Compound Growth and CAGR Calculator

The compound annual growth rate, or CAGR, is the steady yearly return that would turn a starting value into an ending value over a given period. It is the standard way to compare growth across investments and time periods, because it accounts for compounding. Simply dividing a total return by the number of years overstates growth, sometimes by a lot. This calculator gives the CAGR, the total return, the misleading simple average for comparison and how long it would take to double your money at that rate.

Calculator#

How it works#

CAGR = (Ending value / Starting value) ^ (1 / Years) - 1
Years to double = ln(2) / ln(1 + CAGR)

Use fractions of a year for shorter periods, such as 2.5 years. If money was added or withdrawn during the period, CAGR on account balances is distorted; use time weighted returns instead. See Measuring Returns and CAGR.

The rule of 72#

A quick mental shortcut: divide 72 by the annual percentage return to estimate the years to double. At 8%, money doubles in about 9 years; at 12%, about 6 years. The calculator gives the exact figure.

Why CAGR can mislead#

Always pair CAGR with risk measures such as volatility, Sharpe ratio and maximum drawdown. See Sharpe and Sortino Calculator and Drawdown Recovery Calculator.

CAGR versus average annual return#

If an investment gains 50% one year and loses 50% the next, its average annual return is 0%, but its CAGR is about minus 13.4%, and the investor has lost 25%. CAGR, a geometric average, reflects what actually happened to the money. See Volatility.

Using CAGR in planning#

Turn CAGR around to plan: to grow $10,000 into $50,000 in 15 years requires a CAGR of about 11.3%, which is ambitious. Seeing the required rate helps set realistic goals and recognise when promised returns are implausible. See Time Value of Money and Identifying Trading Scams.

Comparing two investments#

To compare two investments fairly, compute CAGR over exactly the same dates for both. A fund that started after a crash will show a flattering CAGR next to one that lived through it. Then look at the worst drawdown and volatility alongside each figure, so you know what each return cost in risk. A slightly lower CAGR with much smaller drawdowns is often the better choice, because it is easier to hold through bad periods without abandoning the plan.

Frequently asked questions#

What is CAGR?#

The compound annual growth rate: the constant yearly return that grows a starting value into an ending value over a set number of years.

How do I calculate CAGR?#

Divide the ending value by the starting value, raise the result to the power of one divided by the number of years, then subtract one.

Is CAGR the same as average return?#

No. Average return is an arithmetic mean that ignores compounding; CAGR is a geometric rate that reflects actual growth.

Next, see how hard it is to climb out of a loss with the Drawdown Recovery Calculator.