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Geometric Mean Return Calculator

Get the true annualized return that compounding actually delivered.

Result

10.53%
65.00%
1.65x

How it is calculated

You give the tool a starting value, an ending value and a number of years; it finds the one constant yearly rate that links them. annualized = (Final ÷ Initial)^(1/Years) − 1. Initial and Final are amounts in the same currency (the unit does not matter, only the ratio), and Years is the length of the period, decimals allowed. Alongside the annualized rate it shows the total return over the whole period, (Final ÷ Initial − 1) × 100, and the growth multiple (Final ÷ Initial) such as 1.65x. Because it works from values, not percentages, it needs both amounts above zero and years above zero; a final value of 0 returns no result. Contributions or withdrawals made during the period are not modelled, so the value must include only growth.

Worked example

An account grows from 10,000 to 16,500 in 5 years. The multiple is 16,500 ÷ 10,000 = 1.65x, so the total return is 65.00%. Raise 1.65 to the power 1/5 = 0.2: 1.65^0.2 ≈ 1.1053. Subtract 1: the geometric mean return is 10.53% per year. A plain average of 65% over 5 years would suggest 13%, which ignores compounding.

Try this example →

Common mistakes

  • Entering percentages instead of amounts. This tool wants the start and end values; use an annualized-return tool if all you have is a total percentage.
  • Including money you added later in the final value. A contribution lifts the end balance without being investment growth, so the rate comes out too high.
  • Averaging yearly returns by hand. A +50% year followed by a −50% year is not 0% on average; the money is down 25% and the geometric figure shows it.
  • Entering the number of data points rather than the number of years. Six year-end balances cover 5 years, not 6.
  • Expecting a result when the end value is zero or negative; the compound rate is not defined there.

Sources

About this calculator

The geometric mean return, also known as the compound annual growth rate (CAGR), measures the smoothed annual rate of return that would take an investment from its starting value to its ending value over a given number of years, accounting for the compounding effect of returns building on returns. It is calculated as (ending value ÷ starting value) raised to the power of (1 ÷ number of years), minus one.

Unlike a simple arithmetic average of yearly returns, which can badly overstate actual performance when returns are volatile — a 50% gain followed by a 50% loss averages to 0% arithmetically but actually leaves the investor down 25% — the geometric mean correctly reflects what compounding really delivered. This is why CAGR is the standard way investment performance is reported over multi-year periods. Start value, end value and the number of years give the compound (geometric) annual return, the steady yearly rate that links the two values.

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