Average calculator

What is an average?

An average is one number that stands in for a whole list. When people say “average” they almost always mean the arithmetic mean: add the values, then divide by how many there are.

Mean and average are the same thing in everyday use. In statistics, “average” is a wider word that also covers the median (the middle value) and the mode (the most common value). This calculator gives you all three, because the right one depends on your data. The NIST Engineering Statistics Handbook defines all three.

How to find the average

The average formula:

average = (x₁ + x₂ + … + xₙ) / n

Three steps:

1. Add all the numbers together.
2. Count how many numbers there are.
3. Divide the total from step 1 by the count from step 2.

The same method works for 3 numbers or 3,000. For long lists, paste them into the calculator above instead of adding them by hand.

Mean, median and mode: which one should you use?

All three describe the middle of a list, and they give different answers when the data is uneven.

Five people earn $38,000, $41,000, $44,000, $47,000 and $250,000. The mean is $84,000, which is more than four of the five people make. The median, $44,000, describes this group far better. One large value pulls the mean toward it, while the median only looks at which value sits in the middle. Our guide to mean vs median explains when to report each one.

When a list has an even count, the median is the average of the two middle values. For 3, 5, 8 and 10, the median is (5 + 8) / 2 = 6.5.

The range is the largest value minus the smallest. It shows how spread out the list is, and the mean, median, mode and range calculator returns all four at once.

How to calculate a weighted average

A weighted average gives some values more say than others. Grades are the usual case: a final exam worth 50% should move your result more than homework worth 20%.

Weighted average formula:

weighted average = Σ(value × weight) / Σ(weight)

The plain average of 90, 80 and 70 is 80. The weighted result is 77 because the lowest score has the biggest weight. Switch the calculator to Weighted average to do this with your own grades. Weights can be percentages or counts, like credit hours, and they do not need to add up to 100. For grades with more parts, the weighted average calculator adds rows as you type.

How to average percentages

You can only average percentages directly when each one comes from the same total. If the totals differ, work with the raw numbers.

Say you scored 90% on a 10-point quiz (9 points) and 60% on a 100-point exam (60 points). The simple average of 90% and 60% is 75%, but that treats a 10-point quiz like a 100-point exam. Your real score is (9 + 60) / (10 + 100) = 69 / 110 = 62.7%.

In the calculator, use Weighted average: enter each percentage as the value and its point total as the weight. The average percentage calculator does the same job and shows the simple and weighted results side by side.

How to calculate an average in Excel and Google Sheets

Both use the same functions. For a worked example with SUMPRODUCT, see how to calculate a weighted average in Excel.

• Plain average: =AVERAGE(B2:B11)
• Average that skips zeros: =AVERAGEIF(B2:B11,">0")
• Weighted average: =SUMPRODUCT(B2:B4,C2:C4)/SUM(C2:C4), where column B has the values and column C the weights
• Median: =MEDIAN(B2:B11)
• Mode: =MODE.SNGL(B2:B11)

Google Sheets also has =AVERAGE.WEIGHTED(B2:B4,C2:C4), which does the weighted average in one step.

AVERAGE ignores empty cells and text but counts zeros, as Microsoft’s AVERAGE function reference explains, and our test of 20 data sets found that Excel and Google Sheets both work this way. If a blank cell should count as zero, type 0 in it. To check a spreadsheet result, copy the column and paste it into the calculator above.

Common mistakes when finding an average

Leaving out zeros

A missed quiz scored 0 still counts toward the total and the count. Removing it makes the average look higher than it is.

Averaging averages

If one class of 10 students averaged 70 and another class of 30 averaged 90, the combined average is 85, not 80. The second class has three times as many students, so it needs three times the weight.

Ignoring outliers

One very large or very small value can drag the mean far from the typical value. If the calculator shows a big gap between mean and median, report the median or both.

Mixing units

Averaging minutes with hours, or dollars with cents, gives a meaningless number. Convert everything to one unit first. For lap times or shifts, the average time calculator converts hours, minutes and seconds for you.