Geometric Mean Return Calculator
Turn a series of yearly returns into the geometric mean annual return โ the true compounded rate. Compares against the arithmetic mean. Educational. Runs in your browser.
One return per year โ separate with commas, spaces, or new lines. A negative year is a loss (e.g. -10 = down 10%).
The geometric mean โ the constant annual rate that reproduces the same compounded result โ is the honest measure of multi-year performance. It is always โค the arithmetic mean, and the gap widens with volatility: +50% then โ50% averages 0% arithmetically but is โ13.40% per year geometrically, because you end with only 75% of your money. Educational; everything runs in your browser.
About this tool
When an investment earns different returns each year, the arithmetic average of those returns overstates what you actually earned โ sometimes badly. The geometric mean is the honest figure: it is the single constant annual rate that, compounded over the period, reproduces the exact ending value. The formula is geometric mean = [(1 + rโ)(1 + rโ)โฆ(1 + rโ)]^(1/n) โ 1, where each rแตข is a yearly return expressed as a decimal. This calculator takes any list of yearly returns and reports that compounded rate, the total cumulative return, and the arithmetic mean alongside it so the difference is visible. The classic illustration is a portfolio that gains 50% one year and loses 50% the next: the arithmetic average is 0%, suggesting you broke even, but you are left with only 75% of your starting money, which is a geometric mean of about โ13.4% per year. The gap between the two means grows with volatility, which is why the geometric mean (equivalently, the compound annual growth rate when applied to the start and end values) is the standard for reporting fund and portfolio performance. It is educational. Everything runs in your browser; nothing is uploaded.
How to use it
- Enter each year's return as a percent, separated by commas, spaces, or new lines.
- A loss is a negative number โ โ10 means the value fell 10% that year.
- Read the geometric mean annual return โ the constant rate that yields the same compounded result.
- Compare it to the arithmetic mean to see how much volatility costs.
Frequently asked questions
- Why use the geometric mean instead of a simple average?
- The arithmetic average of yearly returns ignores compounding and overstates real performance. The geometric mean is the constant annual rate that reproduces the actual ending value, so it is the correct figure for multi-year investment returns.
- How is the geometric mean return calculated?
- Multiply the growth factors (1 + return) for every year, take the n-th root where n is the number of years, then subtract 1. For returns of 25%, โ10%, and 20%: (1.25 ร 0.90 ร 1.20)^(1/3) โ 1 = 1.35^(1/3) โ 1 โ 10.52%.
- Is the geometric mean the same as CAGR?
- Effectively yes. The compound annual growth rate (CAGR) computed from a starting and ending value equals the geometric mean of the underlying yearly returns over the same period. Both describe one smoothed annual rate.
- Why is the geometric mean always lower than the arithmetic mean?
- Because of volatility drag: a loss requires a larger gain to recover, so swings reduce compounded growth. The geometric mean is always โค the arithmetic mean, and the two are equal only when every yearly return is identical.
- What if one year was โ100%?
- A โ100% year means the investment went to zero, so the cumulative value is zero and no positive recovery is possible โ the geometric mean is undefined. The calculator flags this rather than returning a misleading number.
- Is anything uploaded?
- No. All parsing and math run entirely in your browser.