CAGR Calculator

Compound annual growth rate answers a narrow question well: if this had grown at one steady rate every year, what rate would it have been? It smooths out a bumpy history into a single number you can compare against another investment, another business line, or a target.

The formula

CAGR = (ending value ÷ beginning value)^(1 ÷ years) - 1

The exponent is doing the work. Taking the seventh root of a growth multiple asks what number, multiplied by itself seven times, produces that multiple. That is the annual rate.

A worked example

An investment grows from $10,000 to $25,000 over seven years.

• Growth multiple: $25,000 ÷ $10,000 = 2.5
• Seventh root: 2.5^(1÷7) = 1.13985
• CAGR: 1.13985 - 1 = 13.99% a year

Check it by growing $10,000 at 13.99% seven times over: it lands back on $25,000.

Why the simple average misleads

Total growth here is 150%. Divide by seven years and you get 21.43%, which is wrong by a wide margin. The simple average ignores that each year's growth builds on a larger base, so it always overstates the real rate.

The gap widens with the size of the growth. Doubling over ten years is 7.18% a year compounded against 10% averaged. Growing tenfold over ten years is 25.9% compounded against 90% averaged. Anyone quoting the second figure is either confused or selling something.

The volatility blind spot

CAGR only looks at the first and last values. Everything between them is invisible, which is exactly what makes it useful and exactly where it can mislead.

A fund gains 50% in year one and loses 50% in year two. The average of +50% and -50% is zero, suggesting you broke even. In reality $100 becomes $150 and then $75, so you are down 25%. The CAGR over those two years is -13.4%, which is the honest answer.

Two investments can share a CAGR and feel nothing alike. One climbs steadily; the other halves in year three and recovers. The second is far harder to hold, and the single number says nothing about it. Pairing CAGR with the year-on-year figures, as the chart on this page does, is the fix.

Part-years and how to count them

The exponent takes any positive number, so nine months is 0.75 and eighteen months is 1.5. The mistake to avoid is counting the years wrong at the boundaries.

From the end of 2020 to the end of 2024 is four years, not five, even though five calendar years are named. Count the gaps between the values rather than the values themselves. Using five instead of four in the example above would report 11.03% instead of 13.99%, an error of a fifth.

Where CAGR is used

Fund factsheets quote three-year, five-year and ten-year CAGR so returns over different periods can be compared on the same scale. Company filings use it for revenue and user growth. Market research reports use it to project a sector forward, which is where it does the most damage, since a projected CAGR is a guess dressed as a measurement.

For internal targets it works well. A business at $2 million in revenue aiming for $5 million in four years needs a CAGR of 25.7%, which is a far more useful planning figure than "grow 150%".

CAGR and IRR

CAGR assumes one payment in at the start and one out at the end. Add money along the way and it breaks, because it has no way to weight a deposit made in year six against one made in year one.

Internal rate of return handles that case by discounting each cash flow by when it happened. For a portfolio you contribute to monthly, IRR is the right measure and CAGR will flatter or punish you depending on whether the market rose after your contributions. For a single lump sum left alone, the two give the same answer.

Doubling time

A CAGR converts directly into a doubling time using ln(2) ÷ ln(1 + rate). At 13.99% that is 5.3 years. The rough version, dividing 72 by the rate, gives 5.1 years and takes no calculator at all.

Working backwards to a target

Two rearrangements cover most planning questions.

To find the rate a target demands, use the same formula with the target as the ending value. A business at $2 million aiming for $5 million in four years needs (5 ÷ 2)^(1÷4) - 1 = 25.74% a year. Stating it that way makes the plan testable, since a 26% growth rate has staffing and cash implications that "get to five million" hides.

To find the time a target needs at a known rate, use logarithms:

years = ln(target ÷ start) ÷ ln(1 + rate)

Turning $10,000 into $1 million at 10% a year takes ln(100) ÷ ln(1.10) = 48.3 years. At 15% it takes 33.0 years. Fifteen years of difference for five percentage points is the clearest argument there is for caring about the rate.

Projecting forward

Running the rate in the other direction gives an ending value: start × (1 + rate)^years. $50,000 at 8% for twelve years reaches $125,909.

Use this carefully. A CAGR measured over a period that happened to contain a boom will project a future that never arrives, and the further out the projection runs the more of the answer is assumption rather than data. A ten-year forecast built on a three-year CAGR is arithmetic performed on a guess.

Comparing periods of different length

The reason fund factsheets quote CAGR rather than total return is that total returns over different lengths cannot be compared. A 60% total return over three years and an 85% total return over five sound like the second is better. As annual rates they are 16.96% and 13.10%, so the first is comfortably ahead.

Annualising puts everything on the same scale, which is the whole job the measure exists to do. It is also why regulators require the rates alongside the totals in most published performance figures.

Reading the chart

The chart on this page draws the smooth CAGR path as a single curve. Supply the yearly values and the real path appears beside it, touching the smooth line at the first point and the last and wandering everywhere in between.

That picture is the honest summary of what CAGR does. The two lines describe the same investment and tell different stories about holding it. The bar chart underneath shows each year on its own, and any bar below zero is a year the headline rate says nothing about.

Common mistakes

Counting years by calendar labels. 2020 to 2024 is four years of growth. This single error is the most common one in published CAGR figures.

Using it on values that cross zero. A business going from a $50,000 loss to a $200,000 profit has no meaningful CAGR, because the formula needs a positive starting value.

Reading it as a prediction. A 14% historical CAGR describes what happened. It carries no promise about next year, and treating it as a forecast is how sales decks are built.

Comparing different periods. A five-year CAGR ending in a boom and a five-year CAGR ending in a crash are not comparable, however similar the arithmetic looks.