CAGR Calculator

What CAGR measures

A compound annual growth rate answers one question: if this number had grown at the same rate every year, what would that rate be? It takes two values and a length of time and returns a single annual percentage. The values are the start and the end. The time is measured in years, and it can be a fraction, such as 2.5 for thirty months.

The formula is short: CAGR = (ending value / starting value) ^ (1 / years) - 1. Divide first, take the root, then subtract one. The root is the step people skip, and it is the step that makes the answer compound. Raising 1.9 to the power 1/3 asks one question: what number, multiplied by itself three times, gives 1.9?

The same algebra sits inside the way US funds report performance. The SEC rule adopted in 2001 (Release 33-7941) defines average annual total return as the rate T that solves P(1 + T)^n = ERV, where P is a hypothetical $1,000, n is the number of years and ERV is the ending redeemable value, with all distributions reinvested. Solve that equation for T and you have a CAGR. Investor.gov, the SEC's investor education site, keeps a plain definition of annual return as the profit or loss on an investment over a one-year period, which is the ingredient the compounded version smooths into one rate.

One warning before any number: CAGR is a geometric mean, not the average of the yearly returns. The next sections show why that difference changes the answer.

A worked example, line by line

Start with $10,000 that grows to $19,000 in 3 years. Nothing else is known: no deposits, no withdrawals, no yearly returns.

The check matters. Multiply the starting value by (1 + CAGR) once per year and you land back on the ending value, which is the only thing the formula promises.

Two other numbers fall out of the same division. Total growth is 19,000 / 10,000 - 1 = 0.9, or 90%. The growth multiple is 1.9. Total growth of 90% over 3 years is not 30% a year, because each year's gain also earns in the years after it.

A second run with larger numbers: a company books $2.4 million in revenue and $4.1 million five years later. The multiple is 4.1 / 2.4 = 1.70833. The fifth root of 1.70833 is 1.11305, so the CAGR is 11.30%. Check: 2.4 x 1.11305 ^ 5 = 4.1 million. The same arithmetic works for users, stores or square feet, because the unit cancels in the division.

Why the average yearly return is higher

Suppose $10,000 goes up 50% in the first year and down 50% in the second. The first year ends at $15,000. The second year ends at $7,500.

The arithmetic average of +50% and -50% is 0%. The account is down 25%. The CAGR is honest about it: (7,500 / 10,000) ^ (1 / 2) - 1 = 0.86603 - 1 = -13.40%.

The gap has a name, volatility drag, and it grows with the size of the swings. A third example: +20%, +20% and -20% average 6.67% a year. The money multiplies by 1.2 x 1.2 x 0.8 = 1.152, which is 15.2% over three years, and 1.152 ^ (1 / 3) - 1 = 4.83% a year.

So when a fund page or a pitch deck quotes an average annual return, check which mean it used. The arithmetic mean is always at or above the geometric one, and the difference is largest for the bumpiest series. CAGR is the geometric one, which is why it is the fairer number to compare across two investments with different swings.

The third row is the only one where the two means agree. Steady growth leaves nothing for the average to hide.

CAGR is not IRR

Both are annualized rates, and they answer different questions. CAGR uses two values and the clock. IRR uses every cash flow and its date.

Put $1,000 into a project, take $600 back after one year and $600 after two. Total returned is $1,200. The CAGR is (1,200 / 1,000) ^ (1 / 2) - 1 = 9.54%, because the formula only sees the start and the end.

The IRR is the rate that discounts both payments back to exactly $1,000, and that rate is 13.07%. The higher number is not a mistake. Half the money came back after one year and could be put to work somewhere else, and the IRR credits that timing while the CAGR cannot see it.

The two agree in one case: a single outflow at the start and a single inflow at the end. Then the IRR is the CAGR by definition. Add a deposit, a dividend taken in cash, or a partial sale, and the CAGR starts to mislead. Use the IRR calculator for those cases, or the money-weighted return from your broker, which dates each flow the same way.

Running the formula backwards

Two rearrangements cover most real questions.

Ending value = starting value x (1 + CAGR) ^ years. Put $5,000 at 7% for 10 years: 1.07 ^ 10 = 1.96715, and 5,000 x 1.96715 = $9,835.76.

Years = ln(ending value / starting value) / ln(1 + CAGR). To double at 8%: ln(2) / ln(1.08) = 0.69315 / 0.07696 = 9.01 years. The old rule of 72 gives 72 / 8 = 9, close enough for a mental check.

Look down the last two columns. The 20-year balance is 1.63 times the 10-year one at 5%, 1.97 times at 7% and 2.59 times at 10%, so a higher rate does not just add money, it adds money faster as the years pass. That is why one percentage point is worth arguing about on a 401(k) and almost nothing on a one-year CD.

What the number leaves out

• Cash flows. A deposit in year 3 is invisible. If money went in or came out, the CAGR behaves as if it had not, and the rate it reports belongs to no real account.
• Risk. A 23.86% CAGR covers a straight line and a wild ride equally well. Two funds can post the same CAGR with wildly different worst years, and the one that fell 40% in between was harder to hold.
• Fees and taxes. A fund that earns 8% before a 1% annual fee compounds at 7%. On $10,000 over 20 years that is $46,609.57 against $38,696.84, a gap of $7,912.73.
• Inflation. A nominal CAGR buys less than it looks. The real rate is (1 + CAGR) / (1 + inflation) - 1. At 8% with inflation at 3.7%, the 12-month change in the all-items CPI that the Bureau of Labor Statistics reported for September 2026, the real rate is 1.08 / 1.037 - 1 = 4.15%.

Short windows inflate the number. Three months of 10% growth annualizes to 1.10 ^ 4 - 1 = 46.41%, a rate that almost no investment keeps for a full year. A 3-month CAGR is arithmetic, not a forecast, and it should never be compared with a 10-year figure.

How to read a CAGR on a fund page

Fund companies publish 1, 5 and 10 year average annual total returns because the SEC requires a standard method, not because those windows are magic. Under the 2001 rule the fund assumes a $1,000 initial payment, deducts the maximum sales load, reinvests all distributions, and rounds the answer to the nearest hundredth of a percent. Those choices explain most of the gap between a fund's own marketing number and the one in your account.

Three checks keep a comparison fair. Compare the same window, since a 10-year number and a 3-year number are not the same claim. Compare the same share class, since a sales load and a 12b-1 fee change the rate. Check whether the figure is before or after taxes, because the after-tax version discounts a different ending value.

Watch the difference between an APR and a compounded rate. Investor.gov notes that a monthly rate multiplied by 12 gives an APR. At 1% a month that is 12% APR, but 1.01 ^ 12 - 1 = 12.68% a year once the monthly gains compound. A CAGR is always the compounded version, so a quoted APR and a quoted CAGR are not interchangeable.