CAGR calculator

What CAGR tells you and what it hides

Compound Annual Growth Rate is the single rate that would carry a start figure to an end figure over a chosen term if the money compounded steadily every year. It is useful because it collapses a messy history of ups and downs into one annual number that is comparable across funds, assets and time periods. It is useful for exactly that reason, and misleading for the same one: the single number removes every jump and drawdown the money actually went through.

Two investments with the same start, end and term share a CAGR even if one was a smooth line and the other a round trip through a drawdown and a late recovery. A sensible read of CAGR always sits next to the absolute return and the number of years, and against the volatility of that path.

The formula with signs

The arithmetic is one rearrangement of a single identity: end = start times (1 plus CAGR) raised to years. Rearranging gives CAGR = (end divided by start) raised to the power one over years, minus one. Rearranging again gives years = natural log of (end divided by start) divided by natural log of (1 plus CAGR). This page lets you solve any one of the three from the other two.

When the end is below the start, CAGR is negative. For a start of ₹10,000 that falls to ₹5,000 over 5 years, CAGR is (0.5) raised to one over five, minus one, or about minus 12.94 per cent. The formula handles it with no special case: the compound rate is simply a negative number. The absolute return is minus 50 per cent, and the simple per-year rate is minus 10 per cent on a straight line.

Three modes, one arithmetic

Tab one solves for CAGR when start, end and years are known. Tab two solves for end when start, CAGR and years are known. Tab three solves for years when start, end and CAGR are known. In every tab the page fills the missing variable and shows the compounding path on the chart.

In the years tab, the rate and the direction between start and end must agree. A positive CAGR cannot move a figure down, and a negative CAGR cannot move a figure up. The calculator flags this with a Not reachable message rather than returning a silent nonsense number. A rate of exactly zero returns the same message, because an untouched amount neither climbs nor falls.

A worked example that compounds to a familiar figure

A start of ₹1,00,000 that grows to ₹2,00,000 over 7 years: CAGR equals two raised to one over seven, minus one. Two raised to one over seven is 1.104089, so CAGR is 10.41 per cent a year. Check the other direction: 1,00,000 times 1.104089 raised to seven is 1,99,999, which rounds back to 2,00,000. Absolute return is 100 per cent. The simple per-year rate is 14.29 per cent, because 100 divided by 7 is 14.29. The compound figure is lower because compounding does more work in the later years than a simple average admits.

Why CAGR hides volatility

Consider two paths from ₹1,00,000 to ₹2,00,000 over 7 years. Path A grows at a steady 10.41 per cent each year. Path B gives minus 20 per cent in year one, plus 40 per cent in year two, and then grows at about 12.30 per cent for the last five years. Both end at ₹2,00,000. Both have a CAGR of 10.41 per cent. Only Path B puts the holder through a drawdown.

A CAGR alone cannot tell the two apart. For a plan that spends a drawdown or has to sell early, the path matters as much as the rate.

Absolute return next to CAGR

Absolute return is (end minus start) divided by start, expressed as a percentage. It is simpler and more concrete. For a 100 per cent absolute return the end is twice the start, no matter the term. CAGR squeezes the same 100 per cent into a per-year figure, which falls as the term lengthens: 100 per cent over 2 years is 41.4 per cent a year on a compound basis; the same 100 per cent over 20 years is 3.5 per cent a year. Both are correct arithmetic on the same money; they answer different questions.

This page prints the multiple of the start as a tile too. A multiple of 2.5x in nine years is easier to picture than either percentage, and does not depend on a per-year figure at all.

When to use XIRR instead

CAGR assumes exactly one inflow at the start and one outflow at the end. The real world often adds or removes money partway through. If a SIP paid 12 instalments a year for five years, or if a lump sum was followed by top-ups, a single start-and-end CAGR will either ignore those cash flows or distort them. For that case, the mutual fund returns calculator runs XIRR on the actual cash flows and gives a time-weighted annual figure the CAGR here cannot.

CAGR is also not the same as the Internal Rate of Return on a project: CAGR solves for one compound rate between two balances, while IRR solves for the rate that makes the net present value of a stream of cash flows equal to zero. On a two-flow stream the two coincide. On anything more, they diverge.

What this calculator leaves out

• Intermediate contributions or withdrawals. Any top-up or partial sell changes the per-rupee weight the arithmetic assumes.
• Inflation, which eats into the real value of the end figure. Use the inflation calculator to restate the end value in today's rupees.
• Tax on redemption. Equity LTCG, debt slab-rate tax and dividend slab-rate tax all apply to the end figure, not the CAGR.
• Fees. A fund TER chips at the per-year rate every year; the posted CAGR already includes it, so a quoted CAGR on an index is higher than the one actually earned in a fund tracking the same index.
• Any forecast about future years. The calculator uses the rate the reader enters and does not project it.

Frequently asked questions

Courses that teach the subject behind the cAGR calculator