CAGR Calculator
Compound annual growth rate is the steady yearly rate that would have taken one figure to another. It is not what happened — real returns are lumpy — it is the smooth rate equivalent to what happened.
Annual return
10.18% a year
- Annual return
- 10.18%
- Total return
- 220.00%
- Grew by
- $22,000.00
- Multiple
- 3.20x
- Doubling time
- 7 years 2 months
- The compound annual growth rate is the steady rate that would have taken the starting value to the ending one. It is not what happened — real returns are lumpy — it is the smooth rate equivalent to what happened.
- It says nothing about the ride. Two investments with the same CAGR can differ enormously in how far they fell along the way, and that difference is what most people actually experience.
- It also ignores money paid in or taken out along the way. For an account you have been contributing to, the CAGR of the balance is not your return.
About the CAGR calculator
A total return tells you how much something grew. It does not tell you whether that was good, because it says nothing about how long it took. Doubling your money is excellent over three years and unremarkable over twenty. CAGR puts both on the same footing by expressing the whole period as a single annual rate.
Ten thousand becoming thirty-two thousand over twelve years is a 220% total return and a 10.18% compound annual rate. The second figure is the one you can compare against a savings account, another investment or an index, and the first is not.
The word compound matters. CAGR is not the total return divided by the years — that would be 18.3% here, which is wrong, because it ignores that each year's growth happens on top of the previous years'. The correct rate is always lower than the simple average, and the gap widens the longer the period.
What CAGR hides is the ride. Two investments with an identical CAGR can differ enormously in how far they fell along the way, and the depth of the falls is what most people actually experience. It also assumes no money went in or out. For an account you have been contributing to, the CAGR of the balance is not your return — much of the growth was deposits.
What it works out
- The annual rate between any two values
- Total return and the multiple
- How long the money takes to double at that rate
- Investments, revenue, a business, a house — anything with two dated values
The formula
CAGR = ((End ÷ Begin)^(1 ÷ Years) − 1) × 100
Divide the ending value by the starting one to get the multiple, take the year-th root of it, subtract one. The root is what turns a whole-period growth figure into a per-year one, and it is why the answer is not simply the total return divided by the years.
Thirty-two thousand divided by ten thousand is 3.2. The twelfth root of 3.2 is 1.1018, so the rate is 10.18% a year. Dividing the 220% total return by twelve would give 18.3%, which is badly wrong — it treats each year's growth as happening on the original amount rather than on the amount as it stands.
The doubling time follows from the same rate. At 10.18% money doubles in about seven years and two months, which is where the old rule of dividing 72 by the rate comes from — 72 over 10.18 is 7.07.
The single biggest limitation: this assumes nothing was added or taken out. If you have been paying into the account, much of the growth is your own deposits and the rate this produces is not your return.
- Begin
- The value at the start. Must be above zero — there is no growth rate from nothing.
- End
- The value at the end. It can be lower, in which case the rate is negative.
- Years
- The period between them. Fractions are fine.
A worked example
An investment that went from 10,000 to 32,000 over twelve years.
That works out to 10.18 % a year.
- Annual return
- 10.18%
- Total return
- 220.00%
- Grew by
- $22,000.00
- Multiple
- 3.20x
- Doubling time
- 7 years 2 months
Questions
What is CAGR?
The compound annual growth rate: the constant yearly rate that would take the starting value to the ending one over the period. It is a way of expressing any growth, however lumpy, as a single comparable number.
Why is CAGR lower than the average annual return?
Because growth compounds. Ten thousand growing to thirty-two thousand over twelve years is 220% in total, and dividing that by twelve gives 18.3% — but that assumes every year's growth happens on the original amount. The real compound rate is 10.18%.
Is a higher CAGR always better?
Not on its own. It says nothing about how far the value fell along the way, and two investments with the same CAGR can be wildly different to live through. It also says nothing about risk of loss, only about what happened this time.
Can CAGR be negative?
Yes, when the ending value is lower than the starting one. It works exactly the same way and tells you the steady annual rate of decline.
How long does money take to double at this rate?
At 10.18% a year, about seven years and two months. The quick approximation is to divide 72 by the rate, which gives 7.1 here — close enough for mental arithmetic at rates in single or low double figures.
Can I use this if I have been adding money?
Not meaningfully. CAGR assumes a single starting amount left alone. If you have been contributing, much of the growth is deposits rather than return, and the figure will flatter you badly. What you want there is a money-weighted return.
Does this work for revenue or a business?
Yes — anything with a value at two points in time. It is used as often for revenue growth, user counts and market size as for investments, and it means the same thing in all of them.
Should I use CAGR or annualised return?
For a period measured in whole years with no cash flows, they are the same thing. Annualised return is the broader term and covers periods shorter than a year, where extrapolating to an annual figure is often misleading.