Example 1
- List: 2 4 6
4
What average for 2, 4, and 6? 4 — sum 12÷3.
Average Calculator
Enter each number in its own field. The calculator computes the arithmetic mean: sum ÷ count. At 2, 4, and 6 the result is 4. At 3, 4, 5, 4, and 5 the result is 4.2. One extreme value, such as 1000 next to 10, 12, and 11, raises the mean to 258.25 — the median of that list stays 11.5.
Result
Enter at least one number. The mean, the sum, the count, and the median appear here.
The arithmetic mean is the sum of all numbers divided by how many there are. Every value affects the result, including a very large or a very small one. When one number stands far from the others, compare the mean with the median.
How it works
Sum12
Count3
Mean4
Take the scores 4, 5, and 3. The sum is 12, there are 3 numbers, the mean is 12÷3 = 4. Any list works the same way: add the numbers, then divide by how many there are. The list 2 4 6 has a sum of 12 and a mean of 4. The list 3 4 5 4 5 has a sum of 21 and a mean of 4.2.
The result does not have to be one of the numbers you entered. The list 3 6 9 12 has a mean of 7.5. The mean describes a typical value when the numbers are similar. When one number stands far from the others, the list 10 12 11 1000 has a mean of 258.25. The median of that list is 11.5.
You start with three fields. Each number has its own field, and you add more with the Add a number button. Write a decimal with one comma or one period, for example 3.5. Enter 2, 4, and 6, then click Calculate. An empty field is skipped. The calculator also shows the sum, the count, and the median, so you can check the arithmetic.
The median is the middle value after the numbers are sorted from smallest to largest. An arithmetic-series sum assumes a constant step between the numbers. This calculator does not compute that sum. The list −2 0 4 8 10 has a mean of 4.
If every field is empty, the calculator does not show a result. A zero in a field is still a number, and it is part of the sum. Switching the units at the top of the page does not change the numbers you entered: 2, 4, and 6 still have a mean of 4.
The list 2 5 9 11 20 has a mean of 9.4. The list 10 10 10 10 50 has a mean of 18. The list 1 1 2 3 100 has a mean of 21.4. When 100 stands far from the other numbers, compare the mean with the median.
Formula
mean = sum ÷ count
The sum is every number you enter, added together. The count is how many values are on the list. For 2, 4, and 6 the sum is 12, so the mean is 4.
Each number has the same weight here. When the numbers have different weights, use the weighted average calculator.
Theory, arithmetic mean, and median
Definition
The arithmetic mean of a finite list x₁,…,xₙ (n ≥ 1) is m = (x₁ + … + xₙ) / n = (Σ xᵢ) / n. Each element has equal weight 1/n. This calculator sums the numbers you enter and divides by their count: mean = sum / nums.length. Empty fields are skipped; each field holds one number (comma or period in a decimal).
The panel also shows the sum, the count, and the median of the same list. Median: after nondecreasing sort, for odd n it is the middle entry; for even n it is the arithmetic mean of the two middle entries. Computation: sort ascending; if n is odd return s[mid], else (s[mid−1]+s[mid])/2.
The primary result is the mean. A weighted average (unequal weights) is on a separate calculator. Standard deviation and variance live on the dispersion calculators.
Historical and conceptual context
The arithmetic mean is among the oldest location summaries for a set of numbers; probability and statistics systematized it from the eighteenth–nineteenth centuries (including the least-squares context of Gauss–Legendre). The NIST/SEMATECH e-Handbook lists the mean as a basic measure of location.
Keep separate: (1) arithmetic mean; (2) median (more resistant to extremes); (3) mode; (4) weighted mean; (5) geometric and harmonic means. This page computes (1) and, as support, (2) for the same list. Outlier example: 10, 12, 11, 1000 has mean 258.25 and median 11.5 — the mean is pulled hard by 1000.
In school, an unweighted grade average is exactly this formula; when assessments have different weights, use a weighted mean. The grade calculator on a separate page maps a test percent onto letter bands and also offers a weighted mean of components — here the result stays a pure list mean without a letter label.
Formal properties
For xᵢ in ℝ: m in ℝ. Shift: mean(xᵢ + c) = mean(xᵢ) + c. Scale: mean(λxᵢ) = λ·mean(xᵢ). Sum of deviations from the mean: Σ(xᵢ − m) = 0. Order does not affect m (commutativity of addition).
The median Me satisfies: at least half the observations are ≤ Me and at least half are ≥ Me (with the even-n average-of-two-middle definition). For strongly skewed lists Me and m can differ a lot.
Practical domain: n ≥ 1 after skipping empty fields; at most 30 fields on the page. One number per field — a space or semicolon inside one field is an error.
Full derivation
Step 1. Enter numbers in separate fields (three at the start; more via “Add a number”).
Step 2. Sum S = Σ xᵢ; n = count of non-empty fields; m = S/n.
Step 3. Median: sort; take the middle or the average of the two middle values.
Step 4. Examples: 2, 4, 6 → S = 12, n = 3, m = 4. 3, 4, 5, 4, 5 → S = 21, m = 4.2. 10, 12, 11, 1000 → S = 1033, m = 258.25; sorted 10, 11, 12, 1000 → Me = (11+12)/2 = 11.5.
Step 5. 3, 6, 9, 12 → m = 7.5. −2, 0, 4, 8, 10 → S = 20, m = 4. 10, 10, 10, 10, 50 → m = 18.
Special cases
One number → mean equals that number; median equals that number. All equal → m equals that value. Lists with negatives and zero are allowed.
When one value is many times larger than the others, the mean rises sharply while the median stays near the typical middle — hence the side-by-side panel. No numbers → placeholder, no result.
The calculator does not trim outliers, does not compute a geometric mean, and does not apply weights.
Numerical and computational notes
Sum and division run in floating-point arithmetic. The bar chart shows up to the first 16 values with a mean line; longer lists are fully computed while the chart is visually capped.
A decimal is written with one comma or period (3.5). Display format follows en-US. The outlier warning is a simple helper rule, not a published statistical theorem on this page.
In teaching: the mean need not be a list member (7.5 for 3, 6, 9, 12). With even n the median may also sit off the list.
The calculator uses the numbers you enter in separate fields. The primary result is the arithmetic mean; the sum and the count let you check S÷n on paper. The median is computed from the same sorted list — not from a different sample. When you compare groups (two classes or two weeks of measurements), compute the mean separately for each list; this page does not merge several collections automatically.
Related ideas and sources
Related: median, weighted average, standard deviation, variance, geometric / harmonic mean. Related in theory: measures of location, outlier resistance, the first empirical moment.
Sources: NIST/SEMATECH e-Handbook — Measures of Location; Wikipedia — Arithmetic mean; Wikipedia — Median; MathWorld — Arithmetic Mean; descriptive-statistics textbooks (context). Educational tool.
Where it helps
- Average grades, scores, and measurements.
- The typical value per item, with one number for each item.
- Comparing groups of numbers at school and in everyday life.
- Comparing the mean with the median when one number stands far from the others.
How to use
- Enter each number in its own field. You start with three fields, for example 2, 4, and 6. When you need more, click Add a number.
- Write a decimal with one comma or one period, for example 3.5.
- Click Calculate. 2 4 6 gives 4. 3 4 5 4 5 gives 4.2.
- Check the sum, the count, and the median next to the mean. 12÷3 = 4.
- When one number stands far from the others, compare the mean with the median. The list 10 12 11 1000 has a mean of 258.25 and a median of 11.5.
Mean, sum, and median
The arithmetic mean is the sum of the numbers divided by how many you entered. 2, 4, and 6 give 4, because 12 divided by 3 is 4.
- mean
- The sum divided by the count. 3 4 5 4 5 gives 4.2. 10 10 10 10 50 gives 18, not 10.
- sum
- Every entry added together. For 2 4 6 the sum is 12. The calculator shows the sum beside the mean, so you can check 12÷3.
- median
- The middle of the list after you sort it from smallest to largest. With an even count, it is the average of the two middle numbers. For the list 10 12 11 1000 the mean is 258.25 and the median is 11.5.
Examples
Example 2
- List: 3 4 5 4 5
4.2
What is the mean of 3, 4, 5, 4, and 5? 4.2.
Example 3
- List: 10 12 11 1000
258.25
What mean with outlier 1000 next to 10, 12, and 11? 258.25; median 11.5.
Example 4
- Numbers: 2 5 9 11 20
9.4
For the numbers 2, 5, 9, 11, and 20, the sum is 47, so the mean is 9.4.
Example 5
- Numbers: 1 1 2 3 100
21.4
This list has four small numbers and one 100. The mean is 21.4, because 100 raises the sum.
Example 6
- Numbers: 10 10 10 10 50
18
Four tens and a 50 give a mean of 18, not 10.
Example 7
- Numbers: 3 6 9 12
7.5
The list 3 6 9 12 has a sum of 30 and a mean of 7.5. That mean is not one of the numbers on the list.
Example 8
- Numbers: -2 0 4 8 10
4
The number −2 is part of the sum. The list −2 0 4 8 10 has a mean of 4.
Related calculators
FAQ
How do I calculate an arithmetic mean?
Add all numbers and divide the sum by how many there are. For 2, 4, and 6 the sum is 12, and 12÷3 = 4. For 3, 4, 5, 4, and 5 the sum is 21, and 21÷5 = 4.2.
How is the mean different from the median?
Every value affects the mean, including an outlier. The median is the middle value after sorting. For 1, 1, 2, 3, and 100 the mean is 21.4 and the median is 2. For 10, 12, 11, and 1000 the mean is 258.25 and the median is 11.5.
How is the mean different from a weighted average?
Here every number has the same weight: sum ÷ n. A weighted average multiplies values by weights and divides by the total weight — that lives on the weighted-average page (and grade / ECTS pages).
How do I enter several numbers?
Each number has its own field. You start with three fields. Add more with Add a number. In one field, 3.5 and 3,5 are the same number. An empty field is skipped.
What if one number stands far from the others?
The mean moves a lot. For 10, 12, 11, and 1000 the mean is 258.25, while the median of the same list is 11.5. Compare both numbers in the result.
Does the mean have to be one of the numbers on the list?
No. For 3, 6, 9, and 12 the sum is 30 and the mean is 7.5 — that value is not on the list.
Does this calculator compute a weighted grade average?
No. Here you compute a plain arithmetic mean without weights. Weighted grades live on the weighted-average or grade calculator pages.
Is the result the sum of an arithmetic series?
No. An arithmetic-series sum assumes a constant difference between terms. Here the list can be any values: add what you entered and divide by the count.
How do I average grades without weights?
Enter the grades as ordinary numbers, for example 4, 5, and 3. Sum 12÷3 = 4. This page does not convert plus/minus marks or apply weights.
Are negative numbers and zero allowed?
Yes. For −2, 0, 4, 8, and 10 the sum is 20 and the mean is 4. Zero and negatives enter the sum the same way positives do.
Sources
The arithmetic mean is the sum of the numbers divided by how many there are.
Page Updated November 2, 2026.