CAGR Calculator (Compound Annual Growth Rate)
CAGR Calculator (Compound Annual Growth Rate)
The steady yearly growth rate that takes a starting value to an ending value over a number of years — and what the same start would have become at a rate you want to compare with.
Compound annual growth rate
$1,00,000 grew to $2,50,000 in 7 years
CAGR, and the reverse
- start
- the value at the beginning of the period
- end
- the value at the end, including any income reinvested
- years
- the length of the period; part years are allowed
- rate
- any annual rate; the reverse formula turns a rate back into an ending value
- inflation
- the average yearly rise in prices over the period, as a decimal
Worked example
$1,00,000 grew to $2,50,000 in 7 years
end ÷ start = 2,50,000 ÷ 1,00,000 = 2.5
2.51/7 = 1.1399
CAGR = 1.1399 − 1 = 13.99% a year
Check: 1,00,000 × 1.13997 ≈ 2,50,000. At 7% instead it would be $1,60,578
With prices rising 4% a year: real CAGR = 1.1399 ÷ 1.04 − 1 = 9.60% a year
Why CAGR is not the average annual return
| Year 1 | Year 2 | Average of the yearly returns | CAGR | |
|---|---|---|---|---|
| +50% then −50% | $1,50,000 | $75,000 | 0% | -13.40% |
| +100% then −50% | $2,00,000 | $1,00,000 | 25% | 0.00% |
CAGR, the average return, and ROI
CAGR is the single steady rate that would have turned the starting value into the ending value. It is a geometric average, and it is the right one for money, because returns compound. The simple average of yearly returns is not: a gain of 50% followed by a loss of 50% averages 0%, yet $1,00,000 becomes $1,50,000 and then $75,000, a CAGR of -13.40% a year. The more returns swing from year to year, the further the simple average sits above the CAGR, which is why a fund’s average annual return can look better than what its investors actually earned.
The ROI calculator answers a different question: total gain over the whole period. In the example the ROI is 150%, which says nothing about speed until it is spread over the 7 years as a CAGR of 13.99%. Use ROI for the size of a result, CAGR to compare results held for different lengths of time. The comparison lines under the result run the reverse calculation — a start value grown at a rate you choose — so you can set the investment against a deposit or a benchmark over the same period.
A CAGR is also before inflation. To see how much richer the investment made you in what money buys, the page divides out the rise in prices: real CAGR = (1 + CAGR) ÷ (1 + inflation) − 1. On the example, 13.99% a year with prices rising 4% a year is a real CAGR of about 9.60%. At 6% inflation it would be 7.53%. Simply subtracting gives 9.99%, a little too high, and the shortcut gets worse as rates rise. Enter the inflation that actually applied over the period if you know it. When you compare two investments over the same years, inflation affects both equally, so the ordering does not change; the real figure tells you whether either actually grew your purchasing power.
CAGR assumes one amount in at the start and one out at the end. For a SIP, or any investment with money added or taken out along the way, CAGR on the first and last values is misleading and XIRR is the right measure. Include costs and reinvested income in the ending value, and remember CAGR smooths away the ups and downs in between. To project a lump sum forward at a rate, use the lumpsum calculator. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
How is CAGR calculated?
CAGR = (end ÷ start)1 ÷ years − 1. $1,00,000 growing to $2,50,000 in 7 years is a CAGR of 13.99% a year.
Why is CAGR lower than the average annual return?
Because losses need bigger gains to recover from. +50% then −50% averages 0% but leaves $75,000 from $1,00,000, a CAGR of -13.40%. The geometric average (CAGR) is never higher than the simple average, and the gap grows with volatility.
What is the difference between CAGR and ROI?
ROI is the total gain; CAGR is that gain expressed as a yearly compounding rate. Going from $1,00,000 to $2,50,000 is an ROI of 150% and, over 7 years, a CAGR of 13.99%.
Can I use CAGR for my SIP?
Not on the first and last values alone, because the money went in at many different times. Use XIRR, which accounts for the date of every instalment.
What is real CAGR?
CAGR after inflation: (1 + CAGR) ÷ (1 + inflation) − 1. A CAGR of 13.99% with 4% inflation is a real CAGR of about 9.60% a year: the rate at which the investment grew in what money buys.
Related calculators
References
- Bodie Z, Kane A, Marcus AJ. Investments. McGraw-Hill. Risk, return and the historical record: arithmetic versus geometric average rates of return.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. McGraw-Hill. Present values, annuities and growing annuities.
- Central-bank inflation targets used as default inflation by currency: Reserve Bank of India (4% CPI, flexible inflation targeting framework); U.S. Federal Reserve (2% PCE); European Central Bank (2%); Bank of England (2% CPI); Bank of Canada (2%); Reserve Bank of Australia (2–3%); Bangko Sentral ng Pilipinas (3% ± 1). Actual inflation often runs above target.