CALCULATE WITH CONFIDENCE

Averages & Means

Mean Comparison Calculator

Compare harmonic, geometric, arithmetic, and root mean square values on one dataset.

Averages & Means

Compare four classical means

H ≤ G ≤ A ≤ RMS
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Positive values

Use ordinary decimals; blank rows are ignored.

Mean ordering

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Enter valid values to see the result.

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Understand the subject

Why are there different kinds of mean?

Different means preserve different relationships. The arithmetic mean fits additive quantities; the geometric mean fits multiplicative factors; the harmonic mean fits certain rates; and root mean square emphasizes magnitude by squaring first.

For positive values, these four means always follow the same order—but that order does not decide which one answers your real question.

The relationship

The classical ordering of means

All four are equal only when every entered value is equal.

See the separation

The same values, four different centers

HarmonicRates over equal numerator-side exposure

GeometricMultiplicative factors and proportional change

ArithmeticAdditive values with equal influence

RMSMagnitude where signs should not cancel

Worked example

Compare the values 1 and 4

Each method processes the same two positive values through a different relationship.

H = 1.6 ≤ G = 2 ≤ A = 2.5 ≤ RMS = √8.5 ≈ 2.915

Interpret with care

Choose by meaning, not by size

The smallest or largest result is not automatically more conservative or more accurate. Identify what is being held equal—observations, multiplicative periods, distance or another exposure, or squared magnitude—before choosing a mean.

Quick guide

How to use this calculator

  1. Enter strictly positive values so all four means are defined.
  2. Inspect each result and the H≤G≤A≤RMS ordering.
  3. Choose the mean based on the quantity's meaning, not merely its numerical position.

Calculation method

Evaluate four distinct averaging relationships

The same data are processed through reciprocal, multiplicative, additive, and squared relationships. Equality throughout occurs exactly when all entered values are equal.

Worked example

Compare 1 and 4

The means separate because the inputs differ.

H=1.6 ≤ G=2 ≤ A=2.5 ≤ RMS≈2.915

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

All values must be strictly positive for a complete four-mean comparison.

Decision boundary

The ordering theorem does not determine which mean matches a real-world estimand.