CAGR Calculator
Compound annual growth rate from two values or a list of yearly changes, with the arithmetic average beside it and the volatility drag between them.
Start $1,200,000.00
End $2,900,000.00
Period 4.00 years
CAGR 24.68%
Total change 141.67%
Multiple 2.417×
At this rate
doubles in 3.1 years
the rule of 72 says 2.9 years
ten times in 10.4 years
Projected forward
in 1 year $3,615,781.56
in 3 years $5,620,960.87
in 5 years $8,738,138.78
in 10 years $26,329,334.23
CAGR is the geometric mean: the constant rate that would take the start
value to the end value. It is not the average of the yearly changes,
which is always at least as large and which nobody actually receives.
Up 50 percent then down 50 percent averages zero and leaves you down 25
percent, a CAGR of −13.4 percent a year. That is the whole argument for
using the compound figure, and it is why a fund quoting an average
annual return is describing something no investor experienced.
CAGR hides the path completely. Two businesses with the same start and
end points have the same CAGR whether one grew steadily and the other
lost half its revenue in the middle, and the second is a much riskier
business. Look at the yearly figures as well.
The endpoints decide the answer, so choosing them is choosing the
result. A CAGR measured from a trough to a peak flatters, and one
measured across the same period shifted by a year can be half as large.
Any CAGR quoted without its start and end dates is a marketing number.
The rule of 72 is a decent approximation for doubling time, and it
drifts: it is accurate around 8 percent and overstates at high rates.
The exact figure is log 2 divided by log(1 + rate), which is what is
printed above.
Projecting a CAGR forward assumes the rate continues, which is the
assumption that fails. A three-year CAGR from a small base extrapolated
for ten years produces a number larger than the market, and that is the
standard failure mode of a growth projection.
For revenue, check the definition before comparing. Bookings, recognised
revenue, annual recurring revenue and cash collected give four different
growth rates from the same business, and a change of definition
mid-series is the most common way a CAGR gets inflated by accident.
Output is valid and updates as you type.
Fix the highlighted fields to update the output.
Up 50 percent, then down 50 percent. The average of those two years is zero. What actually happened is that you lost a quarter of your money, which is a compound rate of −13.4 percent a year.
That gap is volatility drag, and it is why the average of yearly returns is the number that appears in marketing material and the compound rate is the number that describes what the money did. The arithmetic mean is always at least as large as the geometric one, and they are only equal when nothing varied.
CAGR is the geometric mean: the constant rate that would take the start value to the end value over the period.
How to use
- Put in the starting and ending values and the number of years. Or
- paste the yearly percentage changes, which also gives you the average and the drag between them.
- Read the doubling time, and treat the projection as arithmetic rather than a forecast.
Example
Two years, up 50 percent then down 50:
CAGR, the geometric mean -13.4%
Average of the yearly rates 0%
the gap 13.4%, which is volatility drag
What actually happened
total change -25%
as a multiple 0.7500×
$10,000.00 becomes $7,500.00
at the average instead 1.0000×, which nobody receivedAnd from two endpoints, $1.2M to $2.9M over four years:
CAGR 24.68%
Multiple 2.417×
At this rate
doubles in 3.1 years
the rule of 72 says 2.9 years
ten times in 10.4 yearsPitfalls
The average is not the growth rate. Any series that varies has a compound rate below its average, and the more it varies the bigger the gap. A fund quoting an average annual return is describing something no investor received.
CAGR hides the path completely. Two businesses with the same endpoints have the same CAGR whether one grew steadily and the other halved in the middle and recovered. The second is a much riskier business, and the single figure cannot tell you that.
The endpoints are the whole answer. Measured from a trough to a peak, a CAGR flatters; shifted by a year it can halve. Any CAGR quoted without its start and end dates is a marketing number.
Projecting it forward assumes it continues. A three-year CAGR from a small base, extrapolated for ten years, produces a number larger than the market it operates in. That is the standard failure of a growth projection, and it is why the projection here stops at ten years.
The rule of 72 drifts. It is accurate around 8 percent and overstates at high rates. The exact doubling time is log 2 divided by log(1 + rate), which is what is printed.
Check the revenue definition before comparing. Bookings, recognised revenue, annual recurring revenue and cash collected give four different growth rates from the same business, and a definition that changed mid-series is the commonest accidental inflation of a CAGR.
A negative-to-positive series has no CAGR. If the starting value is negative or zero, the geometric mean is undefined, and any tool that returns a number for it is inventing one.
Compatibility
Arithmetic in the browser: nothing is uploaded and nothing is stored.
The rate is (end / start)^(1/years) − 1, exactly. From a list of yearly changes, the factors are
multiplied and the same root is taken, so the two routes agree when given the same data.
Fractional years work: 4.5 years is a valid period and the root handles it. The doubling and ten-times figures come from logarithms rather than the rule of 72, and the rule is printed next to them so the approximation error is visible.
A yearly change of −100 percent or worse is refused, because the value reaches zero and nothing compounds afterwards: no rate describes a series that hits zero and continues.
Frequently asked questions
What is the CAGR formula?
(ending / beginning)^(1 / years) − 1. In a spreadsheet, =(B2/B1)^(1/4)-1 for four years, or
=RRI(4,B1,B2).