CAGR Calculator

CAGR = (Ending value ÷ Starting value)^(1 ÷ Years) − 1

V₀

The starting value, which must be greater than zero for the rate to exist at all

Vₜ

The ending value, which may be zero — a total loss gives a rate of exactly −100%

n

The number of whole years between the two values

CAGR

The constant annual growth rate that would take V₀ to Vₜ in n years

Use it to compare two runs of different lengths, which is the only way to compare them fairly. A three year investment that tripled and a fifteen year one that quadrupled are not obviously ordered by looking at the totals; their annualised growth rates are 44.225% and 9.682%, and now they are. The same arithmetic is what an annual report calls a compound annual growth rate for revenue, and what a fund factsheet calls an annualised return. Two cautions go with it. First, the rate is a smooth stand-in for a bumpy path — it is the constant rate that would have produced the same endpoint, not a rate anything actually earned, and two investments with the same CAGR can have wildly different risk. Second, it says nothing about the years before or after the two endpoints, so choosing a favourable pair of dates will flatter any series.

1. 10,000 growing to 25,000 over ten years

   1. Multiple: 25,000 ÷ 10,000 = 2.5
   2. Total return: 2.5 − 1 = 150%
   3. Annualised: 2.5^(1 ÷ 10) − 1 = 1.095958 − 1 = 9.596%

   This is the page's default. The check worth doing by hand is the other direction: 10,000 × 1.09596^10 = 25,000.40, so the rate really does reproduce the endpoint when applied evenly for all ten years.

2. 5,000 growing to 8,000 over four years

   1. Multiple: 8,000 ÷ 5,000 = 1.6
   2. Total return: 1.6 − 1 = 60%
   3. Annualised: 1.6^(1 ÷ 4) − 1 = 1.124682 − 1 = 12.468%

   A modest total return spread over only four years produces a rate well into double digits — the shorter the period, the larger the annualised figure for the same total. That asymmetry is why a one-year return annualised to a decade tells you almost nothing.

3. 20,000 falling to zero over five years

   1. Multiple: 0 ÷ 20,000 = 0
   2. Total return: 0 − 1 = −100%
   3. Annualised: 0^(1 ÷ 5) − 1 = 0 − 1 = −100%

   The one case where a total loss still has a well-defined answer, and the answer is exactly −100%: the constant rate that takes any positive value to zero is a complete loss every year. Note that the multiple is 0, so the arithmetic never divides by it. Read the rate as a boundary rather than a forecast — an investment that lost everything did not do so at a steady −100% a year.

The rate this page returns is a summary, and summaries lose things. It is computed from exactly two values and the number of years between them, so it says nothing about what happened in between: two investments that both went from 10,000 to 25,000 over ten years have the same CAGR whether one rose smoothly or fell by half in year three and recovered. It also cannot see the years outside the window you typed, and because of that it is unusually easy to mislead with — pick a peak as the start and a trough as the end and any long-run record looks disastrous; reverse them and it looks spectacular. The starting value must be greater than zero, since growing from nothing to something has no finite annualised rate. The number of years must be a whole number, which rules out the fractional-year calculations some fund factsheets use. Cash flows are not modelled at all: if money was added or withdrawn during the period, the true annualised return is an internal rate of return and this page will give the wrong answer, sometimes badly. Tax, inflation and fees are all absent, so a nominal CAGR of 9.596% over a decade is not 9.596% of real purchasing power. Finally, no currency symbol is attached.

How do I calculate CAGR?

Divide the ending value by the starting value, take that to the power of one over the number of years, and subtract one. For 10,000 growing to 25,000 over ten years: 25,000 ÷ 10,000 = 2.5, then 2.5^(1 ÷ 10) = 1.095958, and 1.095958 − 1 = 9.596%. That is the compound annual growth rate — the single steady rate that would have produced the same endpoint over the same number of years.

What is the difference between CAGR and total return?

Total return is the whole change from start to finish with no reference to time; CAGR spreads that same change out into a rate per year. Going from 10,000 to 25,000 is a total return of 150% whether it happened over one year or twenty. The CAGR is 150.000% over one year and 4.688% over twenty. Both numbers describe the same run, and a page that quotes only one of them is hiding something.

Can CAGR be negative?

Yes, whenever the ending value is below the starting value. Falling from 20,000 to 12,000 over five years is a CAGR of −9.712%, and a complete loss gives exactly −100%. A negative rate is not an error and the arithmetic handles it without special cases, because the ratio of the two values is between zero and one and raising it to a positive power keeps it there.

What happens if the investment goes to zero?

The rate is exactly −100%, and that is a real answer rather than a failure. No positive starting value can reach zero at any rate short of a total loss every year, so −100% is the only rate consistent with the two endpoints. The multiple comes back as 0, which is why the calculation never divides by it. What the page cannot tell you is how long the collapse took — the endpoints say nothing about the path.

Why is the annualised return so high on a short period?

Because annualising multiplies a short run up to a full year. A 60% total return over four years is 12.468% a year, but the same 60% over one year is 60%, and over twenty years it is only 2.378%. The shorter the window, the less the rate means as a description of anything sustainable — a single good quarter annualises to a figure no investment earns for long. Compare rates only across similar periods.

Does CAGR account for money added along the way?

No, and this is the most common way the number is misused. It compares exactly two values and assumes nothing moved in between. If you contributed to the account or withdrew from it, part of the change is your own money rather than growth, and the true annualised figure is an internal rate of return, which weights each cash flow by how long it was invested. A portfolio that grew because you paid into it will show a flattering CAGR on this page.

• Compound Interest Calculator — the forward form of the same equation, for checking an annualised rate — U.S. Securities and Exchange Commission (Investor.gov)
• H.15 Selected Interest Rates — the published rates an annualised return is compared against — Board of Governors of the Federal Reserve System (United States)