Softonic

Geometric Mean Calculator

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The geometric mean is the average to use when your numbers multiply rather than add, investment returns, population growth, ratios, index numbers and any rate of change. Instead of summing the values and dividing, it multiplies them and takes the nth root, so it respects compounding. Paste a list of positive numbers and the calculator returns the geometric mean, the count and the running product, all updated instantly in your browser. Because logarithms of zero and negative numbers are undefined, the tool can drop any value at or below zero for you, or keep such values when you turn that option off, which leaves the result undefined.

How to find the geometric mean

  1. 1

    Enter your numbers

    Type or paste a list separated by commas, spaces or new lines. Only positive values are valid.

  2. 2

    Choose how to handle zeros

    Leave "ignore zero/negative values" on to drop them automatically, or turn it off to keep them and get an undefined result.

  3. 3

    Read the result

    The geometric mean, the count of values used and the total product appear together and update as you type.

The formula

The geometric mean of n positive numbers is the nth root of their product:

GM = (x₁ · x₂ · … · xₙ)^(1/n)

Equivalently, and the way this calculator computes it to stay accurate with large products, it works through logarithms:

GM = exp( (ln x₁ + ln x₂ + … + ln xₙ) / n )

That is exactly why every value must be positive: the logarithm of zero or a negative number is undefined.

Worked example

Take the numbers 2, 8, 32:

  • Product: 2 × 8 × 32 = 512
  • Cube root (n = 3): 512^(1/3) = 8

The arithmetic mean of the same numbers is (2 + 8 + 32) / 3 ≈ 14, far higher. The geometric mean of 8 sits “in the middle” multiplicatively: 2 × 4 = 8 and 8 × 4 = 32, a constant ratio of 4.

Arithmetic vs. geometric mean

Aspect Arithmetic mean Geometric mean
Combines values by Adding Multiplying
Best for Independent quantities (heights, scores) Rates, ratios, growth, returns
Effect of an outlier Large Dampened
Requires Any real numbers Strictly positive numbers
Result vs. the other Always ≥ geometric mean Always ≤ arithmetic mean

Common pitfalls

  • Averaging growth rates. To average a +50% year and a −50% year, convert to growth factors (1.5 and 0.5), take the geometric mean (√0.75 ≈ 0.866) and subtract 1, about −13.4% per year, not 0%.
  • Zeros and negatives. A single zero makes the product zero and the mean meaningless; negatives make it undefined. Decide deliberately whether to exclude them.
  • Percentages vs. factors. Never feed raw percentages like 50 and −50. Convert to factors (1.5, 0.5) first, then average.

Frequently Asked Questions

Use it whenever the values multiply or compound, annual investment returns, population or revenue growth rates, ratios, and index numbers. For independent additive quantities like test scores or heights, the ordinary (arithmetic) mean is correct.

The geometric mean relies on multiplying the values and taking a root, computed through logarithms. The logarithm of zero or a negative number is undefined, so the result would be meaningless. Drop those values or convert negative changes into positive growth factors first.

Convert each percentage to a growth factor (a +20% change becomes 1.2, a −10% change becomes 0.9), take the geometric mean of the factors, then subtract 1 to get the average compound rate.

The numbers you enter are sent to our server to compute the result, and in the step-by-step view they are carried in the page link between steps. They are not stored or shared and are not added to any analytics or report.

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