How do you calculate CAGR?

Divide the ending value by the beginning value, take the root equal to the number of years, and subtract 1. {{$5000}} to {{$8000}} over 4 years: 8000 ÷ 5000 = 1.6; the fourth root of 1.6 is 1.1247; minus 1 is 12.47% a year. On a calculator, raise 1.6 to the power 0.25. The page shows exactly this working.

What is the difference between CAGR and average annual return?

The average adds the yearly percentages and divides by the years; CAGR compounds them. +50% then −30% averages +10% a year but the money went from 100 to 150 to 105, a CAGR of 2.47%. CAGR is the one that matches what actually happened to the money.

What CAGR doubles money in 5, 7 or 10 years?

14.87% for 5 years, 10.41% for 7 and 7.18% for 10 — from doubling time = ln 2 ÷ ln(1 + rate), or the rule of 72 as a rough guide (72 ÷ years). The page shows the doubling time for whatever rate it finds.

Can CAGR be used for revenue, users or anything else?

Yes — anything with a start value, an end value and a number of years: company revenue, a city's population, a website's traffic. The arithmetic is the same; only the interpretation changes.

Is CAGR the same as the return I would see on a mutual fund fact sheet?

Usually yes for the '3-year' and '5-year annualised' figures — those are CAGRs of the fund's value with distributions reinvested. A 'since inception' figure is a CAGR over a fractional number of years.

CAGR Calculator (Compound Annual Growth Rate, with Steps)

The compound annual growth rate between a starting and ending value, with total growth, the simple average for contrast and the doubling time.

Inputs

CurrencyAuto (USD)

Beginning value

1,000100,000,000

Ending value

1,000100,000,000

Years

0.150

Include CalculateEveryday mark

CAGR

14.87%

Beginning value$1,031

Ending value$2,062

+100%

Working: (end ÷ start)^(1 ÷ 5) − 1 = 2.0000^0.2000 − 1 = 0.1487
Beginning value: $1,031
Ending value: $2,062
Total growth over 5 years: 100.00% (2.00×)
Simple average per year (not CAGR): 20.00%
Doubling time at this rate: 5.0 years

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What each CAGR input means

Beginning value: The starting value: an investment, revenue, users, a population.
Ending value: The ending value, in the same unit.
Years: Years between the two. Fractions are fine — 2.5 for two and a half years.

CAGR formula

CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1 · total growth = ending ÷ beginning − 1 · doubling time = ln 2 ÷ ln(1 + CAGR)

\text{CAGR} = \left(\frac{V_{\text{end}}}{V_{\text{start}}}\right)^{1/n} - 1

The compound annual growth rate is the single yearly rate that, applied every year with compounding, would take the starting value to the ending value in the time given. It answers 'what did this earn per year?' honestly, because it accounts for growth on growth: doubling in five years is not 20% a year but 14.87%, since each year's gain is earned on a larger base. Finance texts call it the geometric average return. It smooths out the path — an investment that went up 50% and then down 30% has the same CAGR as one that rose steadily to the same end point — so it says nothing about volatility along the way. The page shows the working, the total growth over the period, the simple average per year for contrast, and how long the money takes to double at that rate.

CAGR worked example

$100,000 that becomes $200,000 in five years: the ratio is 2, the fifth root of 2 is 1.1487, and 1.1487 − 1 = 0.1487, so the CAGR is 14.87% a year. Check: 1.1487⁵ = 2.00. The simple average, 100% ÷ 5 = 20% a year, overstates it, because 20% compounded for five years would give 2.49×, not 2×. At 14.87% money doubles every 5 years by construction; at 7.18% it would take ten.

More CAGR examples

Revenue growing from 50,000 to 80,000 in four years: (80,000 ÷ 50,000)^(1/4) − 1 = 1.6^0.25 − 1, a CAGR of 12.47% — not the 15% a simple average of the 60% total gives.

A portfolio that fell from 10,000 to 7,500 in three years: 0.75^(1/3) − 1 = −9.14% a year (shown as -9.14%), a steeper yearly loss than the −8.33% simple average suggests.

Where the CAGR calculator can give the wrong answer

CAGR needs a single start and end amount with nothing added or withdrawn in between. A portfolio with monthly contributions needs a money-weighted return (XIRR) instead; running it through CAGR credits the contributions as growth.
It hides the path. A steady 14.87% a year and a wild ride that happens to end at the same place have identical CAGRs; look at the yearly returns or a drawdown figure for the risk.
Fractional years are fine (2.5 years for 30 months) and matter: a 40% gain over 2.5 years is 14.4% a year, over 3 years 11.9%.
A falling value gives a negative CAGR, which is correct; a value that went to zero cannot be expressed as a rate at all, and the page refuses zero.
Dividends and coupons that were paid out, not reinvested, are not in the ending value, so CAGR on price alone understates the total return of an income-paying investment.

Spotted a mistake? Tell us

CAGR FAQ

: Divide the ending value by the beginning value, take the root equal to the number of years, and subtract 1. {{$5000}} to {{$8000}} over 4 years: 8000 ÷ 5000 = 1.6; the fourth root of 1.6 is 1.1247; minus 1 is 12.47% a year. On a calculator, raise 1.6 to the power 0.25. The page shows exactly this working.
: The average adds the yearly percentages and divides by the years; CAGR compounds them. +50% then −30% averages +10% a year but the money went from 100 to 150 to 105, a CAGR of 2.47%. CAGR is the one that matches what actually happened to the money.
: 14.87% for 5 years, 10.41% for 7 and 7.18% for 10 — from doubling time = ln 2 ÷ ln(1 + rate), or the rule of 72 as a rough guide (72 ÷ years). The page shows the doubling time for whatever rate it finds.
: Yes — anything with a start value, an end value and a number of years: company revenue, a city's population, a website's traffic. The arithmetic is the same; only the interpretation changes.
: Usually yes for the '3-year' and '5-year annualised' figures — those are CAGRs of the fund's value with distributions reinvested. A 'since inception' figure is a CAGR over a fractional number of years.