CAGR - compound annual growth rate - is the single most useful number for describing how fast an investment grew. It answers a deceptively simple question: if this investment had grown at the same steady rate every year, what would that rate have to be to get from where it started to where it ended? Real returns are never that smooth - a fund might jump 30% one year and slip 8% the next - but CAGR strips out all that noise and gives you one clean per-year figure. That is what makes it the standard yardstick for comparing investments held for different lengths of time. This guide explains exactly how CAGR is worked out so you can reproduce and sanity-check every figure in the CAGR Calculator.
The CAGR formula
CAGR is calculated from just three inputs: the value you started with, the value you ended with, and how many years passed in between. No interim data is needed. The formula is:
- CAGR = ((Final value / Initial value)^(1 / years) − 1) × 100
- where the result is expressed as a percentage per year.
The logic is the reverse of compounding. Compounding takes a rate and grows a starting amount over time; CAGR takes the start and end amounts and time, and solves for the rate that connects them. The ratio Final / Initial is the total growth factor over the whole period; raising it to the power of 1 / years takes the geometric annual root of that growth; subtracting 1 turns the growth factor into a rate; and multiplying by 100 expresses it as a percentage. Because the exponent is a root rather than a simple division, CAGR correctly accounts for the fact that returns compound on themselves year after year - which is exactly why the CAGR Calculator uses this equation rather than dividing total return by the number of years.
A worked example
Suppose you invested 1,00,000 and it grew to 2,50,000 over 5 years. Plug the numbers straight in:
- Growth factor = 2,50,000 / 1,00,000 = 2.5.
- Annual root = 2.5^(1 / 5) = 2.5^0.2 ≈ 1.20112.
- CAGR = (1.20112 − 1) × 100 ≈ 20.11% per year.
So the investment compounded at about 20.11% a year. You can verify it runs the other way: 1,00,000 × 1.20112^5 = 1,00,000 × 2.5 = 2,50,000, right back to the final value. Notice how different this is from the headline total return: the money grew 150% in total (from 1,00,000 to 2,50,000), but that total gain spread across five compounding years works out to only about 20.11% per year, not 150% ÷ 5 = 30%. Dividing the total return by the years overstates the annual rate because it ignores compounding. Try your own start value, end value and tenure in the CAGR Calculator to see the rate for any investment.
Why CAGR beats a simple average
The temptation is to average a run of yearly returns, but a plain average badly misleads whenever returns swing. Imagine an investment that gains 80% in year one and loses 30% in year two. The naive average is (80 − 30) / 2 = 25% a year, which sounds excellent. But work out what actually happened to 1,00,000: it rises to 1,80,000, then falls 30% to 1,26,000. Feed that into CAGR - start 1,00,000, end 1,26,000, 2 years - and the true compounded rate is about 12.25% a year, less than half the naive average. The gap appears because a percentage loss bites a bigger balance than the earlier gain built, and a simple average is blind to that. CAGR uses the geometric root instead of the arithmetic mean, so it always reflects the money you truly ended up with. This is why fund fact sheets quote CAGR rather than an average of annual returns.
CAGR vs total return
Total return is the overall percentage gain across the whole holding period - in the first example, 150%. It is a perfectly good measure of how much you made, but it says nothing about how long it took, which makes it useless for comparison. A 150% total return earned over 5 years is a very different investment from a 150% return earned over 15 years, yet both share the same total-return figure. CAGR solves this by converting any total return into a per-year rate, putting every investment on the same annual footing regardless of horizon. The 150%-over-5-years case is about 20.11% CAGR; the same 150% stretched over 15 years is only about 6.3% CAGR. Whenever you want to rank investments held for different periods, convert each to CAGR first and compare those.
The power of the horizon
Because years sit in the exponent, the same absolute gain implies a wildly different CAGR depending on how long it took. Doubling your money - 1,00,000 to 2,00,000 - is a fixed 100% total return, but the annual rate needed to achieve it collapses as the horizon lengthens: it takes about 25.99% a year to double in 3 years, but only about 5.95% a year to double in 12 years. A quick mental shortcut is the Rule of 72: divide 72 by a CAGR to estimate the years it takes to double at that rate. At roughly 12.25% CAGR, 72 ÷ 12.25 ≈ 5.9 years to double - a handy sanity check you can run without a calculator. The lesson for planning is that a modest-sounding CAGR sustained over a long horizon quietly doubles and redoubles your money.
Where CAGR falls short
CAGR is a summary, and like any summary it hides detail. Its biggest blind spot is that it only looks at the start and end points, so it completely ignores the ride in between - two investments that both went from 1,00,000 to 2,50,000 in 5 years have identical CAGR even if one climbed smoothly and the other crashed 40% midway before recovering. It therefore tells you nothing about volatility or risk, and it can flatter an investment that happened to end on a high. CAGR also assumes a single lump sum left untouched: it does not account for money you add or withdraw along the way, so for a SIP or any series of cash flows you need a different measure such as XIRR rather than plain CAGR. And, like all such figures, the calculator's output is pre-tax and pre-cost. Treat CAGR as a clean way to compare and describe past growth - use it alongside a look at the volatility and your own cash-flow pattern, and reach for the CAGR Calculator whenever you need the annual rate for a start value, end value and period.
Frequently asked questions
- How is CAGR calculated?
- CAGR = ((Final value / Initial value)^(1 / years) − 1) × 100. You take the ratio of the ending to the starting value, raise it to the power of one divided by the number of years, subtract 1, and multiply by 100. For example, 1,00,000 growing to 2,50,000 over 5 years gives (2.5^(1/5) − 1) × 100 ≈ 20.11% per year. It is the constant annual rate that would grow the initial value to the final value with compounding.
- Why is CAGR different from the average annual return?
- A simple average of yearly returns ignores compounding and overstates the true rate whenever returns fluctuate. If an investment gains 80% then loses 30%, the naive average is 25% a year, but 1,00,000 actually ends at 1,26,000, a CAGR of only about 12.25%. CAGR uses the geometric root rather than the arithmetic mean, so it always reflects the money you genuinely ended up with - which is why fund fact sheets quote CAGR, not an average.
- What are the limitations of CAGR?
- CAGR only uses the starting and ending values, so it ignores everything in between - it says nothing about volatility, and two investments with very different rides can share the same CAGR. It also assumes a single lump sum with no additions or withdrawals, so for SIPs or irregular cash flows you need XIRR instead. Finally, the figure is pre-tax and pre-cost. Use CAGR to compare and describe growth, but pair it with a look at risk and your own cash-flow pattern.