Geometric Mean Calculator
Geometric Mean Calculator
Enter a list of positive numbers to calculate their geometric mean — the Nth root of their product. Unlike the regular (arithmetic) mean, the geometric mean is the mathematically correct way to average rates of change, growth percentages, and ratios.
Averaging investment returns is the classic example of why this matters: a 50% gain followed by a 50% loss does not net out to a 0% average using the arithmetic mean, but the geometric mean correctly shows the actual compounded result is a net loss. The geometric mean is undefined for zero or negative values, since a real root of a negative product isn't defined in the general case — that's why it's specifically suited to growth rates, ratios, and other strictly positive quantities rather than general-purpose datasets that might include zero or negative numbers.
- Formula: Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n) — the nth root of the product of all n values.
- Requires positive numbers: the geometric mean is undefined for zero or negative values, since you can't take a real root of a negative product in the general case — this calculator quietly excludes any non-positive entries.
- Why it matters for growth rates: averaging investment returns of +50% and −50% with a simple mean gives 0%, suggesting no net change — but the actual result is a 25% loss, which the geometric mean correctly reflects.
When should I use geometric mean instead of arithmetic mean?
Use geometric mean whenever you're averaging multiplicative values like growth rates, investment returns, or ratios — use arithmetic mean for additive quantities like everyday measurements, prices, or counts.
What happens if my dataset includes a zero or negative number?
This calculator excludes non-positive values before calculating, since the geometric mean is mathematically undefined for them — if your data legitimately includes zero or negative growth rates, consider expressing them as growth multipliers (e.g. −50% becomes 0.5) instead.
Geometric Mean Calculator
Enter a list of positive numbers to calculate their geometric mean — the Nth root of their product. Unlike the regular (arithmetic) mean, the geometric mean is the mathematically correct way to average rates of change, growth percentages, and ratios.
Averaging investment returns is the classic example of why this matters: a 50% gain followed by a 50% loss does not net out to a 0% average using the arithmetic mean, but the geometric mean correctly shows the actual compounded result is a net loss. The geometric mean is undefined for zero or negative values, since a real root of a negative product isn't defined in the general case — that's why it's specifically suited to growth rates, ratios, and other strictly positive quantities rather than general-purpose datasets that might include zero or negative numbers.
- Formula: Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n) — the nth root of the product of all n values.
- Requires positive numbers: the geometric mean is undefined for zero or negative values, since you can't take a real root of a negative product in the general case — this calculator quietly excludes any non-positive entries.
- Why it matters for growth rates: averaging investment returns of +50% and −50% with a simple mean gives 0%, suggesting no net change — but the actual result is a 25% loss, which the geometric mean correctly reflects.
When should I use geometric mean instead of arithmetic mean?
Use geometric mean whenever you're averaging multiplicative values like growth rates, investment returns, or ratios — use arithmetic mean for additive quantities like everyday measurements, prices, or counts.
What happens if my dataset includes a zero or negative number?
This calculator excludes non-positive values before calculating, since the geometric mean is mathematically undefined for them — if your data legitimately includes zero or negative growth rates, consider expressing them as growth multipliers (e.g. −50% becomes 0.5) instead.