How it works
A percentage change compares an ending value with a starting value. A compound annual growth rate (CAGR) goes one step further: it is the steady yearly rate that would take the starting value to the ending value over the same number of years, with each year's growth building on the last, as the compounding and CAGR lesson explains.
Percentage change = (end − start) ÷ start × 100
CAGR = (end ÷ start)1 ÷ years − 1
Change needed to get back to the start = (start − end) ÷ end × 100
The calculator also shows the simple yearly rate, the total change divided by the number of years. It ignores compounding, so for growth it is always higher than the CAGR, and quoting it as an "average return" flatters the result.
It works for any positive amount: an investment's value, an index level, a company's revenue or its earnings per share.
Worked example
Worked example: ₹50,000 becomes ₹80,000 in four years
| Percentage change: (80,000 − 50,000) ÷ 50,000 | +60% |
|---|---|
| The end value is | 1.6 times the start |
| CAGR: (80,000 ÷ 50,000)^(1 ÷ 4) − 1 | about 12.47% a year |
| Simple yearly rate: 60% ÷ 4 | 15% a year |
| Change needed to fall back to ₹50,000 | −37.5% |
Growing at a steady 12.47% a year for four years gives the same result as the actual path. The simple rate of 15% a year overstates it, because it ignores that later growth builds on earlier growth.
Percentage changes are not symmetric: a rise of 60% is undone by a fall of 37.5%, and a fall of 50% needs a rise of 100% to recover, as the percentages lesson explains.
Limitations
- A CAGR describes only the start and the end. Two investments with the same CAGR can have taken very different paths, one smooth and one with deep falls along the way, as the volatility and drawdowns lesson shows.
- The dates matter. Starting at a market low makes a CAGR look better; starting at a peak makes it look worse.
- Money added or withdrawn along the way is not handled. For a portfolio with regular investments, use a money-weighted measure such as XIRR, as the benchmarks and performance lesson explains.
- A past CAGR is not a forecast. It describes what happened over one chosen period.