Find the average (arithmetic mean) of a list of numbers, along with the sum, count, median, geometric mean, minimum, maximum, and range. Enter your values below separated by commas, spaces, or new lines.
The average calculator instantly finds the average — also called the arithmetic mean — of any set of numbers you enter. Just type your values separated by commas, spaces, or new lines, and the calculator returns the mean along with a full statistical summary: the sum, the count of values, the median, the geometric mean, the smallest and largest values, and the range. Whether you are averaging test scores, monthly expenses, temperatures, or measurements from an experiment, this tool does the arithmetic for you and shows exactly how the result was reached.
Finding an average is one of the most common calculations in everyday life, school, business, and science. It condenses a whole list of numbers into a single, representative value that tells you what is "typical" for the group. This page not only computes the answer but also explains what an average really means, how it is calculated, when to use it, and how it differs from other measures of center like the median and the geometric mean.
An average is a single number that represents the center or typical value of a group of numbers. In everyday speech, "average" almost always refers to the arithmetic mean: you add up all the values and divide by how many there are. If five friends earn different amounts of money, the average income tells you what each would earn if the total were shared equally among them.
The average is a measure of central tendency — a way of summarizing a data set with one representative figure. It is intuitive, easy to compute, and widely understood, which is why it appears everywhere from report cards and sports statistics to economic indicators and scientific research.
The formula for the arithmetic mean is simple:
average = (sum of all values) ÷ (number of values)
In symbols, if your values are x₁, x₂, …, xₙ, then the mean is:
x̄ = (x₁ + x₂ + … + xₙ) / n
To calculate an average by hand, follow three steps:
For example, suppose five students scored 56, 75, 88, 45, and 92 on a test. The sum is 56 + 75 + 88 + 45 + 92 = 356. There are 5 scores, so the average is 356 ÷ 5 = 71.2. That single number summarizes how the class performed as a whole.
Beyond the plain average, this calculator reports a complete picture of your data so you never have to reach for a second tool:
The arithmetic mean is only one way to describe the "center" of a data set. The other two common measures are the median and the mode, and knowing when to use each is important:
A classic example is household income. A few very high earners pull the mean income up, so the median income — the figure at which half of households earn more and half earn less — is usually reported as a better picture of the "typical" household. When the mean and median are close, the data is roughly symmetric; when they differ a lot, the data is skewed.
The geometric mean is a different kind of average, found by multiplying all n values together and taking the n-th root:
geometric mean = (x₁ × x₂ × … × xₙ)1/n
It is the right average to use when you are dealing with things that multiply rather than add — growth rates, investment returns, ratios, and index numbers. For example, if an investment grows by 10% one year and 30% the next, the geometric mean of the growth factors (1.10 and 1.30) gives the true average annual growth rate, which the arithmetic mean would overstate. The geometric mean is always less than or equal to the arithmetic mean, and it is only defined when every value is positive, which is why the calculator shows it only in that case.
This calculator treats every value as equally important. Sometimes, though, some values should count more than others — this is a weighted average. A student's GPA is a weighted average, because a 4-credit course counts more toward the final number than a 1-credit course. To compute a weighted average, you multiply each value by its weight, add those products, and divide by the sum of the weights:
weighted average = Σ(value × weight) ÷ Σ(weight)
If all the weights are equal, the weighted average reduces to the ordinary arithmetic mean this page computes. For grade-point calculations specifically, a dedicated GPA calculator is the easier tool.
Averages are everywhere. Here are just a few of the countless places they turn up:
In each of these cases, the average boils a long list of numbers down to one figure you can compare, track over time, or use to make a decision.
Let's walk through a full example so the process is completely clear. Imagine you tracked how many hours you slept over one week: 7, 6.5, 8, 5, 7.5, 9, and 6 hours. To find your average nightly sleep:
The calculator also sorts the list to find the median. Sorted, the nights are 5, 6, 6.5, 7, 7.5, 8, 9, and the middle value (the 4th of 7) is 7 — so here the mean and median agree, which tells you the week's sleep was fairly balanced with no extreme nights pulling the average around. The minimum was 5 hours, the maximum 9 hours, and the range was 9 − 5 = 4 hours. Together these numbers describe not just your typical night but also how much your sleep varied.
Now suppose one night you had almost no sleep — say 1 hour instead of 5. The new sum is 45, and the mean drops to about 6.43, but the median stays at 6.5. That gap between the mean and median is the fingerprint of an outlier, and it is exactly why looking at several statistics at once, as this calculator does, gives you a truer sense of your data than the average alone.
Averages are simple, but a few errors trip people up again and again:
Using the calculator is quick:
You can mix whole numbers, decimals, and negative numbers freely. If you enter something that is not a number, the calculator will let you know so you can fix it.
A few habits will keep your averages meaningful:
In everyday use they are the same thing. "Average" is the general word, and the "arithmetic mean" is the specific calculation — adding all the values and dividing by how many there are — that people almost always mean when they say "average."
Add all the numbers together to get the sum, count how many numbers there are, then divide the sum by the count. For example, the average of 4, 8, and 15 is (4 + 8 + 15) ÷ 3 = 27 ÷ 3 = 9.
Yes. The arithmetic mean works with negative numbers, decimals, and zero. Just enter them as they are — the calculator handles the signs automatically. (Note that the geometric mean is only defined when every value is positive.)
You can separate values with commas, spaces, or new lines — or any mix of these. This makes it easy to paste numbers copied from a spreadsheet column or a comma-separated list.
When a data set contains outliers or is heavily skewed, the mean can be pulled toward the extreme values and misrepresent the "typical" case. The median, being the middle value, is not affected by how large or small the extremes are, so it often gives a more realistic picture in those situations.
The geometric mean is used for quantities that multiply, such as growth rates, investment returns, and ratios. It gives the correct "average factor" over several periods, whereas the arithmetic mean would overstate it. It requires all values to be positive.
This Average Calculator is provided for educational and general informational purposes. While it uses the standard formulas for the mean, median, and geometric mean, you should verify results independently for critical academic, financial, or scientific work.