Guide
CAGR explained: one steady growth rate between a start and an end value
Suppose a fund was worth 1,00,000 ten years ago and is worth 3,10,585 today. What was its yearly return? Returns in real life jump about: up 25 percent one year, down 8 the next. The compound annual growth rate, CAGR, answers the question with a single number: the steady yearly rate that would have turned the first value into the last in the same time. It lets you compare an investment with a deposit, a business with its competitor, or one decade with another.
The formula
CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1. The root undoes the compounding, so the result is the rate that, applied each year to the running total, reproduces the end value. The same relationship can be turned around: ending value = starting value × (1 + CAGR)^years, starting value = ending value ÷ (1 + CAGR)^years, and years = ln(ending ÷ starting) ÷ ln(1 + CAGR). The page offers all four through its Find menu.
A worked example
The default is 1,00,000 growing to 3,10,585 in 10 years. The CAGR is 12.0000%, total growth is 210.59% and the growth multiple is 3.106 times. At that rate the money doubles in 6.12 years, and the last year’s gain alone is 33,276.98. A second example is a business whose revenue rose from 24,00,000 to 51,00,000 in four years: the CAGR is 20.7368% and revenue would double in 3.68 years. Setting the mode to Ending value with 12% for ten years gives 3,10,584.82, which confirms the first result.
Why not simply average the returns?
Take a fund that gains 50 percent one year and loses 50 percent the next. The average return is zero, yet 100 becomes 150 and then 75, a loss of 25 percent. CAGR gives the true figure, about −13.4 percent a year. The arithmetic mean overstates the growth whenever returns vary, and the bigger the swings the bigger the error. For that reason published fund factsheets quote annualised returns rather than averages.
Choosing the period
Years may be fractional: 18 months is 1.5 and 30 months is 2.5. Use the exact time between the two values, because the CAGR changes with it. A start date just before a crash or just after one can swing the result by several points, so quote the period beside the number, and when comparing two assets use the same dates for both.
Edge cases
If the ending value is lower than the starting value, the CAGR is negative and the table shows the value shrinking year by year. A starting or ending value of zero cannot be used, because the ratio is undefined. When you solve for years with a growth rate of zero, there is no answer, since the value never changes; the page says so. If the target lies on the wrong side of the starting value, for example a higher end value with a negative rate, it explains that too.
Limits
CAGR describes the past or a target, not the future. It hides the volatility and the sequence of returns, and it does not account for deposits, withdrawals, fees or tax. For several dated cash flows use the XIRR calculator, and for a plan with regular deposits use the SIP calculator.
Related tools
- XIRR Calculator finds the yearly return when money moved in and out on different dates.
- Rule of 72 Calculator gives a quick mental estimate of the same doubling time.
- ROI Calculator reports the gain as a percentage without annualising it.
- Compound Interest Calculator projects forward from a rate rather than backwards from two values.
Checked against the current version of the CAGR Calculator on .