Enter values, choose weighting, and view every calculation step. Export reports and inspect plots quickly. Built for learners, analysts, teachers, traders, and curious problem-solvers.
This page computes the standard or weighted geometric mean, explains each step, shows the log-based method, draws a Plotly chart, and lets you export results to CSV or PDF.
The chart compares each input value and overlays the computed geometric mean as a horizontal reference line.
| Example | Values | Weights | Formula snapshot | Geometric mean |
|---|---|---|---|---|
| Simple set | 2, 8, 32 | 1, 1, 1 | (2 × 8 × 32)1/3 | 8 |
| Four values | 5, 10, 20, 40 | 1, 1, 1, 1 | (40000)1/4 | 14.1421 |
| Weighted set | 2, 4 | 1, 2 | (21 × 42)1/3 | 3.1748 |
| Growth multipliers | 1.05, 1.10, 0.95 | 1, 1, 1 | (1.05 × 1.10 × 0.95)1/3 | 1.0313 |
The standard geometric mean of positive values x1, x2, ..., xn is:
GM = (x1 × x2 × ... × xn)^(1/n)
A stable logarithmic form is:
GM = exp((ln x1 + ln x2 + ... + ln xn) / n)
For weighted data, use:
Weighted GM = exp(Σ(w × ln(x)) / Σw) = (Π x^w)^(1/Σw)
Every input value must be strictly greater than zero, because logarithms of zero or negative numbers are undefined.
It measures the typical central value for positive numbers multiplied together, especially ratios, growth factors, and indexed changes. It is often better than the arithmetic mean when values compound.
Use it for returns, growth rates, scaling factors, and proportional changes. The arithmetic mean is better for additive quantities, while the geometric mean is better for multiplicative behavior.
Yes. Switch to weighted mode and enter one positive weight for each positive value. The calculator then applies the weighted logarithmic formula and shows each weighted contribution.
The formula relies on logarithms. Since logarithms of zero and negative values are undefined in real-number calculations, the geometric mean also requires every value to be greater than zero.
Logarithms make the calculation more stable and clearer for large datasets. They avoid overflow from huge products and still return the same geometric mean after exponentiation.
Standard mode gives every value equal importance. Weighted mode gives some values more influence by multiplying each logarithm by its weight before dividing by the total weight.
Yes. It is commonly used for investment returns, growth multipliers, inflation adjustments, and performance comparisons across periods because it respects compounding.
They include the main result, summary metrics, and the detailed per-item step table. This makes it easier to archive, share, or review the full calculation later.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.