Mean Calculator

StatisticsLast updated: August 17, 2026

The mean is the most basic statistic there is: it summarizes the center of a data set with a single number. The arithmetic mean, by far the most common one, is the sum of all values divided by how many there are; the geometric mean is the better choice for proportional growth and multiplicative series, and the harmonic mean gives the correct answer when you are averaging rates and speeds.

Just paste your numbers, separated by commas, spaces, or line breaks: the arithmetic, geometric, and harmonic means, the median, the sum, and the count are all computed at once. It is a practical tool for students working out a grade average, for anyone summarizing sales or expenses, and for researchers describing a data set.

Both decimal points and decimal commas are accepted (e.g. 7.5 or 7,5). At least 1 value is required.

Formula

Arithmetic mean: x̄ = (x₁ + x₂ + … + xₙ) / n
Geometric mean:  G = (x₁ · x₂ · … · xₙ)^(1/n)
Harmonic mean:   H = n / (1/x₁ + 1/x₂ + … + 1/xₙ)

Averaging proportional changes (interest, price increases, returns) with the arithmetic formula is a common mistake; for a chain of successive growth rates the correct answer comes from the geometric mean.

How to Calculate

  1. Paste your numbers into the box — separate them with commas, spaces, or line breaks.
  2. Decimals may be written with either a point or a comma (e.g. 7.5 or 7,5).
  3. Read the arithmetic, geometric, and harmonic means together with the median and the sum in the results section.
  4. Use the interpretation line as a hint about which mean fits your data.

Worked Examples

Average of exam scores

For a student who scored 60, 70, 80, and 90 on four exams, the arithmetic mean is (60+70+80+90)/4 = 300/4 = 75. The median is 75 as well; because the scores are spread symmetrically, the two measures coincide.

Arithmetic mean (x̄): 75.00 · Geometric mean: 74.16 · Harmonic mean: 73.31

How the geometric mean differs

For the values 2, 8, and 32 the arithmetic mean is 14.00 while the geometric mean is 8.00: that value is the cube root of the product 2 · 8 · 32. The harmonic mean works out to 4.57. For series that grow multiplicatively, the geometric mean represents the center far better.

Arithmetic mean (x̄): 14.00 · Geometric mean: 8.00 · Harmonic mean: 4.57

Data with negative values (temperatures)

For the temperatures -2, 5, 12, and 9 °C the arithmetic mean is 24/4 = 6 °C and the median is 7 °C. Because the data contains a negative value, the geometric and harmonic means cannot be computed and are shown as —.

Arithmetic mean (x̄): 6.00 · Geometric mean: — · Harmonic mean: —

Frequently Asked Questions

How do you calculate the arithmetic mean?
Add up all the values and divide by how many there are. For 60, 70, 80, and 90 the total is 300, and dividing by 4 gives a mean of 75. This is what people normally mean by 'the average', and it is what Excel's AVERAGE function returns.
When should you use the geometric mean?
Use it when the values are related multiplicatively — annual growth rates, investment returns, successive price increases. For an investment that grows 10% in one year and 30% in the next, the average annual growth is not the arithmetic 20% but √(1.10 × 1.30) − 1 ≈ 19.6%. It can only be computed from positive values.
When should you use the harmonic mean?
Use it for averaging rates, especially speeds. A car that travels out at 60 km/h and back at 120 km/h has an average speed not of the arithmetic 90 but of the harmonic mean, 2/(1/60 + 1/120) = 80 km/h. The same applies whenever an identical distance is covered at different rates.
What is the difference between the mean and the median?
The mean uses every value and is pulled around by extreme observations; the median is the middle value of the sorted data and is resistant to them. In skewed distributions such as salaries the median represents the center better; in symmetric distributions the two are close together.
Is there an ordering that always holds among the three means?
Yes. For any data set of positive values the ordering harmonic ≤ geometric ≤ arithmetic holds (the AM-GM-HM inequality). The three coincide only when every value is identical.
Why is the geometric mean not computed when there are negative numbers?
The geometric mean takes the nth root of the product of the values, so negative or zero values make it undefined or meaningless. The harmonic mean has the same problem, since a zero can land in the denominator. In those cases use the arithmetic mean or the median.