What CAGR means
Compound Annual Growth Rate, or CAGR, is a single number that shows how much an investment or metric grew each year on average over a period of time. It turns a start value and an end value into an average annual growth rate that, if repeated each year, would get you from the start to the end.
CAGR does not show year by year ups and downs. It gives a smooth annual growth rate that explains total growth.
Why it matters
CAGR is useful when you want to compare growth across investments, companies, or products. It answers the question: if growth happened at a steady rate every year, how big would that rate be?
It is simple and easy to compare. That makes it very common in reports, pitches, and performance summaries.
The formula
CAGR = (Ending Value / Beginning Value)^(1 / n) - 1
Where:
- Ending Value is the final amount.
- Beginning Value is the initial amount.
- n is the number of years.
If n is months, convert to years by dividing months by 12.
A clear example
Say you invest $1,000 and it grows to $1,600 in 3 years.
- Ending / Beginning = 1600 / 1000 = 1.6
- Take the 1/3 power: 1.6^(1/3) ≈ 1.168
- Subtract 1: 1.168 - 1 = 0.168
CAGR ≈ 0.168 or 16.8% per year.
That means a steady 16.8% each year would turn $1,000 into $1,600 in 3 years.
Step by step for manual calculation
- Divide the ending value by the beginning value.
- Raise the result to the power of 1 divided by the number of years.
- Subtract 1.
- Convert to percent by multiplying by 100.
Quick checklist:
- Use years for n unless you convert months.
- Make sure the beginning value is positive and not zero.
- If values include intermediate cash flows, use a different method like IRR or XIRR.
Excel and Google Sheets
Easy formula: =(Ending/Beginning)^(1/Years)-1
Example: =(1600/1000)^(1/3)-1
There is also a RATE formula for investments with cash flows: =RATE(nper, pmt, pv, fv) But for simple start-to-end without cash flows, the power formula above is best.
Python
Simple snippet: growth = (ending / beginning) ** (1 / years) - 1
Use floats and check that beginning > 0.
When you should use CAGR
- Comparing the growth of two companies or products over the same period.
- Showing average revenue or user growth in a clear summary.
- Converting total return into an annualized rate.
When not to use CAGR
- When you need to see volatility or year by year returns. CAGR hides swings.
- When there are deposits or withdrawals during the period. Those need IRR or XIRR.
- When the starting value is zero or negative. The formula breaks down then.
- When you want a simple arithmetic average of yearly returns. The arithmetic mean can overstate growth when returns vary.
Limits and caveats
- CAGR assumes constant compounding with no cash flows. Real investments often vary.
- Two investments can have the same CAGR but very different risk profiles.
- Short periods can give misleading results if a big one-time gain skews total growth.
- Negative returns work, but be careful when values cross zero.
Quick comparisons
- CAGR vs arithmetic average: CAGR is a geometric average. It reflects compounding. The arithmetic average is just the plain mean of yearly returns and can be higher when returns vary.
- CAGR vs IRR: IRR accounts for cash flows at different times. Use IRR when money goes in and out during the period.
Bottom line
CAGR is a clear, simple way to annualize total growth. Use it for side by side comparisons and summaries. Do not use it to measure volatility or evaluate cash flow timing. When you need a fuller picture, add year by year returns or use IRR.
If you want, provide your starting value, ending value, and number of years and I will compute the CAGR and show the steps.