Geometric Mean Calculator
Multiplies three positive numbers together and takes the cube root to give the geometric mean, which suits growth rates and ratios.
Recent
Formula
How the calculation works
The calculator multiplies the three values together to get a single product of the whole set.
It then takes the cube root of that product, because three numbers are being averaged.
The result is the value that, if repeated three times, would multiply to the same product as the original set.
Common mistakes
- Entering a zero or a negative number, since the geometric mean here is only defined for positive values.
- Using the geometric mean for values that are added rather than multiplied, where the ordinary average is the right choice.
When to use it
- Use it to average percentage growth rates over several years, where the arithmetic mean would overstate the result.
- Use it to find a central ratio for measurements that multiply, such as returns or scale factors.
Worked example
The geometric mean of 4, 9 and 25 is the cube root of 900, which is about 9.65.
Common questions
When is the geometric mean better?
It suits rates and ratios that compound, such as yearly growth, where the arithmetic average would be pulled up by large values.
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