CAGR calculator

What is compound annual growth rate (CAGR)?

Most values do not rise by the same amount each year. They jump, dip and jump again. CAGR asks one question. If the value had grown at one fixed rate every year, what rate would land exactly on the end value?

Say $5,000 became $8,000 over 6 years. The CAGR is about 8.15% a year. Here is that steady path. The real path may have looked nothing like it, but it starts and ends in the same place.

A CAGR also tells you how fast a value doubles. At 8% a year, that takes about 9 years.

Find the doubling time for any rate with the rule of 72 calculator →

The CAGR formula, step by step

Here is the same $5,000 to $8,000 example worked out:

1. Divide the end value by the start value. 8,000 ÷ 5,000 = 1.6. The value grew 1.6 times.
2. Raise that to the power of 1 ÷ years. With 6 years, 1.6^(1/6) is about 1.0815.
3. Take away 1. That leaves 0.0815.
4. Multiply by 100 for a percent: 8.15% a year.

You can run it backward too. Multiply $5,000 by 1.0815 six times, and you are back at about $8,000.

Run a rate forward from today with the future value calculator →

CAGR vs ROI (total return)

ROI means return on investment. It is the whole gain or loss, as a percent of what you started with. It is also called total return. The calculator above shows it as total growth.

ROI ignores time. A 50% gain looks the same over 1 year or 20 years. CAGR fixes that by turning the gain into a rate for each year. Here are two made-up examples that both start at $4,000:

A has the bigger ROI. B grew faster each year. Use ROI to see how much you gained in all. Use CAGR to compare things held for different lengths of time.

How to work out the return on a stock or fund

1. Start value: what you paid, with any fees to buy.
2. End value: what it is worth now, plus any dividends you were paid in cash.
3. Time: the years between the two, or the two dates.
4. Enter all three above. You get the total return and the CAGR.

Here is a made-up example. You paid $2,500 for some shares. Four years later they are worth $3,200, and you were paid $180 in cash dividends. Count the dividends, and the total return is 35.2%, a CAGR of about 7.83%. Leave them out, and you get 28%, or about 6.37% a year.

Percentage loss: why a loss needs a bigger gain to recover

To find a percent gain or loss, divide the change by the start value. $800 that grows to $1,000 is a 25% gain. $1,000 that falls to $800 is a 20% loss. It is the same $200, but the start is different.

That is why a loss takes a bigger gain to undo. Say $10,000 falls 50% to $5,000. A 50% gain only brings it to $7,500. It takes a 100% gain to get back to $10,000.

This table is plain math. It is not a guess about any market.

CAGR vs average return

A simple average adds up each year’s percent change and divides by the number of years. It ignores compounding, so it can paint a rosy picture. Here is $1,000 that rose 50% one year and fell 50% the next:

The simple average of +50% and −50% is 0%, which says you broke even. But $1,000 became $750. The CAGR is about −13.4% a year, and that is the number that matches what really happened to the money.

Funds must show their "average annual total returns" for the past 1, 5 and 10 years. To compare one with a CAGR, use the same start and end dates.

See the S&P 500’s past average return next to its CAGR in the S&P 500 calculator →

How to find CAGR in Excel or Google Sheets

Put the start value in B1, the end value in B2 and the number of years in B3. Then use either formula:

• =(B2/B1)^(1/B3)-1 is the formula written out.
• =RRI(B3,B1,B2) does the same math. RRI takes the years first, then the start value, then the end value.
• With dates in C1 and C2 instead of years, use =(B2/B1)^(1/YEARFRAC(C1,C2,1))-1.

Format the cell as a percent. All three work the same way in Google Sheets. This calculator counts the days between two dates and divides by 365.25, so YEARFRAC may differ in the last decimal.

Negative CAGR, zero and other odd cases

• End below start: the CAGR is negative. $8,000 that fell to $2,000 over 3 years shrank about 37% a year.
• End of zero: the CAGR is −100% a year, no matter how many years it took.
• Start of zero or less: there is no CAGR. You cannot divide by zero, and growth from nothing has no rate. The same goes for a value that swings from a loss to a gain.
• Zero years: there is no CAGR either. A yearly rate needs some time to pass.

The calculator above tells you which case you hit instead of showing a wrong number.

Partial years and dates

Years do not have to be whole. $20,000 that became $26,000 in 2.5 years has a CAGR of about 11.07% a year. If you know the dates but not the years, switch the calculator to dates. It counts the days and divides by 365.25. January 1, 2020 to July 1, 2023 is 1,277 days, or about 3.5 years.

Be careful with spans under a year. $1,000 that became $1,100 in 6 months gained 10%. Stretched to a full year, that is a CAGR of 21%. That does not mean the next 6 months will repeat it.

What CAGR leaves out

• The bumps. Two values can share a CAGR, one rising smoothly and one crashing and recovering. CAGR cannot tell them apart.
• Money in and out. CAGR assumes nothing was added or taken out. If you made deposits, the CAGR of your balance mixes your savings with growth.
• Inflation, fees and taxes. CAGR counts none of them. A 7% CAGR with 3% inflation is about 3.9% a year after inflation.
• The future. A CAGR describes the past span you picked. Pick different dates and you can get a very different rate.

See how much is left after inflation and fees with the investment calculator →

Grow a value at a fixed rate with the compound interest calculator →