CAGR calculator (compound annual growth rate)

What CAGR means

CAGR, the compound annual growth rate, answers one question: if something had grown at exactly the same rate every year, what rate would get it from where it started to where it ended? It is the standard way to express growth over several years as a single annual number, used for investment returns, company revenue, a country's GDP, a user base or house prices.

It exists because the obvious alternative is misleading. If an investment doubles in five years, it is tempting to say it returned 20% a year (100% divided by 5). It did not. Twenty percent a year compounded for five years turns $1 into $2.49, not $2. The correct annual rate is 14.87%, because each year's growth is earned on a balance that already includes the previous years' growth. CAGR builds that compounding in.

The same logic makes CAGR the fair way to compare things measured over different periods. A fund that gained 40% over three years (11.87% a year) did better than one that gained 60% over five (9.86% a year), even though 60 is the bigger number. Put both into the calculator and the comparison is immediate.

The CAGR formula

CAGR = (EV ÷ BV)^1/n − 1

Where EV is the ending value, BV the beginning value and n the number of years. The number of years does not have to be whole: 30 months is 2.5 years, and the formula works the same way. On a spreadsheet the formula is =(EV/BV)^(1/n)-1, or =RRI(n, BV, EV) in Excel and Google Sheets.

Turned around, the same relationship gives the ending value from a rate:

EV = BV × (1 + CAGR)ⁿ

That is the "find ending value" mode in the calculator. $10,000 at 8% a year for 2.5 years gives $12,121.58, because 1.08 to the power of 2.5 is 1.2122. If the ending value is lower than the beginning value, CAGR is negative: $10,000 falling to $8,000 over three years is −7.17% a year. If the ending value is zero, CAGR is −100% and the formula has nothing more to say.

A worked example (hypothetical)

A hypothetical portfolio starts at $10,000 and is worth $25,000 seven years later, with nothing added or withdrawn.

1. Ratio: $25,000 ÷ $10,000 = 2.5, a multiple of 2.50×, or a total return of 150%.
2. Annualise: 2.5^1/7 = 1.1399.
3. Subtract one: CAGR = 13.99% a year.

The year-by-year table in the calculator shows what that smoothed path looks like: $11,398.52 after year one, $14,809.68 after year three, $19,241.67 after year five and $25,000.00 after year seven. Notice the growth in each year gets larger in money terms ($1,398.52 in year one, $3,067.33 in year seven) even though the rate is the same, which is compounding at work.

The simple average, 150% ÷ 7 = 21.43% a year, overstates the yearly rate by more than seven percentage points. Quoting that figure as an annual return is one of the most common ways growth gets exaggerated, sometimes innocently. Remember too that this is a past result in a made-up example: a portfolio that compounded at 14% for seven years can return far less, or lose money, over the next seven.

Where CAGR misleads, and what to use instead

It hides the ride. Two investments can both show a 10% CAGR over ten years while one rose steadily and the other fell by half in the middle. CAGR cannot tell them apart. Read it next to the largest drawdown; the drawdown calculator shows how much any fall needs to recover.

It is sensitive to the start and end dates. Starting a measurement at a market low and ending at a high produces a flattering CAGR; shifting either date by a few months can change it substantially. When you see a CAGR quoted, check the window.

It ignores money moving in and out. If you added $5,000 halfway through, comparing the first and last balances would count your own deposit as growth. For accounts with regular contributions, use a money-weighted return (the internal rate of return, XIRR on a spreadsheet) instead.

Use real figures where it matters. CAGR on a nominal value includes inflation. To get the real growth rate, divide rather than subtract: at 3% inflation, a 7% nominal CAGR is about 3.9% in real terms (1.07 ÷ 1.03 − 1). Simply subtracting gives 4%, close enough at low rates but increasingly wrong as rates rise.

For a single period with no compounding question, the ROI calculator is simpler. To see how long a given CAGR takes to double money, try the rule of 72 calculator.

CAGR versus average annual return

The most common confusion around CAGR is the difference between it and the plain average of yearly returns. The arithmetic average adds each year's percentage and divides by the number of years. CAGR, the geometric average, asks what single rate would have produced the same final amount. When returns vary, the two always differ, and the arithmetic average is always the higher of the two.

Take a hypothetical $10,000 that rises 20% in year one, falls 10% in year two and rises 15% in year three. The arithmetic average is (20 − 10 + 15) ÷ 3 = 8.33% a year. But the money went $10,000 to $12,000 to $10,800 to $12,420, and putting $10,000, $12,420 and 3 years into the calculator gives a CAGR of 7.49%. The gap is the cost of volatility: a loss is applied to a larger balance than the gain that preceded it.

The extreme case makes it obvious. A gain of 50% followed by a loss of 50% averages 0%, yet $10,000 becomes $15,000 and then $7,500. The CAGR over those two years is −13.40%, which is what actually happened to the money.

So when a fund, a product or a person quotes an "average return", ask which average. The arithmetic one describes a typical year; only CAGR describes the growth of the money over the whole period.

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