How it works
The average (arithmetic mean) adds up every value in the list, then divides by how many values there are.
Worked through, for a list of 15, 20 and 25: add the values to get 60, count how many numbers were entered (3), then divide the total by that count, so 60 ÷ 3 = 20. A list of one value returns that value unchanged, because a number divided by one is still that number.
The mean is a total divided by a count, so it lands between the smallest and largest values without usually being one of them, and one very large or very small value pulls it further than the rest of the list would suggest. The median answers a different question: it is the middle value once the list is sorted, and it is unaffected by how extreme the other values are. The guide to mean, median and mode covers when each is the more useful summary.
Formula: Average = sum of the values ÷ number of values.
Examples
A short list
The average of 10, 20 and 30 is (10 + 20 + 30) ÷ 3 = 20.
Values that are not whole numbers
The average of 4.5 and 5.5 is (4.5 + 5.5) ÷ 2 = 5.
A longer list of ten values
The average of 12, 15, 9, 18, 6, 12, 21, 15, 12 and 10 is (12 + 15 + 9 + 18 + 6 + 12 + 21 + 15 + 12 + 10) ÷ 10 = 130 ÷ 10 = 13. The mean, 13, is not one of the values entered.
An average that repeats rather than ending
The average of 1, 2 and 4 is (1 + 2 + 4) ÷ 3 = 7 ÷ 3 = 2.3333333333 to 10 decimal places. The same digit carries on repeating, so the answer is a rounded display of a result with no exact decimal form.
Common uses
- Comparing like-for-like periods, such as the average daily sales, mileage or hours worked over the same number of days or weeks.
- Reducing repeated readings of one measurement to a single figure, such as the mean of ten stopwatch times.
- Summarising a scoring average across several rounds, matches or submissions.
- Finding the typical amount spent per item across a shopping basket or a month of bills.
Things to keep in mind
- This calculator finds the mean specifically. The median (the middle value) and the mode (the most frequent value) can both differ from the mean, especially when a list has a few unusually large or small values — a Mean, Median & Mode Calculator that reports all three is planned.
- An empty list has no average, so at least one value is required.
- Every value counts towards both the total and the count, duplicates, zero and negative numbers included, so a list of -5, 0 and 5 has a mean of 0. Nothing is filtered out and no value is given extra weight; a weighted average is a different calculation and is not offered here.
- Fractions are not accepted: entries are read as whole or decimal numbers. Convert each fraction first with the Fraction Calculator, or add the fractions exactly and divide that total by how many there are — the fractions, decimals and percentages guide covers both routes.
- Every entry must be a finite number. Results keep 12 significant digits, which removes floating-point artefacts such as 0.30000000000000004, and are displayed to at most 10 decimal places.