How to use this calculator
Type or paste your numbers into the box, separated by commas, spaces or new lines. A column copied from a spreadsheet works fine. Don’t use commas inside numbers: write 1200 rather than 1,200, or the calculator will read it as two values.
The results update as you type:
- the mean (the usual average), with the median and mode beside it
- the count, sum, smallest and largest values, and the range
- the geometric mean, when every value is above zero
- step-by-step working for the mean, median and mode
Anything that isn’t a number is ignored and listed in a note so you can fix it.
The formulas
The mean is the sum of the values divided by how many there are:
The median is the middle value of the sorted list. With an odd count n, it’s the value in position (n + 1) ÷ 2. With an even count, it’s the average of the values in positions n ÷ 2 and n ÷ 2 + 1.
The mode is the value that appears most often. The range is the largest value minus the smallest.
The geometric mean is the nth root of the product of the values:
Worked example
Eight test scores: 85, 92, 78, 92, 88, 95, 70, 84.
- Sum: 85 + 92 + 78 + 92 + 88 + 95 + 70 + 84 = 684.
- Mean: 684 ÷ 8 = 85.5.
- Sort for the median: 70, 78, 84, 85, 88, 92, 92, 95. There are 8 values, an even count, so the median is the average of the 4th and 5th: (85 + 88) ÷ 2 = 86.5.
- Mode: 92 appears twice and every other score once, so the mode is 92.
- Range: 95 − 70 = 25.
- Geometric mean: the 8th root of the product of all eight scores, about 85.1303.
For positive numbers, the geometric mean is never above the arithmetic mean, and the two are equal only when every value is the same.
Mean, median or mode: which one to use
Each “average” answers a slightly different question:
| Measure | What it tells you | Best for | Weak spot |
|---|---|---|---|
| Mean | The total shared equally | Test scores, temperatures, most measurements | Pulled by outliers |
| Median | The middle value | Incomes, home prices, wait times | Ignores how far out the extremes are |
| Mode | The most common value | Shoe sizes, survey answers, categories | May not exist, or there may be several |
| Geometric mean | The typical growth factor | Investment returns, growth rates, ratios | Needs all values above zero |
Here’s how one outlier changes the picture. Six salaries, in thousands of dollars: 40, 45, 50, 55, 60 and 250.
- Mean: 500 ÷ 6 ≈ 83.33, higher than five of the six salaries.
- Median: (50 + 55) ÷ 2 = 52.5, which describes a typical salary much better.
- Range: 210, which flags the outlier right away.
When the mean and median differ noticeably, the calculator adds a note telling you which way the data is skewed.
Why growth rates need the geometric mean
Suppose an investment gains 10% one year and loses 10% the next. The arithmetic mean of +10% and −10% is 0%, which suggests you broke even. You didn’t: $100 becomes $110, then $99.
The geometric mean of the growth factors 1.10 and 0.90 is about 0.99499, which works out to a loss of roughly 0.5% a year. That correctly reproduces the $99. With bigger swings the gap widens. Gains and losses of 20% give a geometric mean factor of about 0.97980, and gains and losses of 50% give about 0.86603.
To use the calculator for this, enter growth factors rather than percentages: 1.10 for +10% and 0.90 for −10%. For compounding over many years, see the compound interest calculator.
Tips
- Check your count. The count in the results should match the number of values you meant to enter. A stray comma in “1,200” splits it into 1 and 200.
- Look at the spread too. Two data sets can share a mean and still look very different. The standard deviation calculator measures how tightly values cluster around the mean.
- Weighted averages need weights. If some values count more than others, such as a final exam worth 40% of a grade, a plain average is wrong. Use the grade calculator for weighted course grades, or the GPA calculator for credit-weighted grade points.
- Averaging percentages is only fair when they’re based on the same total. Otherwise, add up the underlying counts and divide, or use the percentage calculator on the totals.
How the calculator handles decimals
Computers store decimals in binary, so naive code can report 0.1 + 0.2 as 0.30000000000000004. This calculator adds numbers using compensated summation and cleans up floating-point leftovers before display, so 0.1 and 0.2 give a sum of exactly 0.3 and a mean of exactly 0.15. Results show up to 4 decimal places, and any figure that has been rounded is marked with ≈ in the steps. The geometric mean is computed with logarithms, so long lists of large numbers won’t overflow.
Frequently asked questions
How do you calculate the average?
Add all the values together and divide by how many there are. For the scores 85, 92, 78, 92, 88, 95, 70 and 84, the sum is 684 and there are 8 scores, so the average is 684 ÷ 8 = 85.5. This is the arithmetic mean, which is what most people mean by "average."
How do you find the median?
Sort the values from smallest to largest and take the middle one. If there's an even number of values, there are two middle values, and the median is their average. For 70, 78, 84, 85, 88, 92, 92, 95, the middle pair is 85 and 88, so the median is 86.5.
What if there's no mode, or more than one?
If no value appears more than once, the data has no mode. If two or more values tie for the most appearances, they are all modes; data with two modes is called bimodal. The calculator lists every tied value.
When should I use the median instead of the mean?
Use the median when a few extreme values could distort the picture, as with house prices, salaries or response times. The mean is pulled toward outliers while the median isn't. If the two are close, your data is fairly symmetric and either one works.
What is the geometric mean used for?
The geometric mean multiplies the values and takes the nth root. It's the right average for growth rates and ratios, such as average annual investment returns, because those compound. It only works when every value is positive.
Does the order of the numbers matter?
No. The mean, mode, range and geometric mean don't depend on order, and the calculator sorts the values itself to find the median. You can paste numbers in any order.
Updated November 2026. Results are estimates for educational purposes and depend on the inputs you provide.