Find the compound annual growth rate between two values and see the year-by-year path it implies.
CAGR, the compound annual growth rate, is the constant yearly rate that would take a starting value to an ending value over a given number of years. It is the standard way to describe how an investment, a revenue line or a customer base grew, because it collapses a messy trajectory into a single comparable number. Going from R$ 10,000 to R$ 25,000 in five years is a CAGR of 20.11% a year: multiply by 1.2011 five times and you land back on R$ 25,000.
The formula is the final value divided by the initial one, raised to the power of one over the number of years, minus one. The reason it is not simply the total growth divided by the years is compounding: in the example above the total growth is 150%, and dividing that by five would suggest 30% a year — half again as much as the real rate. The year-by-year table makes the gap visible, showing what the value would be at the end of each year at the compound rate. Fractional periods work the same way; 18 months is 1.5 years and the exponent handles it with no special case.
CAGR is a description, not a prediction, and it deliberately hides the path. A fund that jumped 80% and then fell 40% can have the same CAGR as one that grew steadily to the same endpoint, and they are very different things to have lived through — CAGR says nothing about volatility, drawdowns or the risk of either. It also ignores contributions and withdrawals made along the way, as well as taxes and inflation, so what really matters is how far the nominal rate sits above inflation. Use it to compare, not to forecast: this is an educational calculation and not a recommendation to invest in anything. All the math runs in JavaScript on your own device and nothing you type leaves the page.
CAGR = ((final value ÷ initial value) ^ (1 ÷ number of years)) − 1, expressed as a percentage. The value after n years is initial value × (1 + CAGR)^n.
Divide the final value by the initial value, raise the result to the power of one divided by the number of years, and subtract one. From R$ 10,000 to R$ 25,000 in 5 years: (25,000 ÷ 10,000)^(1 ÷ 5) − 1 = 20.11% per year.
The average adds up the yearly growth rates and divides by how many there are, which ignores compounding and almost always overstates the result. CAGR is the single rate that actually reproduces the ending value.
Yes. When the final value is lower than the initial one the rate is negative, describing a constant yearly shrinkage. Both values must be above zero, since a final value of zero or less has no real compound rate.
Yes — convert to years first: 18 months is 1.5 and 30 months is 2.5. The field accepts decimals, so the exponent handles fractional periods correctly.
No. Everything is calculated in JavaScript on your device. Nothing you type is transmitted or stored.
Vai.la turns any URL into a short link with click statistics, QR Code and your own biolink.
Vai.la is not responsible for how the tools are used or for decisions made based on their results.