How it works
The formula is CAGR = (ending value / starting value)1 / years − 1. It answers one question: at what constant annual rate would the starting value have grown into the ending value? The total return is ending value / starting value − 1. The doubling time uses the rule of 72, which divides 72 by the CAGR in percent. It is a quick estimate that works well for moderate rates and becomes noticeably less accurate at very high ones; the exact value is ln(2) / ln(1 + CAGR). The chart compares the compounded path with a straight line between the two values. Worked example with the default values: 10,000 growing to 25,000 in 8 years is a total return of +150% and a CAGR of about 12.14% per year; the rule of 72 gives a doubling time of about 5.93 years (exact: about 6.05).
Keep the limits in mind. CAGR only looks at the first and the last value, so it says nothing about fluctuations or drawdowns in between: two investments with the same CAGR can have taken very different paths. It also assumes that no money was added or withdrawn during the period; if it was, a money-weighted or time-weighted return is the better measure. A past CAGR describes what happened and is not an estimate of future returns.