Enter a starting value, an ending value and the number of years between them to get the compound annual growth rate. The second section shows how long any growth rate takes to double your money.
| Year | Value | Gain that year |
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CAGR is the steady yearly rate that would take the starting value to the ending value over the same period: CAGR = (end ÷ start)1 ÷ years − 1. Growing 10,000 to 18,000 over 5 years is a CAGR of 12.47% a year, even if the real path went up and down along the way.
CAGR is better than a simple average for comparing investments, revenue or populations over different periods, because it accounts for compounding. A +50% year followed by a −50% year averages 0% but actually loses 25%; CAGR shows that as −13.4% a year.
The exact time to double at rate r is ln 2 ÷ ln(1 + r). The Rule of 72 is a mental shortcut: 72 ÷ the rate in percent. At 8%, the exact answer is 9.01 years and the Rule of 72 gives 9. The shortcut is most accurate between about 6% and 10%.
Compound annual growth rate: the constant yearly growth rate that would turn the starting value into the ending value over the period, assuming gains are reinvested. It smooths out year-to-year volatility into one comparable figure.
CAGR = (ending value ÷ starting value)^(1 ÷ number of years) − 1. For 10,000 growing to 18,000 in 5 years: 1.8^0.2 − 1 = 0.1247, or 12.47% a year.
A quick way to estimate doubling time: divide 72 by the annual percentage rate. At 6%, money doubles in about 12 years. It works because ln 2 ≈ 0.693 and 72 has many easy divisors.
The average (arithmetic mean) of yearly returns ignores compounding and overstates growth when returns vary. CAGR is the geometric mean, so it matches what actually happened to the money.
Yes. If the ending value is below the starting value, CAGR is negative and shows the average yearly decline. Doubling time doesn’t apply in that case.
