Find the Compound Annual Growth Rate (CAGR) between two values, over any number of years.
Takes the nth root of the growth multiple, smoothing an uneven multi-year return into a single annual rate.
CAGR: (Ending ÷ Beginning)^(1/years) − 1
CAGR, the compound annual growth rate, is the one steady yearly rate that would take a starting value to an ending value over a given number of years. A CAGR calculator needs only those three numbers.
It is used far beyond personal investing. Companies quote revenue and profit CAGR in annual reports, analysts compare the Nifty's or Sensex's long-run growth, and property buyers use it to judge how fast a flat's price has grown. In each case the actual path was bumpy, and CAGR replaces it with one smooth rate so that different investments or businesses can be compared on the same footing.
It is the right tool when there is one starting value and one ending value, with nothing added or taken out in between.
1. Write down the beginning value B, the ending value E and the number of years n. Years can be a decimal, such as 3.5.
2. Divide to get the growth multiple: E ÷ B.
3. Raise the multiple to the power 1 ÷ n. On a calculator use the xʸ key, or compute exp(ln(E ÷ B) ÷ n).
4. Subtract 1 and multiply by 100: CAGR = ((E ÷ B)^(1/n) − 1) × 100.
5. Check it: B × (1 + CAGR ÷ 100)ⁿ should give back E.
If a value grows at a constant rate r each year, after n years it becomes B(1 + r)ⁿ. Setting this equal to the observed ending value E gives (1 + r)ⁿ = E ÷ B. Taking the nth root of both sides gives 1 + r = (E ÷ B)^(1/n), so r = (E ÷ B)^(1/n) − 1. Nothing else about the path matters. Whether the value rose evenly, crashed and recovered, or jumped in the last year, the CAGR depends only on where it started, where it ended and how long it took.
If a stock rises 50% in year one and falls 50% in year two, the simple average of the yearly returns is 0%. But ₹100 becomes ₹150 and then ₹75, a real loss. The CAGR is (0.75)^(1/2) − 1, about −13.4% a year, which matches what happened. CAGR is the geometric mean of the yearly growth factors, and it is always equal to or lower than the arithmetic average of the yearly returns. The more volatile the path, the bigger that gap.
CAGR assumes a single investment at the start and a single value at the end. If money was added or withdrawn along the way, as with a SIP, a CAGR computed from total invested and final value is meaningless, because much of the money was not invested for the full period. Use XIRR in that case. CAGR also hides risk: two funds with the same 12% CAGR can have very different worst years. And for periods under a year, annualising a short burst of growth can produce an unrealistically large number.
Anand bought shares of a listed company for ₹2,50,000 seven years ago, added nothing since, and the holding is worth ₹6,10,000 today.
Answer: CAGR 13.59%
Dividing the total percentage gain by the number of years, which overstates the yearly rate.
Applying CAGR to a SIP using total invested as the beginning value.
Counting calendar years wrongly, for example treating January 2019 to December 2024 as five years instead of six.
Reading a high CAGR as low risk; CAGR says nothing about the ups and downs along the way.
Annualising a few months of returns and expecting that rate to continue.
Comparing the long-run growth of two stocks, indices or funds held as lump sums.
Reading company annual reports that state revenue or profit CAGR.
Checking how fast a property's price has actually grown between purchase and sale.
Setting a realistic return assumption for other calculators from historical data.
Does CAGR reflect year-to-year volatility?
No. CAGR turns everything into one smooth, steady rate. Two investments can have the same CAGR, even if one had a much bumpier journey to get there than the other.