Geometric mean calculator

Paste a list of positive numbers separated by commas, spaces or new lines. You get the geometric mean, the nth root of their product, plus the arithmetic mean and the count.

NumbersPositive numbers separated by commas, spaces or semicolons.

Geometric mean6

Arithmetic mean: 6.33333333333
Count: 3

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How to use it

Enter your numbers.
Read the geometric mean. The arithmetic mean is shown for comparison.

How it works

The geometric mean is (x₁ × x₂ × … × xₙ)^(1/n). The calculator takes the mean of the natural logs and raises e to that power, which gives the same value and does not overflow on long lists.

Worked example

For 4, 9 and 6:

Product: 4 × 9 × 6 = 216
Cube root of 216 = 6
Arithmetic mean: 19 / 3 ≈ 6.333

Tips

To average percentage growth, convert each to a factor first (5% becomes 1.05), take the geometric mean, then subtract 1.
Do not mix units in one list.

Frequently asked questions

What is the geometric mean?

The nth root of the product of n numbers. For 4 and 9 it is the square root of 36, which is 6.

When should I use the geometric mean?

When values multiply, such as growth factors, ratios or index numbers. The average of growth factors 1.10 and 1.20 over two periods is the square root of 1.32, about 1.149.

Why must the numbers be positive?

The root of a product that includes zero is zero, and a negative product has no real root for an even count. This calculator accepts only numbers above zero.

How is it different from the arithmetic mean?

For positive numbers that are not all equal, the geometric mean is always smaller than the arithmetic mean. For 4 and 9 they are 6 and 6.5.

More in Math

All tools in this category: Math ·Updated November 3, 2026