Average Calculator
Find the arithmetic mean, median, mode, sum, count, minimum, maximum, range, midrange and—when defined—geometric and harmonic means.
Average, median and mode formulas
The arithmetic mean is the sum of all values divided by the number of values:
Mean = (x₁ + x₂ + … + xₙ) ÷ n
The median is the middle value after sorting. For an even count, it is the mean of the two middle values. The mode is the most frequent value; a dataset may have no mode or more than one mode.
Range = maximum − minimum and midrange = (minimum + maximum) ÷ 2.
For positive values, the geometric mean is (x₁ × x₂ × … × xₙ)1/n, and the harmonic mean is n ÷ Σ(1/x).
Checked examples
| Dataset | Mean | Median | Mode | Range |
|---|---|---|---|---|
| 1, 2, 3, 4, 5 | 3 | 3 | No mode | 4 |
| 1, 2, 3, 4 | 2.5 | 2.5 | No mode | 3 |
| 1, 2, 2, 3 | 2 | 2 | 2 | 2 |
| 1, 1, 2, 2, 3 | 1.8 | 2 | 1 and 2 | 2 |
| −4, 0, 4 | 0 | 0 | No mode | 8 |
| 10, 10, 10 | 10 | 10 | 10 | 0 |
| 1, 2, 4 | 2.3333333333 | 2 | No mode | 3 |
How to use the Average Calculator
- Paste or type the dataset in the numbers box.
- Separate observations with commas, spaces, semicolons or new lines.
- Select Calculate average.
- Review the arithmetic mean and the additional measures of center and spread.
Which average should I use?
- Arithmetic mean: the standard average for values with equal importance.
- Median: useful when extreme values may distort the mean.
- Mode: identifies the most common value and works with repeated observations.
- Geometric mean: appropriate for positive multiplicative changes, ratios or growth factors.
- Harmonic mean: useful for averaging positive rates when the same numerator quantity is held constant.
Limits and interpretation
- The calculator accepts 1–10,000 finite numbers, including negatives, decimals and scientific notation.
- Commas separate observations. Enter 1250 rather than 1,250 when you mean one thousand two hundred fifty.
- Repeated numbers must be entered repeatedly because frequency affects the mean, median and mode.
- The geometric and harmonic means are reported only when every value is positive.
- The arithmetic mean can be strongly affected by outliers. Compare it with the median and range.
- Displayed results are rounded; calculations retain full JavaScript numeric precision.
Frequently asked questions
Are average and mean the same?
In everyday arithmetic, “average” usually refers to the arithmetic mean. Median, mode, geometric mean and harmonic mean are other measures of central tendency.
Can a dataset have two modes?
Yes. If two or more values share the highest repeated frequency, the calculator reports each of them.
What happens if no number repeats?
The dataset has no mode. Its arithmetic mean and median remain valid.
Does the order of the numbers matter?
No. The mean, median, mode, sum and range are unchanged when the observations are reordered.
Related calculators
Use the Weighted Average Calculator when values have unequal importance, or the Standard Deviation Calculator for variance, spread and z-scores.