Mean Calculator (Arithmetic, Geometric, Harmonic)
Just enter your numbers and instantly get all three means at once: arithmetic, geometric, and harmonic.
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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 โง geometric โง 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 รท (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 โง geometric โง 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 รท (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 โฅ geometric mean โฅ harmonic mean always holds.
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