What this calculator answers
The compound annual growth rate, or CAGR, is the single steady yearly rate that would take a start value to an end value over a given number of years.
The first field, Calculate, chooses which of four quantities to solve for; you enter the other three:
- Growth rate (CAGR): the default, the yearly rate from a start value, an end value and a number of years.
- End value: what a start value grows to at a given rate.
- Number of years: how long a start value takes to reach an end value at a given rate.
- Start value: how much is needed at the start to reach an end value at a given rate.
Every mode also shows the total return over the whole period and the gain or loss in money.
The formula
Writing S for the start value, E for the end value, t for the number of years and r for the yearly rate:
r = (E / S)^(1 / t) − 1, E = S·(1 + r)^t, t = ln(E / S) / ln(1 + r), S = E / (1 + r)^t
The four expressions are one relation solved for each quantity in turn: the first gives the rate, the second the end value, the third the number of years and the fourth the start value. ln is the natural logarithm.
In every mode the total return is T = E / S − 1 and the gain or loss is G = E − S, shown with a plus sign for a gain and a minus sign for a loss. In the rate mode the headline is the CAGR. In the end-value, years and start-value modes the headline is the solved quantity, and the rate you entered appears in the results below it and in the steps.
Worked examples
The growth rate
Suppose a balance of $10,000 grows to $19,671.51 over 10 years. With Calculate at Growth rate (CAGR), enter a Start value of 10,000, an End value of 19,671.51 and a Number of years of 10. Divide the end value by the start value, take the tenth root and subtract one: the result is a CAGR of 7%.
The end value
Run the other way. Choose End value and enter a Start value of 10,000, a Growth rate (CAGR) of 7 and a Number of years of 10. Ten years at 7% multiply $10,000 by 1.07 ten times and reach $19,671.51, the same end value, for a gain of $9,671.51. That is how the four modes check one another: each solves the same relation for a different unknown.
The number of years
How long does $10,000 take to reach $20,000 at 7% a year? Choose Number of years and enter a Start value of 10,000, an End value of 20,000 and a Growth rate (CAGR) of 7. The calculator divides ln(2), the logarithm of the doubling needed, by ln(1.07), the logarithm of one year’s growth, and shows 10.245 years.
The start value
How much is needed today to have $20,000 in 5 years at 7% a year? Choose Start value and enter an End value of 20,000, a Number of years of 5 and a Growth rate (CAGR) of 7. The calculator divides $20,000 by 1.07 to the power of 5 and shows a Start value of $14,259.72 as the headline, with a total return of 40.26% over the 5 years.
A falling value
CAGR works for losses too. Take $10,000 that falls to $7,500 over 3 years. The calculator shows a CAGR of -9.14%, a total return of -25%, and the Gain or loss row shows -$2,500.00. The yearly loss is more than a third of the total fall, because each year’s loss is taken from a smaller balance than the year before.
CAGR in a spreadsheet
Microsoft Excel has two functions that give the same rate as this calculator. Both return a rate per period, so entering the number of years as the number of periods gives a yearly rate, the CAGR. For the calculator’s default, $10,000 growing to $20,000 in 5 years:
=RRI(5, 10000, 20000)
=RATE(5, 0, -10000, 20000)
RRI takes the number of periods, the present value and the future value, in that order (Microsoft Support, RRI function). Here it gives 0.148698…, shown as 14.87% once the cell is formatted as a percentage with two decimal places: the CAGR this calculator shows. Microsoft’s own example, =RRI(96, 10000, 11000), returns 0.0009933 per period for $10,000 growing to $11,000 over 96 periods.
RATE gives the interest rate per period of an annuity, a series of equal payments such as a loan’s (Microsoft Support, RATE function). Its first four arguments are the number of periods, the payment, the present value and the future value. With nothing paid in between, the payment is 0. The start value goes in as a negative number because it is money paid in: Microsoft’s page on the PV function says that money you pay out, a bank deposit for example, is entered as a negative number, and money you receive as a positive one. RATE then returns the same result as RRI.
CAGR versus a simple average
A simple average of yearly returns can be far from the CAGR. Business LibreTexts (Bigel, Introduction to Financial Analysis, 14.17) gives an example: a 50% loss in one year and a 100% gain the next. The simple average of the two returns is 25%, yet $100 falls to $50 and climbs back to $100, so nothing was gained. The geometric average multiplies the two growth factors, 0.5 × 2 = 1, takes the square root and subtracts one, which gives 0%. Enter a Start value of 100, an End value of 100 and a Number of years of 2, and this calculator shows the same CAGR of 0%.
That is no coincidence: over whole years, CAGR is the geometric average of the yearly growth factors, minus one. The OpenStax Business Statistics text gives the reason a plain average misleads: an arithmetic mean adds the returns up, so it leaves out the interest earned on interest. As a rule of arithmetic, whenever the yearly returns differ, the simple average comes out higher than the CAGR; the two agree only when every year’s return is the same.
What the result does not include
CAGR smooths the path. A value that fell sharply and recovered can share a CAGR with one that rose evenly, so it says nothing about the ups and downs in between.
For a period shorter than a year, the yearly rate is an extrapolation: it assumes the short-term move would repeat for the rest of the year. In the rate and years modes the calculator warns in that case, because the GIPS performance standards say returns for periods under a year must not be annualized. The end-value and start-value modes do not warn, because they apply a yearly rate you enter instead of turning a short-term return into one.
It also ignores deposits and withdrawals made during the period. If money was added or taken out along the way, the figure no longer describes the return on the original amount. For regular contributions, use the investment calculator instead.
The CAGR is measured in the same money as the two values: if they are not adjusted for inflation, neither is the CAGR. Taxes and fees count only if they have already been taken out of the end value.
FAQ
What is a good CAGR?
There is no single good figure. A CAGR means something only next to another rate over the same years, such as inflation, which shows whether the money's buying power grew; the return of a market index you could have held instead; or what a savings account paid over that time. The span matters too. A high CAGR over a year or two, or one measured from the bottom of a crash, says little about how the same investment does over a longer period.
Does CAGR describe the path an investment took?
No. CAGR smooths the path into one steady yearly rate. Two investments with the same start value, end value and number of years have the same CAGR however bumpy each journey was.
Does CAGR account for money added or withdrawn along the way?
No. It compares one start value with one end value. If you made deposits or withdrawals in between, use the investment calculator, which handles regular contributions.
Why does the number-of-years mode refuse some inputs?
That mode divides by the logarithm of one plus the rate, so the rate cannot be 0%, the end value must be above 0 and different from the start, and the rate must point the same way as the move from start to end. It also refuses inputs that would need more than 1,000 years.
Can I use CAGR for a period shorter than a year?
The calculator will compute it, and in the rate and years modes it shows a warning when the period is under a year. A return over a few months is turned into a yearly rate by assuming it repeats, which can produce very large figures. The CFA Institute's performance standards (GIPS) say returns for periods under a year must not be annualized.