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CAGR Calculator: Compound Annual Growth Rate
Turn a start value, an end value and a number of years into one smooth yearly growth rate. You can also project an end value from a rate, or find how long a target takes.
The CAGR formula and its inverses
Compound annual growth rate is the single yearly rate that would take a value from its start to its end if growth were perfectly smooth: CAGR = (End ÷ Start)1 ÷ t − 1, with t in years. Rearranged, it also answers the other two questions on this page:
- End value:
End = Start × (1 + CAGR)t - Time to a target:
t = ln(End ÷ Start) ÷ ln(1 + CAGR)
For example, a value that doubles in 10 years has a CAGR of 20.1 − 1, which is about 7.18%.
CAGR compared with an average return
An arithmetic average of yearly returns can be misleading. Suppose an investment gains 50% in year one and loses 50% in year two. The average of the two is 0%, yet 100 becomes 150 and then 75, a loss of 25% overall. The CAGR of that path is about −13.4% a year, which is the figure that matches reality. This is why growth over several periods should be reported with the compound rate and not by averaging percentages.
The simple average per year in the results is shown for contrast. It is total change divided by years, so over periods longer than a year it exceeds the CAGR for any overall gain, and the gap widens as the period lengthens.
Where CAGR is used
- Investments: comparing funds over different periods, once you account for fees and income.
- Business metrics: revenue, users or profit over several years.
- Economics: population, prices or output between two census or survey dates.
- Planning: checking whether a growth target is realistic compared with what has been achieved.
The time-to-target mode is handy for rough goals, such as how long a balance takes to double or triple at a given rate. The rule of 72 calculator gives a quicker estimate for doubling alone.
Limits and cautions
CAGR describes two endpoints. It says nothing about the path in between, the risk taken or the effect of deposits and withdrawals; if money was added during the period, use an internal rate of return instead. Start and end dates also matter: changing either by a year can alter the rate noticeably, especially for volatile series. A past CAGR is a description, not a forecast, and a projection from it assumes the future resembles the past. When comparing several series, such as sales in different regions, use the same start and end dates for each so the rates are comparable. Use the same units and currency for both values.
Worked example
A company's yearly revenue rose from 45,000 to 82,000 over six years. What steady yearly growth rate does that equal?
Inputs
| What do you want to find? | Growth rate (CAGR) |
|---|---|
| Start value | 45000 |
| End value | 82000 |
| Number of years | 6 |
Result
From 45,000.00 to 82,000.00 over 6.00 years.
| Start value | 45,000.00 |
|---|---|
| End value | 82,000.00 |
| Total change | 82.22% |
| Years | 6.00 |
| Simple average change per year | 13.704% |
| Time to double at this rate | 6.93 years |
Smooth growth path
| Year | Value | Change in the year |
|---|---|---|
| Year 1 | 49,733.16 | 4,733.16 |
| Year 2 | 54,964.16 | 5,231.00 |
| Year 3 | 60,745.37 | 5,781.21 |
| Year 4 | 67,134.65 | 6,389.28 |
| Year 5 | 74,195.97 | 7,061.31 |
| Year 6 | 82,000.00 | 7,804.03 |
- Formula: CAGR = (end ÷ start)^(1 ÷ years) − 1. It is a smooth rate that links two points and hides any ups and downs between them.
Financial disclaimer: Results are estimates for planning and education. They are not financial, tax or legal advice. Fees, taxes, rates and rules vary by lender, product and country, so confirm figures with your provider or a qualified adviser before making decisions.
Frequently asked questions
How do I calculate CAGR?
Divide the end value by the start value, raise the result to the power of one over the number of years, and subtract one. Multiply by 100 for a percentage.
Is CAGR the same as average annual return?
No. An average of yearly returns ignores compounding, while CAGR gives the steady rate that links the start and end values. The two differ, often by a lot, when returns are volatile.
Can CAGR be negative?
Yes. If the end value is below the start value, the result is negative, meaning an average yearly decline.
What if I have deposits or withdrawals during the period?
CAGR assumes none. With cash flows, use a money-weighted measure such as the internal rate of return.
How many years should I use?
Use the exact time between the two values, including fractions if needed, such as 2.5 for thirty months.
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References and sources
- Standard finance and investment texts: compound annual growth rate and geometric mean return.
- Investor.gov (U.S. SEC): educational material on investment returns. Link