Calculators
Average Calculator
Calculate and compare four useful types of averages.
Compare arithmetic, weighted, geometric, and harmonic means in one place. Separate values and optional weights with commas, spaces, semicolons, or new lines.
Arithmetic mean
25
Weighted mean
Add weights
Geometric mean
22.133638394
Harmonic mean
19.2
Count: 4 · Sum: 100
About This Tool
An average summarizes several values with one representative number, but different kinds of averages answer different questions. This calculator keeps the common arithmetic mean together with weighted, geometric, and harmonic means so you can calculate them from the same data and understand why the results differ. Everything is calculated locally in your browser. Arithmetic mean supports negative and zero values; geometric and harmonic means are shown only when every entered value is positive.
How To Use It
- Enter two or more values separated by commas, spaces, semicolons, or new lines. A single value also works and has itself as its arithmetic mean.
- Optionally enter one non-negative weight for every value to calculate a weighted mean. Weights can be counts, credits, percentages, or other relative importance values and do not need to add to 100.
- Compare the displayed means and choose the one that matches the structure of your problem rather than assuming every type of average is interchangeable.
Examples
Arithmetic mean
For 10, 20, 30, and 40, the sum is 100 and the count is 4, so the arithmetic mean is 100 ÷ 4 = 25.
Weighted course scores
For scores 80, 90, and 70 with weights 2, 3, and 1, the weighted mean is (80×2 + 90×3 + 70×1) ÷ (2+3+1) = 83.333…
Geometric mean
For 1, 4, and 16, the product is 64. Its cube root is 4, so the geometric mean is 4. It is useful for multiplicative factors and proportional changes.
Harmonic mean
The harmonic mean is based on reciprocals and is often appropriate when averaging rates over equal quantities, such as speeds over equal distances. The quantities and assumptions must match the situation.
Useful Notes
Arithmetic mean
Add all n values and divide by n: mean = (x₁ + x₂ + … + xₙ) / n. It is the familiar average for additive measurements, but extreme values can pull it strongly upward or downward.
Weighted mean
Multiply each value by its weight, add those products, and divide by the total weight: weighted mean = Σ(wᵢxᵢ) / Σwᵢ. A value with twice the weight contributes twice as much to the result. At least one weight must be positive.
Geometric mean
For positive values, the geometric mean is the nth root of their product. The calculator uses logarithms internally to reduce overflow risk. It is commonly useful for multiplicative ratios, growth factors, and index-style comparisons, but the interpretation depends on the data.
Harmonic mean
For positive values, harmonic mean = n / Σ(1/xᵢ). It gives relatively more influence to smaller values and is useful for some rate problems when the averaging basis is equal. It should not be substituted automatically for an ordinary mean.
Average versus median and mode
The word average often means arithmetic mean, but median and mode describe a data set differently. Median is the middle ordered value and can be more resistant to outliers; mode identifies the most frequent value. Use the Statistics Calculator when you need those measures and measures of spread together.
FAQ
Which average should I use?
Use arithmetic mean for ordinary additive values, weighted mean when observations have different importance, geometric mean for appropriate multiplicative data, and harmonic mean for certain rates with an equal averaging basis. The problem context determines the correct choice.
Do weights need to add to 100?
No. Only their relative sizes matter. Weights 20, 30, and 50 give the same weighted mean as 0.2, 0.3, and 0.5.
Why are geometric and harmonic means unavailable with zero or negative values?
This calculator uses their standard real-valued positive-data definitions. Zero or negative inputs make those formulas undefined or require additional conventions that could be misleading in a general-purpose tool.
Is the arithmetic mean always representative?
No. Strongly skewed data or outliers can make the mean unrepresentative of a typical observation. Compare the median and distribution when the shape of the data matters.
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