Average Calculator
Paste any list of numbers — separated by commas, spaces or new lines — and get the average plus every related statistic at once.
How to calculate an average
The average — more precisely the arithmetic mean — is the single number that best summarises a list. You add every value up and divide by how many values there are:
average = sum of all values ÷ how many values
Take the list 10, 20, 30, 40, 50. The sum is 150 and there are 5 numbers, so the average is 150 ÷ 5 = 30. Paste those five numbers into the calculator above and you will see the same answer, along with the median, mode, range and standard deviation of the same list.
Doing it by hand, step by step
- Add every number together. 10 + 20 + 30 + 40 + 50 = 150.
- Count how many numbers you have. Five. Count the values, not the gaps between them — this is where most by-hand mistakes creep in.
- Divide the sum by the count. 150 ÷ 5 = 30.
Mean, median and mode are three different averages
“Average” in everyday speech means the mean, but statistics recognises three, and they answer different questions. The calculator returns all three at once so you can compare them.
| Measure | What it is | Best used when |
|---|---|---|
| Mean | Sum ÷ count | Values are fairly evenly spread with no extreme outliers |
| Median | The middle value once sorted | The data is skewed, or a few extreme values would distort the mean |
| Mode | The value that appears most often | You want the most common outcome, or the data is categories rather than quantities |
With an even count there is no single middle value, so the median is the mean of the two central numbers. For 4, 8, 8, 12 the two middle values are 8 and 8, giving a median of 8 — which happens to match the mean here, though usually it will not.
When the median tells the truth and the mean does not
This is the most useful thing to understand about averages. A single extreme value drags the mean towards itself but barely moves the median.
Consider six salaries: 30,000, 32,000, 34,000, 36,000, 38,000 and 900,000. The mean is about 178,333 — a figure higher than five of the six people actually earn. The median is 35,000, which genuinely describes a typical person in that list. Neither number is wrong; the mean answers “what if the total were shared equally?” while the median answers “what is typical?”
This is exactly why reports on income, house prices and response times almost always quote the median. Whenever you see an average quoted with no median beside it, and you suspect a few large values are present, treat the figure with care.
Weighted averages: when some numbers count more
A plain mean treats every value as equally important. Often they are not — a final exam may count for more than a quiz, or a large purchase for more than a small one. A weighted average multiplies each value by its weight, adds those products, then divides by the total weight:
weighted average = Σ(value × weight) ÷ Σ(weight)
Suppose three assessments score 80, 90 and 70, worth 20%, 30% and 50% of the grade. The weighted average is (80×0.2) + (90×0.3) + (70×0.5) = 16 + 27 + 35 = 78. The simple mean would have been 80 — two marks higher — because it ignores that the weakest score carried the most weight. Enter weights in the optional second box to calculate this; the calculator also shows the unweighted mean underneath so you can see the difference.
Reading the rest of the summary
Alongside the averages, the calculator reports four figures that describe how spread out your numbers are:
- Range is the largest value minus the smallest. It is the simplest measure of spread, and it is entirely determined by the two most extreme values.
- Minimum and maximum are those two extremes, shown so you can spot a mistyped value immediately.
- Standard deviation measures the typical distance from the mean. A small value means the numbers cluster tightly; a large one means they are widely scattered. This calculator reports the sample standard deviation, dividing by n−1, which is the right choice when your numbers are a sample drawn from some larger group. It is left blank for a single value, because one number has no spread to measure.
Averages of percentages and growth rates
One trap worth knowing: you usually cannot take a plain mean of percentages or growth rates. If an investment gains 50% one year and loses 50% the next, the mean of +50% and −50% is 0%, yet 100 becomes 150 and then 75 — a real loss of 25%. Rates that compound multiply rather than add, so they need a geometric mean instead.
For year-on-year investment growth, the CAGR calculator handles this correctly by annualising total growth. To see how a rate compounds forward over many periods, use the compound interest calculator. And if you are averaging the price you paid across several purchases of the same stock, that is a weighted average by quantity — the stock average calculator is built for exactly that case.
Common mistakes to avoid
- Miscounting the values. Dividing by the wrong count is the most frequent error. The calculator shows the count it detected, so check it matches what you pasted.
- Averaging averages. The mean of several group means is only correct if every group is the same size. Otherwise you need a weighted average using the group sizes as weights.
- Leaving a stray value in the list. A misplaced decimal point or an extra zero moves the mean noticeably while leaving the median almost untouched — a large gap between the two is often the first sign of a typo.
- Using the mean on skewed data. For incomes, prices and waiting times, quote the median as well.
- Adding thousands separators inconsistently. If you separate values with spaces or new lines, commas inside numbers are read as thousands separators, so “1,000 2,000” is correctly understood as two numbers. If you separate values with commas only, write plain digits.
For everyday percentage work — a percentage of a number, or the percent change between two values — the percentage calculator is the quicker tool.