CAGR stands for compound annual growth rate. It answers one narrow question: if something had grown by the same percentage every year, what percentage would take it from its starting value to its ending value over the period? It is a smoothing device. It tells you nothing about what happened in between.
The formula
CAGR = (End value ÷ Start value)1 / n − 1
where n is the number of compounding periods (usually years) between the start and the end.
The most common slip is getting n wrong. From the end of year 0 to the end of year 5 there are five periods, not six. If a report says a market grows "from 2025 to 2030", n is 5.
A worked example
All figures in this example are hypothetical. They describe an imaginary market and are chosen only to make the arithmetic easy to follow.
Suppose an imaginary market is valued at 200 (in any currency unit) in the base year and is forecast to reach 320 five years later.
- Divide end by start. 320 ÷ 200 = 1.6. The market grows by 60% in total.
- Take the n-th root. With n = 5, raise 1.6 to the power of 1/5 (0.2). The result is approximately 1.0986.
- Subtract one. 1.0986 − 1 = 0.0986, or about 9.86% per year.
In a spreadsheet you can write this as =(320/200)^(1/5)-1. You can verify the answer by compounding forward:
| Year | Value (hypothetical) |
|---|---|
| 0 (base year) | 200.00 |
| 1 | 219.71 |
| 2 | 241.37 |
| 3 | 265.16 |
| 4 | 291.29 |
| 5 | 320.00 |
CAGR versus AAGR
AAGR, the average annual growth rate, is the simple arithmetic mean of each year's growth. It can differ sharply from CAGR when growth is uneven. Take a second hypothetical path that starts at 200 and also ends at 320, but bumps around on the way:
| Year | Value (hypothetical) | Growth that year |
|---|---|---|
| 0 | 200 | – |
| 1 | 260 | +30.00% |
| 2 | 230 | −11.54% |
| 3 | 290 | +26.09% |
| 4 | 280 | −3.45% |
| 5 | 320 | +14.29% |
The AAGR here is about 11.08%, but the CAGR is still 9.86%, because CAGR depends only on the first and last values. AAGR overstates compound growth whenever there is volatility. If a report quotes an "average growth rate" without saying which kind, ask.
What CAGR hides
Volatility
Both paths above share the same CAGR. One is smooth and one is not. If timing matters to you, look at the year-by-year series, not just the summary rate.
Choice of start and end points
Starting a CAGR in a depressed year makes growth look strong; starting at a peak makes it look weak. Check whether the base year was unusual.
Price versus volume
A value CAGR mixes changes in quantity with changes in price. In inflationary periods, nominal value growth can look healthy while unit volumes are flat. Look for whether a report uses nominal or constant prices.
Small bases
Very high CAGRs are often a feature of tiny starting values. Growing from 1 to 10 is a CAGR of nearly 59% over five years, but the absolute change is small. Always look at the absolute numbers alongside the rate.
Running the formula backwards
Reports often give a start value and a CAGR but not the end value, or the reverse. You can rearrange the formula to fill the gap:
End = Start × (1 + CAGR)n
and, going the other way, Start = End ÷ (1 + CAGR)n.
Using the hypothetical example again: 200 × 1.09865 is about 320. If a report’s own numbers do not survive this round trip, one of them has been rounded heavily, mislabelled or mistyped.
A quick sanity check
The "rule of 72" gives a rough mental check: divide 72 by the growth rate in percent to estimate how many years it takes to double. At roughly 10% a year, doubling takes about seven years. If a report claims a market will triple in five years at a single-digit CAGR, the numbers do not agree with each other.
Unfamiliar term? See the glossary.