How CAGR is calculated
CAGR, the compound annual growth rate, is the steady yearly rate that would turn a starting value into an ending value over a period:
CAGR = (ending value ÷ starting value)1 ÷ years − 1
With two dates, the years are the days between them ÷ 365.25, so leap years are counted fairly.
Worked example
The calculator’s starting values: $10,000 grows to $16,000 over 5 years.
- Growth multiple: $16,000 ÷ $10,000 = 1.6
- CAGR: 1.61 ÷ 5 − 1 = 9.86% a year
- Check: $10,000 × 1.09865 ≈ $16,000
The total growth is 60%, but dividing by 5 years to get 12% a year overstates it, because each year’s growth builds on the last. CAGR is the rate that compounds to the right total.
CAGR and average returns
CAGR is not the same as the average of the yearly returns. If $10,000 rises 50% one year and falls 50% the next, the average yearly return is 0%, but the investment ends at $7,500: a CAGR of −13.40%. CAGR describes what actually happened to the money; a simple average can’t.
It does smooth over the path. Two investments with the same CAGR can have had very different ups and downs along the way.
If you added or took out money
Plain CAGR only uses the starting and ending values, so any money you added along the way gets counted as growth. Choose “Yes” under “Money added or taken out along the way?” and enter each amount with its date. The calculator then works out the money-weighted annualized return: the yearly rate at which everything you paid in, grown to the end date, equals everything you took out plus the ending value. Spreadsheets call this XIRR. It isn’t CAGR, and the results say so.
For example, $10,000 invested on January 1, 2021, with $2,000 more added on January 1, 2023, is worth $16,000 on January 1, 2026. Plain CAGR says 9.86% a year, but $2,000 of that increase was your own money. The money-weighted return is 6.33% a year.
The timing matters. If instead you’d added $10,000 on January 1, 2025, and ended with $21,000, plain CAGR would say 16.00% a year, while the money-weighted return is 1.62%: most of the money was invested for only the last year.
Periods shorter than a year
A CAGR for less than a year assumes the growth would carry on at the same pace for a full year. 10% growth in six months becomes 21.00% a year, which may never happen. The calculator shows a caution when the period is shorter than a year.
Assumptions and limitations
- The values you enter should be on the same basis, for example both including reinvested dividends, and both before or both after fees.
- Taxes and inflation aren’t taken into account.
- The money-weighted return counts 365-day years from the start date, the same convention as spreadsheet XIRR functions. If money flows in and out repeatedly, there can occasionally be more than one rate that fits; the calculator reports the one it finds, or says when none exists.
- Past growth doesn’t predict future returns.
Questions
Can CAGR be negative?
Yes. If the ending value is below the starting value, CAGR is negative. An ending value of 0 is −100%.
Can I use it for things other than investments?
Yes. CAGR works for any quantity that grows over time, such as a business’s revenue or a city’s population, as long as nothing was added from outside the growth itself.
How do I project an investment forward?
Use the Compound Interest Calculator. CAGR measures growth that has already happened.