How this calculator works
Compound Annual Growth Rate (CAGR) smooths a multi-year change into a single, constant annual growth rate. It answers the question: if this value had grown by the same percentage every year, what would that percentage be?
CAGR is useful for comparing investments or business metrics that grew unevenly year to year, since it strips out volatility and expresses the overall change as one comparable number. It is not the same as the average of the yearly returns; it is the geometric growth rate that reproduces the actual ending value.
The formula
CAGR (%) = [(Ending value ÷ Beginning value)^(1 ÷ years) − 1] × 100Total growth (%) = (Ending value ÷ Beginning value − 1) × 100Applying the CAGR every year for the same number of years, compounded, reproduces the ending value exactly: Beginning value × (1 + CAGR)^years = Ending value.
Worked example: $10,000 growing to $20,000 over 5 years
- Divide the ending value by the beginning value: 20,000 ÷ 10,000 = 2.
- Raise that ratio to the power of 1 ÷ 5 (one over the number of years): 2^0.2 ≈ 1.148698.
- Subtract 1 and convert to a percentage: (1.148698 − 1) × 100 ≈ 14.87% CAGR.
- Check: $10,000 × (1.1487)^5 ≈ $20,000, confirming the rate reproduces the ending value, even though the total growth over the 5 years is 100%.
Frequently asked questions
Is CAGR the same as the average annual return?
No. A simple average of yearly percentage returns can overstate growth when returns are volatile, because it ignores compounding. CAGR is the geometric growth rate, which correctly accounts for gains and losses compounding on each other.
What if the value went down and then up?
CAGR only looks at the beginning and ending values, not the path between them, so it will not show volatility along the way. Two investments with very different year-to-year swings can have the same CAGR if they start and end at the same values.
Can CAGR be negative?
Yes. If the ending value is lower than the beginning value, CAGR is negative, showing the constant annual rate of decline over the period.
How is CAGR different from ROI?
ROI is the total percentage change over the whole period. CAGR converts that total change into an equivalent constant yearly rate, which makes it easier to compare investments held for different lengths of time.
How can I use a known CAGR to project a future value?
Rearrange the CAGR relationship to solve for the ending value instead: Ending value = Beginning value × (1 + CAGR)^years, using CAGR as a decimal. This is the same round-trip check used in the worked example on this page, where $10,000 growing at a CAGR of about 14.87% for 5 years reproduces the $20,000 ending value — applying that same formula with a different starting amount or number of years projects a new ending value the same way.