Geometric Mean

Tap a term to see what it means, or .

Calculate

Example: an investment returned +10%, −20% and +30% in three years in a row, that is, it was multiplied by 1.1, 0.8 and 1.3. What was the average return per year? Change the values to work out your own case.

Values x_i All positive, separated by spaces or commas.

Step by step

What each term means

Geometric Mean (G): The value that, multiplied by itself n times, gives the same product as the data. It is the right average for factors that multiply, such as growth rates and indices.
Root Index (n): The number of values. The n-th root undoes the product of n factors, just as dividing by n undoes the sum in the arithmetic mean.
Product (Πxᵢ): The product of all the values: x₁ · x₂ · … · xₙ. For many values, it is safer to add up the logarithms, which gives the same result without the calculation blowing up.