CALCULATE WITH CONFIDENCE

Averages & Means

Weighted Geometric Mean Calculator

Combine positive multiplicative values using non-negative importance weights.

Averages & Means

Weight multiplicative values

Stable logarithmic evaluation
Paired rows

Use ordinary decimals; complete every field in each paired row.

Weighted geometric mean

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Add one positive value and matching non-negative weight per row.
  2. Use consistent weight meaning across every row.
  3. Read the normalized weighted geometric mean; weights need not sum to one.

Calculation method

Average logarithms with normalized weights

The logarithm of each value is multiplied by its weight. Their weighted sum is divided by total weight before exponentiation.

Worked example

Weight two growth factors

Factors 1.10 and 1.20 with weights 1 and 3 give more influence to 1.20.

G = exp[(1 ln1.10 + 3 ln1.20)/4]

Supported inputs

Precision and limits

List size

Add 1–100 labelled value rows.

Decimal size

Each value may contain up to 200 digits and 100 decimal places.

Exactness

Exact rational results are never replaced by a rounded decimal; approximations are labelled.

Domain

Values must be strictly positive; weights may be zero but their total must be positive.

Weight meaning

The arithmetic is valid only when a weighted multiplicative center is meaningful for the entered quantities.