≈ even when this example has an exact mathematical answer.
[(200 ÷ 800)1/2 − 1] × 100 = −50%
The equivalent annual rate is −50%: halving 800 gives 400, then halving again gives 200. Total change is −75%, not −100%.
[(110 ÷ 100)1/0.5 − 1] × 100 = 21%
The observed change is 10% over half a year. Annualizing that compound rate gives 21%; it does not establish that a full year actually achieved or will achieve that result.
CAGR (%) = [(ending value ÷ starting value)1 / years − 1] × 100
The growth multiple is ending value divided by starting value. Its power of 1 ÷ years is the equivalent annual growth factor. Subtract 1 and multiply by 100 to express that factor as an annual percentage. Total percentage change is (growth multiple − 1) × 100 and applies to the entire entered period.
This is a geometric rate, which accounts for compounding. Dividing the total percentage change by the number of years gives a different arithmetic measure. CAGR summarizes endpoints; it cannot reveal volatility, the order of yearly changes, or the largest loss within the period.
Use this calculator for comparable values and no intervening cash flows. Additional deposits or withdrawals can change the ending balance without representing growth. This tool does not calculate a money-weighted return, IRR, XIRR, or a cash-flow-adjusted portfolio return. It does not add dividends, deduct fees or taxes, adjust inflation, convert currencies, or predict future performance.
The starting value must be positive and the ending value nonnegative. Equal endpoints give exactly 0%. For an ending value of zero, the endpoint formula gives −100% for any allowed duration; this is the calculator's complete-loss convention, not a reconstruction of the path to zero. A zero start would require division by zero, and negative endpoints can make fractional powers non-real, so those cases are not supported.
Duration can be fractional and must equal at least 1 month and no more than 1,000 years. Months are divided by 12; this is a duration conversion, not a calendar day-count convention. Inputs accept up to 64 characters, 15 integer digits, and 10 decimal places. For exactly one month, choose Months and enter 1.
Input ratios, total change, and duration conversions are held as exact fractions. The power calculation uses 80 significant digits in an isolated decimal context; this is numerical approximation, not an exact symbolic root. CAGR and annual factors are marked ≈ except for the equal-value and zero-ending cases. Auxiliary results get ≈ only when display rounding changes their exact value.
Display values use the selected maximum decimal places, remove trailing zeros, and round halfway values away from zero. Changing display precision does not recalculate from a rounded result or create a new history entry. Extremely small nonzero growth can display as ≈ 0%; small multiples and annual growth factors can also round to ≈ 0×. A notice identifies these cases. Very large annualized rates can occur when a large increase is measured over a short period.
Reference: FINRA — How Are Your Investments Doing? Returns, Explained explains annualizing compounded returns and why a simple average of total growth over years differs. This calculator applies the endpoint growth formula under the scope described above.
CAGR is a constant compound annual rate connecting the endpoints. An arithmetic average of individual annual rates can differ. For example, a 50% increase followed by a 50% decrease leaves 75% of the starting value; the arithmetic average is 0%, but CAGR is negative.
Yes. Eighteen months and 1.5 years use the same duration. The minimum is one month. For periods below a year, the result is an annualized equivalent, not an observed full-year change.
Total growth describes the entire period. CAGR describes an equivalent one-year compounding rate. In the example, 20% compounded for 3 years gives 72.8% total growth because each year's growth applies to the updated value.
Yes. With a positive start and a smaller positive end, CAGR falls between −100% and 0%. An ending value of zero uses the −100% complete-loss convention. Negative starting or ending values are not supported.
No. Deposits, withdrawals, and their timing need additional information and a suitable cash-flow-aware method. Entering only the initial and final balances can mistake new money for growth. This tool does not calculate IRR or XIRR.