CAGR calculator
A compound annual growth rate is the single yearly rate that would have taken a figure from where it started to where it finished. It is two numbers and a duration, and every year in between can be anywhere at all without moving it.
The formula
CAGR = (ending value / beginning value) ^ (1 / years) - 1
Divide the end by the start to get the total multiple, take the year-th root of it to find the rate that repeated that many times produces the same multiple, and subtract one to turn a multiplier into a rate. The result is a percentage. Run backwards, the same relationship gives the ending value from a rate: beginning value times one plus the rate, to the power of the years.
Illustrative inputs The calculator loads with a figure that doubles over five years, and with a series underneath it that reaches the same place by a very uneven route. Both are invented round numbers picked so the arithmetic can be checked by hand, and neither is any company's filed accounts. Replace them with the two figures you are actually comparing.
Beginning value, ending value, years
Revenue, earnings, free cash flow, dividends per share or a portfolio balance at the start of the period. It has to be above zero: a rate compounded out of a loss has no meaning.
The same line, the same units, at the end of the period. Mixing a restated figure with an unrestated one is the most common way this arithmetic goes wrong before the arithmetic starts.
The number of periods, not the number of figures. Five annual reports cover four years of growth, and counting the reports instead of the gaps is the second most common error here.
| Step | Value |
|---|---|
| Ending over beginning | 2.00 |
| Total change over the whole period | 100.00% |
| That multiple, taken to the power of one over the years | 1.15 |
| Compound annual growth rate | 14.87% |
| Year | Value if every year grew at the rate |
|---|---|
| Start | 100 |
| Year 1 | 114.87 |
| Year 2 | 131.95 |
| Year 3 | 151.57 |
| Year 4 | 174.11 |
| Year 5 | 200 |
The same arithmetic, run forwards
The rate above is a question about the past. Put a rate in and you get the other question: what a figure becomes if it compounds at that rate for that long. The answer is not a forecast, and the page will not call it one. It is what the assumption you typed implies, which is a different and more honest thing.
Beginning value, rate, years
Where the figure stands today. A negative starting value is allowed here, because compounding a loss at a rate is arithmetic even when it is not a growth rate.
A rate you are assuming, not one anybody has measured. Enter a negative number for a decline. Minus one hundred percent or lower ends the series in the first year and is refused.
How long the assumption is held for. The further out this goes the more of the answer is the assumption and the less of it is the starting figure.
| Step | Value |
|---|---|
| One plus the rate, to the power of the years | 2.01 |
| End of year 1 | 115 |
| End of year 2 | 132.25 |
| End of year 3 | 152.09 |
| End of year 4 | 174.9 |
| End of year 5 | 201.14 |
| Total change over the period | 101.14% |
| Ending value | 201.14 |
What the rate is hiding
A compound annual growth rate is a straight line drawn through two points. Every point between them can be anywhere at all and the rate does not move. Type the series in and this measures the distance between the line and what actually happened: how many years came in under the headline rate, which single year did the most work, and what the rate would have been without it.
The series, one value per period
Separate them with commas or spaces. Start with the beginning value and finish with the ending one, so six numbers describe five years of growth. Anything that is not a number is left out and counted, never read as zero.
| Period | From | To | Change |
|---|---|---|---|
| Year 1 | 100 | 104 | 4.00% |
| Year 2 | 104 | 108 | 3.85% |
| Year 3 | 108 | 190 | 75.93% |
| Year 4 | 190 | 195 | 2.63% |
| Year 5 | 195 | 200 | 2.56% |
| Measure | Value |
|---|---|
| The compound rate the two ends of this series imply | 14.87% |
| Periods measured | 5 |
| Periods that grew more slowly than that rate | 4 |
| The single largest year | Year 3, 75.93% |
| The rate with the single best year taken out | 3.26% |
A rate of 14.87% that four years out of five never reached
The example above doubles from 100 to 200 over 5 years, which is a compound annual growth rate of 14.87%. The series underneath it ends in exactly the same place, so it produces exactly the same rate. It went 100, 104, 108, 190, 195, 200.
4 of the 5 years grew more slowly than the headline rate. Year 3 on its own grew 75.93%. Take that single year out and hold the value flat across it, and the remaining four years compound at 3.26%. The headline rate is not a description of this business growing steadily. It is one event, spread evenly across five years by the arithmetic.
This is not a criticism of the measure. Smoothing is what it is for, and comparing two companies over one window needs a single number. It is a warning about reading one out of a table without the series next to it, because the rate is identical whether the growth was steady, front-loaded, back-loaded, or one acquisition.
Two of the three inputs are yours
The beginning and ending values are lines in a statement. The period is not: it is the window you chose, and choosing it is most of the work. A rate measured from the bottom of a cycle and one measured from the top are different numbers about the same company, and neither is wrong.
| Input | Where it comes from |
|---|---|
| Beginning value | Whichever line you are measuring, from the annual report covering the start of the window. Use the figure as restated in a later report where one exists: acquisitions, disposals and accounting changes all move prior-year comparatives, and a restated start against an unrestated end measures the restatement as well as the growth. |
| Ending value | The same line, from the most recent annual report. Same units, same currency and the same definition of the line. Revenue that changed from gross to net recognition partway through the window is two different measures with one name, and the rate between them means nothing. |
| Years | The number of intervals, not the number of figures. Six annual reports span five years of growth. Counting the reports gives a rate that is too low by roughly a fifth at this length, and it is the most common error in this arithmetic. |
What this page will not compute
A rate out of a beginning value of zero or below. A company whose earnings went from a loss of 50 to a profit of 100 did not grow at any percentage: there is no rate that compounds a negative number into a positive one, and the arithmetic that appears to produce one is reading the minus sign as part of the magnitude. The product stores n/a for these rather than a number, and so does this page, with the reason printed where the figure would have been. Zero would be worse than n/a, because zero sorts.
It will also not choose your window, and it will not call the second panel a forecast. Compounding a rate forward tells you what the assumption you typed implies, which is a true statement about your assumption and not a claim about the company. Every number in that panel is downstream of a rate you supplied, and the page keeps it that way so nobody has to guess whose estimate it is.
Doing this over ten years of filings
Typing two numbers in is fine for one company. Inside the product the same rates are computed from ten years of filed accounts for revenue, earnings per share, free cash flow and book value, over three-year and five-year windows, and each one expands into the two statements it came from with the fiscal years and the filing dates attached. Where a window starts on a negative or missing figure the stored value is n/a and it says which. It is a subscription and it wants a card for the trial, which is worth saying on a page that has just done the arithmetic for nothing. What it costs.
- WACC calculator computes the rate a cash flow is discounted at, which is the other half of turning a growth rate into a value.
- Methodology states how the product computes its stored growth rates and what it stores when a figure cannot be computed.
What this leaves out
A growth rate is arithmetic on two figures you chose. It is not a valuation, not a view on any security, and not advice. Nothing about a past rate says the next year repeats it.
The rate says nothing about volatility, about how the growth was funded, or about whether it was bought. A company that doubled revenue by issuing shares and acquiring a competitor shows the same rate as one that doubled it by selling more, and revenue per share would separate them where revenue does not.
Inflation is not removed. A nominal rate over a decade contains whatever the price level did, and comparing a nominal rate in one currency with one in another compares two monetary regimes as much as two businesses.
The series panel measures the path you type. It cannot tell you whether a year was large because of an acquisition, a fifty-third week, a disposal or a change in accounting policy, and those four have very different implications for the year after.
Nothing you type here is sent anywhere. The arithmetic runs in your browser and no input is stored, logged or transmitted.