mathematics calculator

Average Calculator

Calculate arithmetic, weighted, geometric, and harmonic means plus median, mode, range, and RMS.

Result

Enter values and choose Calculate.

Formula version 1.0.0 · Up to 1,000 finite values.

Descriptive statistics

Average formulas and worked examples

Different averages answer different questions. Choose a mode that matches the data and interpretation.

Arithmetic and weighted means

mean = Σx / n; weighted mean = Σ(wx) / Σw.

Example: mean of 2, 4, 9 is 5.

Geometric and harmonic means

geometric = (Πx)^(1/n); harmonic = n / Σ(1/x).

Geometric inputs cannot be negative; harmonic inputs cannot be zero.

Median and mode

The median is the middle sorted value (or mean of two middle values). Modes are the most frequent values.

Example: 1, 2, 2, 7 has median 2 and mode 2.

Range and RMS

range = max − min; RMS = √(Σx²/n).

How to use this calculator

Choose a Calculation type that matches the question you need to answer.
Enter 1 to 1,000 finite numbers in Values, separated by commas, spaces, semicolons, or new lines.
For Weighted average, enter one nonnegative number in Weights for every value; the total weight must be greater than zero.
Select Calculate, then read Result together with Count, Sum, Min, Max, and Show calculation steps.

Symbols and units

Symbol	Meaning	Unit or domain
`x`	One value in the entered data set	Same unit as the data
`n`	Number of entered values	Count from 1 to 1,000
`Σ`	Sum of the following terms over all values	Depends on the summed term
`w`	A nonnegative weight assigned to a value	Relative weight
`Π`	Product of all entered values	Product of input units
`min / max`	Smallest / largest entered value	Same unit as the data
`RMS`	Root mean square, √(Σx²/n)	Same unit as the data

Checked examples

Arithmetic mean of four values

Inputs: Calculation type: Arithmetic mean; Values: 2, 4, 6, 8

Calculation: (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4

Result: 5

The four values have an arithmetic mean of 5.

Check: average-general.test.ts — calculates arithmetic and weighted means

Weighted average

Inputs: Calculation type: Weighted average; Values: 78, 122, 131; Weights: 200, 300, 500

Calculation: (78×200 + 122×300 + 131×500) ÷ (200 + 300 + 500) = 117,700 ÷ 1,000

Result: 117.7

Larger weights make 131 contribute more to the result than 78 or 122.

Check: average-general.test.ts — calculates arithmetic and weighted means

Median and tied modes

Inputs: Calculation type: Mode; Values: 1, 1, 2, 2, 3

Calculation: 1 occurs twice; 2 occurs twice; 3 occurs once.

Result: 1, 2

The data set is bimodal because two values share the highest frequency.

Check: average-general.test.ts — returns multiple modes and range

Assumptions, rounding, and limits

Tokens are parsed as numbers after splitting on commas, spaces, semicolons, or new lines; an empty or nonnumeric token set is invalid.
Arithmetic mean, median, mode, range, and RMS accept finite negative, zero, and positive values.
Geometric mean rejects negative values; if any value is zero, the result is zero.
Harmonic mean rejects zero because reciprocals of zero are undefined.
Weighted average requires matching value and weight counts, nonnegative weights, and a positive total weight.
The mode result can contain more than one value when frequencies tie.
Calculations retain JavaScript numeric precision; the interface rounds displayed values to at most 10 decimal places using half-up display formatting.
An average describes the supplied data only; it does not establish causation, sampling quality, or which statistic is appropriate for a decision.

Frequently asked questions

Which average should I use?

Use the arithmetic mean for ordinary additive data, a weighted mean when observations contribute unequally, the geometric mean for multiplicative growth factors, and the harmonic mean for rates over equal quantities. Median is often more resistant to extreme values.

Why does the geometric or harmonic mean reject my values?

This implementation does not accept negative geometric-mean inputs, and the harmonic mean cannot include zero because it sums reciprocals.

Can a data set have more than one mode?

Yes. The calculator returns every value tied for the highest frequency, so a data set can be bimodal or multimodal.

Sources and review

National Institute of Standards and Technology: NIST Digital Library of Mathematical Functions: Means — Accessed 2026-10-25
National Institute of Standards and Technology: Measures of Location — Accessed 2026-10-25

Formula version: average.general@1.0.0
Formula review: Formula review: Equatara formula review
Editorial review: Editorial review: Equatara editorial review
Last verified: 2026-10-25
Applicability: Global, unit-neutral descriptive mathematics
Next review: On material formula/source change, or by 2028-10-25.

Found a problem?

Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.

Calculate averages and summary values