Geometric Mean Calculator
The right average for growth rates and returns.
The right average for growth rates and returns.
Optional.
Optional.
Geometric mean
42.426407
Arithmetic mean is 45
The geometric mean multiplies rather than adds, so it is the right average for things that compound — growth rates, returns, ratios. Averaging +50% and −50% arithmetically suggests you broke even; geometrically it correctly shows a loss, because 1.5 × 0.5 is 0.75.
How the Geometric Mean Calculator works
The geometric mean multiplies rather than adds, making it the right average for anything that compounds — growth rates, investment returns, ratios. Averaging +50% and −50% arithmetically suggests you broke even; geometrically it correctly shows a loss, because 1.5 × 0.5 is 0.75.
Also known as: average growth rate calculator · geometric mean formula · compound average return · how to calculate geometric mean
Where to go next
The Geometric Mean question rarely arrives on its own. These are the ones that usually come with it:
- Harmonic Mean Calculator — The right average for speeds and rates.
- Exponential Growth Calculator — Growth or decay, with doubling time and half-life.
- Average Calculator — Mean, median, mode, range, and standard deviation.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
What is the geometric mean?
The nth root of the product of n values. For 1, 2 and 4 it is the cube root of 8, which is exactly 2.
When should I use it instead of the arithmetic mean?
Whenever the values compound rather than add. Growth rates, returns and ratios all belong to the geometric mean; quantities that simply total up belong to the arithmetic.
Why does averaging +50% and −50% not give zero?
Because they compound. A 50% gain then a 50% loss leaves 0.75 of what you started with — a 25% loss overall, which only the geometric mean reveals.
Can it handle zero or negative values?
No. A zero makes the product zero and a negative makes the root undefined, so this page returns nothing rather than a misleading figure.
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