Mean Calculator
Calculate the arithmetic, geometric, and harmonic mean of any list of numbers — all three at once, instantly.
The Three Types of Mean
Given the values 2, 8, 18:
- Arithmetic mean — sum divided by count: (2 + 8 + 18) / 3 = 9.33
- Geometric mean — nth root of the product: ∛(2 × 8 × 18) = ∛288 = 6.60
- Harmonic mean — count divided by sum of reciprocals: 3 / (1/2 + 1/8 + 1/18) = 4.41
These three always satisfy the inequality harmonic ≤ geometric ≤ arithmetic (4.41 ≤ 6.60 ≤ 9.33). All three are equal only when every value in the list is identical.
When to Use Each Mean
| Mean | Best for | Example |
|---|
| Arithmetic | Symmetric data, test scores, counts | Class grades, temperature readings |
| Geometric | Growth rates, ratios, investment returns | Annual portfolio returns, population growth |
| Harmonic | Rates where the numerator is fixed | Average speed, price-to-earnings ratios |
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Frequently Asked Questions
What is the difference between arithmetic, geometric, and harmonic mean?
The arithmetic mean is the simple average: sum divided by count. The geometric mean multiplies all values and takes the nth root — useful for rates and ratios. The harmonic mean divides the count by the sum of reciprocals — useful when averaging rates like speed or price-to-earnings. For any dataset, harmonic ≤ geometric ≤ arithmetic (all three are equal only when all values are identical).
How do I enter numbers?
Type or paste your numbers into the input field, separated by commas (e.g. 2, 8, 18) or spaces (e.g. 2 8 18). Decimal numbers are supported — use a period as the decimal point (e.g. 1.5, 3.14). Do not mix commas and spaces in the same input.
Why does the geometric mean show a dash?
The geometric mean is only defined for positive numbers. If your list contains zero or any negative value, the geometric mean cannot be calculated and the result shows —.
Why does the harmonic mean show a dash?
The harmonic mean requires all values to be non-zero, because it involves dividing by each number. If any value in the list is zero, the result shows —.
When should I use the geometric mean?
Use the geometric mean when your values represent multiplicative factors or growth rates. For example, if an investment grows by 10% one year and 50% the next, the geometric mean of 1.10 and 1.50 gives the equivalent constant annual growth rate. The arithmetic mean would overstate the true average return.
When should I use the harmonic mean?
Use the harmonic mean when averaging rates or ratios where the distance (not time) is fixed. A classic example: if you drive 60 km/h for one leg and 30 km/h for the same-length return leg, the harmonic mean of 60 and 30 gives the correct average speed (40 km/h), which is lower than the arithmetic mean (45 km/h).