Mean Calculator (Arithmetic, Geometric, Harmonic)
Just enter your numbers and instantly get all three means at once: arithmetic, geometric, and harmonic.
Last updated:
Input
Positive numbers only. Separate multiple values with line breaks, commas, or spaces.
Result
Arithmetic mean
24
Geometric mean
19.583
Harmonic mean
16.0428
Data count
5 values
Comparison of the three means
| Type of mean | Value | Common uses |
|---|---|---|
| Arithmetic | 24 | Everyday average that splits the total evenly |
| Geometric | 19.583 | Average for growth rates and multiplicative factors |
| Harmonic | 16.0428 | Average for speeds, unit prices, and other ratios |
Except when all values are equal, the relationship arithmetic ≧ geometric ≧ harmonic mean always holds.
How it works
- The arithmetic mean is the most common average: add up all the values and divide by how many there are. It suits things like test scores or amounts of money, where you want to split the total evenly.
- The geometric mean multiplies all the values together and takes the nth root. Use it for growth rates such as year-over-year sales or interest rates, where changes compound through multiplication.
- The harmonic mean is the reciprocal of the average of the reciprocals, calculated as n ÷ (sum of 1/x). It is ideal for averaging ratios such as round-trip speeds or unit prices across several places.
- Except when all values are equal, the order arithmetic ≧ geometric ≧ harmonic mean always holds. The larger the gap between the three values, the more spread out your data is.
- The geometric and harmonic means are only defined for positive numbers, so data containing zeros or negatives is not supported. Remove those values before entering.
- Numbers can be separated by line breaks, commas, or spaces, and the result is recalculated automatically as you type.
Frequently asked questions
- What is the difference between the arithmetic and geometric mean?
- The arithmetic mean adds all values and divides by the count, suited to sharing a total evenly. The geometric mean multiplies all values and takes the nth root, and is used for average growth rates such as year-over-year sales or interest rates that compound multiplicatively.
- How is the harmonic mean calculated, and when is it useful?
- The harmonic mean is the reciprocal of the average of reciprocals, computed as n ÷ (sum of 1/x). It suits averaging rates or ratios, such as an average round-trip speed or an average unit price across locations.
- Can I include zero or negative numbers?
- The geometric and harmonic means are defined only for positive numbers, so data containing zero or negatives is not supported; remove those values first. Also, unless all values are equal, arithmetic mean ≥ geometric mean ≥ harmonic mean always holds.
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