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MasterMath

CAGR Calculator

Growing from 1,000 to 1,500 in ten years is 50% total growth, but a CAGR of 4.14% a year, not the 5% you get by dividing. Work out the rate that actually compounds.

Currency and number format for

Compound annual growth

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Compound annual growth—
Total growth—
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How this was worked out

    The formula

    CAGR = (ending ÷ starting)^(1 ÷ years) − 1

    Where it comes from

    The compound annual growth rate is the steady rate that would take you from the starting value to the ending one over the same period. Real growth is never that smooth, but the CAGR is what makes two investments comparable regardless of how bumpy the ride was.

    How to work it out by hand

    1. Divide the ending value by the starting value
    2. Raise that to the power of one divided by the number of years
    3. Subtract one
    4. Multiply by 100 for a percentage

    What is worth knowing

    The reason CAGR beats a simple average is compounding: growing 4.14% ten years running turns 1,000 into 1,500, whereas 5% a year would reach 1,629. The naive average always overstates, and the error grows with both the period and the volatility. What CAGR hides is that volatility: two investments with the same CAGR can have taken completely different paths, and one of them may have been down 60% along the way. That is why CAGR is usually read alongside maximum drawdown.

    Frequently asked questions

    What is the difference between CAGR and average return?

    The average adds the yearly returns and divides; CAGR compounds them. Whenever returns vary, the average is higher than the CAGR, and the gap grows with volatility.

    Can CAGR be negative?

    Yes, whenever the ending value is below the starting one. It then tells you the steady annual rate at which the investment shrank.

    Does CAGR show risk?

    Not at all. It smooths the whole period into one figure and says nothing about the falls along the way. Pair it with the maximum drawdown.

    Does it work for anything other than money?

    Yes. It is used for revenue, users, population or any quantity that grows over time.