CAGR calculator
Divide 72 by a growth rate and you get roughly the years to double. At 8% it is almost exact: 72 ÷ 8 gives nine years against a true 9.006, an error of one part in a thousand. The approximation is calibrated near there and drifts in both directions. It runs 1.9% high at 4%, 0.9% high at 6%, 1.0% low at 10%, 1.9% low at 12% and 3.2% low at 15%. Outside that range it degrades quickly: 5.3% low at 20% and 7.3% low at 25%, where 72 ÷ 25 says 2.88 years and the real answer is 3.106. The exact doubling time, log 2 divided by the log of one plus the rate, is in the row above. The rule survives because it is close enough across the range people actually use and you can do it without a calculator.
CAGR is the ending value divided by the starting value, raised to one over the number of years, minus one. Ten thousand growing to eighteen thousand over six years is a CAGR of 10.29% a year, and would double every 7.08 years at that rate.
How to calculate CAGR
CAGR describes a smooth path that almost never happened. It is the constant rate that would have produced the same endpoints, and that makes it excellent for comparison and misleading as a description of the journey. An investment that fell 40% and then trebled has a healthy CAGR and was a nightmare to hold. Anyone using it to compare volatile assets should look at the drawdowns alongside it, because the same CAGR can come from wildly different experiences.
The averaging trap
Take a year of +50% followed by a year of −40%. The arithmetic mean of those two returns is +5% a year, and $100 turned into $150 and then into $90. The geometric mean, the figure this page computes, is −5.132% a year, and that is the figure that actually reproduces the endpoints. The arithmetic mean of a series of returns is always at least the geometric mean and is strictly larger whenever the returns vary at all, so any claimed "average annual return" that was reached by adding up yearly percentages and dividing is overstated. The gap widens with volatility, which means the overstatement is largest exactly where the caution is most needed.
Only two data points reach this page
A start value, an end value and a number of years. Everything between them is invisible to the calculation, including the shape of the run, the timing of any money added or withdrawn, and the currency the values were measured in. A CAGR computed across a period when money was paid in or taken out is not a return at all, it is a description of how two balances relate; use money-weighted return for that case instead.
What people use it for
- Comparing investment returns over different periods
- Reporting revenue growth in a business plan
- Working out an implied growth rate from two data points
- Checking a claimed average return
- Testing a rule-of-72 estimate against the exact doubling time
Questions
The constant annual rate that would take the starting value to the ending value over the period. $10,000 becoming $18,000 over six years is 10.292% a year.
An arithmetic average of yearly returns overstates growth when returns vary. A +50% year and a −40% year average to +5% arithmetically and to −5.132% geometrically, and only the second one turns $100 into $90.
The geometric mean, always. It is the definition: the rate that reproduces the ending value from the starting one. The arithmetic mean equals it only when every yearly return is identical.
Divide 72 by the growth rate for an approximate doubling time. It is within about 2% between 4% and 12%, essentially exact at 8%, and 7.3% low by the time the rate reaches 25%.
7.08 years at 10.292%. The rule of 72 would say 6.99, which is a little over one per cent optimistic.
Yes, when the ending value is lower than the start. The rate is reported correctly; the doubling row goes blank, because nothing doubles at a negative rate.
Because the growth rate is zero or negative and there is no finite answer. Nothing has gone wrong; the calculation is declining to invent an answer.
No. Two investments with the same CAGR can have completely different volatility. Look at the largest drawdown as well as the rate.
Not meaningfully. Contributions and withdrawals change the ending value without changing the return, so the figure would mix the two. A money-weighted return handles that case.
ROI is the total return over the whole holding, CAGR is the annual rate that produces it. Eighty per cent total growth over six years is a CAGR of 10.292%.
No. Enter a decimal for part-years; eighteen months is 1.5. The exponent handles it directly.
Only if the values you enter are. Two nominal figures give a nominal CAGR. To get a real one, restate both values in the same year’s money first.