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
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Paired rows

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

Weighted geometric mean

—

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Feedback

Understand the subject

What is a weighted geometric mean?

A weighted geometric mean combines positive multiplicative factors when some observations represent more exposure or importance than others. It is the multiplicative counterpart of a weighted average.

The relationship

The defining relationship

The positive xi are factors and wi are non-negative weights. Only their relative size matters: multiplying every weight by the same constant changes nothing.

See the idea

More weight gives a factor more influence

Worked example

Weight two growth factors

Factors 1.10 and 1.20 with weights 1 and 3 give Gw = exp[(ln 1.10 + 3 ln 1.20) ÷ 4] ≈ 1.174.

Interpret with care

Choose the relationship that fits

Use it for factors or ratios that compound. Do not use it for ordinary additive amounts such as money totals or test points.

For a side-by-side view of the classical means, use the Mean Comparison Calculator.

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.