Calculate arithmetic, geometric & harmonic mean instantly
Data Set
Results
Inequality check
Harmonic 5.1612903 ≤ Geometric 8 ≤ Arithmetic 12.4
HM ≤ GM ≤ AM always holds for positive numbers (equality when all values are equal).
Parsed numbers (5)
About the three means
The mean calculator computes all three classical means of your data set in one click. Paste in any list of numbers separated by commas or spaces and instantly see the arithmetic mean (simple average), geometric mean (for rates and growth), and harmonic mean (for speeds and ratios). Perfect for students, data analysts, and anyone working with statistics.
The arithmetic mean is the simple average (sum divided by count). The geometric mean is the nth root of the product of all values, best for multiplicative data like growth rates. The harmonic mean is n divided by the sum of reciprocals, ideal for averaging rates such as speed over equal distances.
Use geometric mean when your values represent ratios, percentages, or multiplicative growth — for example, annual investment returns, population growth rates, or index ratios. Arithmetic mean overstates performance in these cases because it ignores compounding.
Both the geometric and harmonic mean are only defined for strictly positive numbers. If your data set contains zero or any negative value, those two means are mathematically undefined, so the calculator displays N/A and shows only the arithmetic mean.
Yes, for any set of positive real numbers the harmonic mean is always less than or equal to the geometric mean, which is always less than or equal to the arithmetic mean. Equality holds only when all values in the data set are identical.