Math for MoneyWhat CAGR tells you
Growth over several years is hard to compare when the periods differ. Going from $10,000 to $20,000 is a total return of 100.00% whether it takes 5 years or 10 years, but the speed is very different: 14.87% a year in the first case and 7.18% a year in the second. CAGR puts results like these on the same footing by converting any start value, end value and time span into a per-year rate.
It works for anything measured at two points in time: an investment balance, a share price, a company's revenue, the price of a home, a salary. The dollar sign in the calculator is only a label. Any unit works as long as both values use the same one.
The CAGR formula
CAGR = (Ending value ÷ Starting value)1 ÷ years − 1
Using the example above ($10,000 to $20,000 in 5 years):
- Divide the ending value by the starting value: 20,000 ÷ 10,000 = 2.00. This is the growth multiple.
- Raise it to the power of 1 ÷ years: 2.001/5 = 2.000.2 = 1.1487.
- Subtract 1: 1.1487 − 1 = 0.1487, or 14.87%.
You can check the answer by running it forward: 10,000 × 1.14875 = $20,000. That forward calculation is ordinary compound interest, so entering the CAGR as the rate in the compound interest calculator, with annual compounding and no monthly contribution, reproduces the ending value.
The other figures in the result are simpler. Total return is the ending value divided by the starting value, minus 1 (+100.00% here). The gain or loss is the ending value minus the starting value (+$10,000). The multiple is the ending value divided by the starting value (2.00×).
CAGR versus average annual return
The two are easy to confuse and can be far apart. Take a hypothetical investment of $10,000 with three uneven years:
| Year | Return that year | Value at year end |
|---|---|---|
| 1 | +40% | $14,000 |
| 2 | −30% | $9,800 |
| 3 | +20% | $11,760 |
- Average annual return: (40 − 30 + 20) ÷ 3 = 10.00%.
- CAGR: (11,760 ÷ 10,000)1/3 − 1 = 5.55%.
If the investment had really grown 10.00% every year it would be worth $13,310, not $11,760. The average overstates the result because a loss shrinks the base that the next gain is earned on: after a 30% drop, a 30% rise does not get you back to where you were. CAGR is the figure that matches what actually happened to the money. The two are equal only when the return is the same every year.
The limits of CAGR
- It hides volatility. CAGR describes a smooth path that did not happen. The investment in the table above and one that rose a steady 5.55% every year have the same CAGR, but one of them fell 30% in a single year. CAGR says nothing about how rough the ride was or how much risk was taken.
- It ignores money added or taken out. Only the two end points count. If you deposited more along the way, the ending value is higher because of your deposits, and CAGR will overstate the growth. Withdrawals make it understate. For accounts with cash flows, use a money-weighted return (IRR) or a time-weighted return instead.
- It depends heavily on the start and end dates. Starting the measurement just after a slump or ending it at a peak produces a flattering rate. Moving either date by a year can change the answer a lot.
- It is a record of the past, not a forecast. A rate that was achieved over one period is not a rate you can count on for the next.
- Short periods are extrapolated. For a period under one year, CAGR scales the change up to a full year. A 10.00% gain in six months becomes 21.00%, which may have little to do with what a full year would bring.
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Frequently asked questions
What is the difference between CAGR and average annual return?
The average annual return adds up each year's return and divides by the number of years. CAGR is the single rate that, compounded every year, takes you from the starting value to the ending value. The average ignores the fact that a loss shrinks the base the next gain is earned on, so it is higher than the CAGR whenever returns vary. For example, returns of +40%, −30%, +20% average 10.00% a year, but $10,000 would end at $11,760, which is a CAGR of 5.55%.
Can CAGR be negative?
Yes. If the ending value is lower than the starting value, the CAGR is negative and shows the yearly rate of decline. For example, $10,000 falling to $8,000 over 3 years is a CAGR of −7.17%. An ending value of zero gives −100%.
How do I calculate CAGR for a period in months or days?
Convert the period to years first: divide months by 12, or days by 365. Eighteen months is 1.5 years. Be careful with periods shorter than a year, because CAGR then projects a short-term change over a full year. A 10.00% rise in six months annualizes to 21.00%, which says nothing about whether the second half of the year will look like the first.
Does CAGR work if I added or withdrew money along the way?
No. CAGR only looks at the starting and ending values, so any deposit is counted as if it were investment growth and any withdrawal as if it were a loss. For an account with contributions or withdrawals, use a money-weighted return (the internal rate of return, XIRR in a spreadsheet) or a time-weighted return, which many brokers and funds report.
How do I calculate CAGR in Excel or Google Sheets?
With the starting value in A1, the ending value in B1 and the number of years in C1, enter =(B1/A1)^(1/C1)-1 and format the cell as a percentage. Both programs also have a built-in function that gives the same result: =RRI(C1, A1, B1).
What is a good CAGR?
There is no universal benchmark. A growth rate only means something next to an alternative measured over the same period, such as a broad market index or a savings rate, and next to the risk that was taken to earn it. A high CAGR over a short or unusually favorable period is also much weaker evidence than a moderate one sustained over many years.