Average Calculator

What this calculator does

So, you have got a pile of numbers, a run of test scores, a week of temperatures, a column of prices, and you want the single number that stands in for the lot. That is the average, and this works it out for you.

Paste the numbers in, and it hands you three things: the sum, how many numbers there were, and the average itself. Nothing to sign up for, and it all runs right here in your browser.

Using the calculator

1. Type or paste your numbers into the box, separated by commas: 8, 5, 9, 12.
2. Pick a precision from the dropdown if you want, which sets how many significant digits the answer is worked out to. Leave it be for everyday sums.
3. Press Calculate.

You get the sum, the count, and the average back together. Reset clears the box for the next set.

What an average actually is

The average this tool finds is the arithmetic mean, which is the one nearly everyone means by "average". You add up all the numbers and share the total out equally across how many there were.

Think of it as the fair-share figure. If four people earned 10, 20, 30 and 40 between them, the total is 100, and if they split it evenly they would get 25 each. That 25 is the mean. It is also the balance point of the set: the spot where the numbers above it and the numbers below it even out.

Worth knowing that "average" is a loose word, and the mean is only one kind. There is also the median, the middle value when you line them up, and the mode, the one that turns up most often. They can disagree, sometimes by a lot, and which one is fairest depends on your numbers. More on when the mean can mislead further down.

The formula | sum ÷ count

The mean is as plain as formulas get:

average = (sum of all the values) ÷ (how many values there are)

Add everything up, then divide by the count. That is the whole calculation, and it is exactly what the tool does: it shows you the sum and the count on the way, so you can see where the answer came from.

A worked example

Say five test scores came in at 8, 5, 9, 12 and 6.

1. Add them up: 8 + 5 + 9 + 12 + 6 = 40.
2. Count them: there are 5.
3. Divide: 40 ÷ 5 = 8.

So the average score is 8. Notice it landed inside the spread, between the lowest (5) and the highest (12), which a mean always does. If your answer ever falls outside the range of your numbers, something has gone wrong in the adding.

How it calculates, and the precision setting

Most average calculators do the sum in ordinary browser maths, which is fine until you are adding long decimals, where tiny rounding errors can creep into the last digits. This one is built differently. It runs the arithmetic through Decimal.js, a library made for exact decimal work, so the sum and the average stay clean no matter how awkward the numbers.

That is what the precision dropdown is for. It sets how many significant digits the calculation carries, and it goes a long way up, into the hundreds. For a handful of whole numbers you will never need it. But if you are averaging values with many decimal places and you care about the far end of the result, turning the precision up means the answer is worked out to that many digits rather than being quietly rounded.

One honest note, the same as with any average: the result is only ever as trustworthy as the numbers you feed in. Extra digits of precision make the arithmetic exact, not the measurement. If your readings were good to two decimals, round the average back to two decimals when you are done.

The one thing to watch: outliers

The mean has a soft spot, and it is worth knowing before you trust one. Because every value gets added in, a single number that is wildly bigger or smaller than the rest can drag the whole average toward it.

Picture nine people in a room earning around 30,000 each, and then one earns 3,000,000. The mean income of that room shoots up past 300,000, a figure that describes nobody actually standing there. In a case like that the median, the middle value, tells a truer story. So when your numbers include one or two extremes, treat the mean with a little care, and glance at the middle value too. For a fast look at those extremes, the minimum and maximum calculator pulls out the smallest and largest in one go. And if some of your numbers should count for more than others, that is a job for the weighted average calculator.

Questions people ask

How do you calculate an average?

Add all the numbers together, then divide by how many there are. For 8, 5, 9, 12 and 6, that is 40 ÷ 5 = 8.

What is the difference between the mean and the median?

The mean is the total shared out evenly. The median is the middle value once the numbers are in order. They match for tidy, balanced data, but when there are extreme values the median often gives a fairer picture.

Can I paste numbers separated by something other than commas?

This tool reads comma-separated numbers, so 8, 5, 9, 12 is the format to use.

What is the precision setting for?

It sets how many significant digits the calculation is carried to. For whole numbers it makes no visible difference, but for long decimals it lets you keep more digits in the answer instead of rounding early.

Does it work with negative numbers and decimals?

Yes. Negatives, decimals and a mix of both are all fine. They are added and divided just the same.

References

A note on where this comes from. The arithmetic mean is the most basic measure of central tendency in statistics, the standard "typical value" of a set of numbers, set out in any statistics reference including the NIST/SEMATECH e-Handbook of Statistical Methods. The exact-decimal arithmetic is handled by the Decimal.js library rather than the browser's ordinary floating-point maths. For further reading, see Arithmetic mean.

1. NIST/SEMATECH, e-Handbook of Statistical Methods, on measures of location and the mean. https://www.itl.nist.gov/div898/handbook/
2. Decimal.js, an arbitrary-precision decimal library, used here so sums and averages avoid floating-point rounding.