Average Calculator

Use this Average Calculator to find the average of any set of numbers, calculate a weighted average, find the mean, median and mode, average percentages, solve for a missing value, or combine averages from groups of different sizes. Enter your values and the calculator will show the result along with the numbers used in the calculation.

An average can be useful for test scores, prices, measurements, business data, sports statistics, survey results, household expenses and many other situations. The most common average is the arithmetic mean, but the correct method depends on what your numbers represent. This calculator includes several methods so you can choose the calculation that actually matches your data.

How to Use the Average Calculator

The calculator has six modes because there is more than one way to calculate an average. The standard Average / Mean mode is the right choice when every number should contribute equally. The other modes handle situations where some values are more important, percentages represent groups of different sizes, you need additional statistics, or you do not yet know every value in the data set.

Start by selecting the mode that best describes your calculation. Enter the values requested by that mode, choose how many decimal places you want to display, and press the calculation button. The result section shows the main answer along with supporting figures so you can see how the answer was produced instead of receiving only a single unexplained number.

Average / Mean Mode

Choose Average / Mean when you simply want the arithmetic average of two or more numbers. Enter the numbers separated by commas, spaces or new lines. The calculator adds the values together and divides the sum by the number of values entered. It also shows the sum, count, median, range, minimum and maximum so you can better understand the data behind the average.

This is the mode to use for questions such as “what is the average of 10, 20 and 30?” or “what is my average monthly expense over the last six months?” As long as each observation should count equally, the ordinary arithmetic mean is usually what people mean when they ask for the average.

Weighted Average Mode

Use Weighted Average when the numbers should not all have equal influence. Enter each value beside its weight. A weight can represent a percentage, course credit, number of units, frequency, quantity sold or any other measurement that determines how much that value contributes to the result.

The weights do not have to total 100. A set of weights of 2, 3 and 5 produces the same relative weighting as 20, 30 and 50. The calculator divides by the actual total of the weights, which means any consistent weighting scale can be used.

Mean Median Mode Mode

Select Mean Median Mode when you want more than the arithmetic average. This mode sorts the data and calculates the mean, median, mode, range, minimum, maximum, first quartile, third quartile, interquartile range, population standard deviation and sample standard deviation. It is useful for schoolwork, statistics and situations where one number does not fully describe the data set.

Average Percentage Mode

Average Percentage has two possible calculations. If you enter only percentages, each percentage counts equally and the calculator returns their arithmetic mean. If you also enter a weight or group size for every percentage, the calculator uses a weighted percentage average instead.

This distinction matters because simply averaging percentages can produce a misleading answer when the percentages came from groups of different sizes. A percentage based on 1,000 observations should normally have more influence than a percentage based on only 10 observations if you are trying to calculate the combined result.

Missing Value Mode

Missing Value works backward from a target average. Enter all the numbers you already know and the average you want the complete set to have. The calculator determines the single additional number required to reach that target.

Combine Averages Mode

Combine Averages is designed for situations where you know the average of several groups but the groups contain different numbers of observations. Enter each group average and its group size. The calculator reconstructs the total represented by each group and then calculates the true combined average.

What Is an Average?

An average is a number used to summarize a collection of values. Instead of examining every observation individually, an average gives you one figure that represents the center or typical level of the data. In ordinary conversation, the word “average” most often refers to the arithmetic mean.

Suppose five daily temperatures are 18, 20, 21, 24 and 22 degrees. The individual temperatures tell you what happened each day, while the average summarizes all five days in one number. Add the values to get 105, then divide by five. The average is 21 degrees.

That summary can be useful, but no average tells the entire story. Two sets of values can have exactly the same average while being distributed very differently. The numbers 19, 20, 21, 22 and 23 have an average of 21, but so do 1, 1, 21, 41 and 41. Their centers are the same even though their spread is dramatically different.

This is why the calculator also provides measures such as minimum, maximum, range and median. When the shape or spread of the data matters, those additional numbers can give important context that the arithmetic mean alone cannot provide.

How to Calculate an Average

To calculate the arithmetic average of a set of numbers, first add every number together. The result of that addition is the sum. Next, count how many values are in the set. Divide the sum by the count, and the result is the arithmetic mean.

For example, suppose your numbers are 14, 18, 22 and 30. Add them together:

14 + 18 + 22 + 30 = 84

There are four numbers, so divide 84 by 4:

84 ÷ 4 = 21

The average is 21. The calculation does not depend on the order of the values. You would get the same result if you entered 30, 14, 22 and 18 because the total and number of observations remain unchanged.

Average Formula

The standard arithmetic mean formula can be written as:

In statistics, the arithmetic mean of a sample is often represented by x̄. The summation symbol Σ is used to represent adding the observations together, while n represents the number of observations. That produces the familiar expression x̄ = Σx ÷ n.

The NIST Engineering Statistics Handbook discusses the mean and other measures of location used to describe where data are centered. For a broader introduction to measures of center, OpenStax Introductory Statistics also explains mean, median and mode.

Examples of Calculating an Average

The same formula works whether you are averaging two numbers or hundreds of observations. The following examples show how the calculation changes as more values are added.

Average of Two Numbers

To find the average of two numbers, add them and divide by two. If the numbers are 20 and 30, the total is 50. Divide 50 by 2 and the average is 25.

The average of two numbers always lies halfway between them on a number line. For example, the average of 10 and 18 is 14 because 14 is four units above 10 and four units below 18.

Average of Three Numbers

Suppose the values are 8, 12 and 25. Add them to get 45, then divide by three. The average is 15. Notice that the average does not have to be one of the numbers in the original data set.

Average of Four Numbers

For 5, 10, 15 and 30, the total is 60. There are four observations, so 60 ÷ 4 gives an average of 15. The relatively large value of 30 pulls the mean higher than several of the other observations.

Average of Five Numbers

For the values 12, 18, 25, 35 and 40, the sum is 130. Divide 130 by 5 to get an average of 26. This is the example loaded by default when the calculator first opens.

Can an Average Be a Decimal?

Yes. The average does not need to be a whole number even when every original value is a whole number. If you average 5 and 8, the result is 6.5. Nothing is wrong with the calculation simply because the answer falls between two whole numbers.

Decimal results are common when the sum is not evenly divisible by the number of observations. The decimal-place selector in the calculator lets you control how much precision is displayed without changing the underlying calculation.

Can You Average Negative Numbers?

Negative numbers can be averaged in exactly the same way as positive numbers. Suppose the observations are -10, -5, 5 and 10. Their sum is zero, so the average is also zero.

If the negative values have greater magnitude than the positive values, the average can be negative. For example, -20, -10 and 6 have a total of -24. Divide by three and the average is -8.

This can be useful when working with temperature changes, profits and losses, measurement errors, elevation changes or any data set where values can fall below zero.

Does Zero Count When Calculating an Average?

Yes, if zero is a real observation in your data. Zero contributes nothing to the sum, but it still increases the number of observations by one. That means including zero can change the average substantially.

Consider 10 and 20. Their average is 15. If you add a real third value of zero, the data become 0, 10 and 20. The total remains 30, but it is now divided by three, so the average falls to 10.

A blank entry is different from zero. A blank means no observation was provided; zero means an observation was provided and its value really is zero. Mixing those concepts is a common source of incorrect averages in spreadsheets and data analysis.

Weighted Average Calculator

A weighted average is used when some values should contribute more heavily than others. Instead of giving every observation identical influence, each value is multiplied by a weight. The weighted products are added together and divided by the total of the weights.

Suppose three scores are 80, 90 and 70, with weights of 20, 30 and 50. Multiply each score by its weight:

• 80 × 20 = 1,600
• 90 × 30 = 2,700
• 70 × 50 = 3,500

The weighted sum is 7,800. The total weight is 100. Divide 7,800 by 100 and the weighted average is 78.

If you calculated the ordinary average instead, you would get 80 because (80 + 90 + 70) ÷ 3 = 80. The weighted result is lower because the score of 70 carries half of the total weight and therefore has much more influence than the score of 80.

Do Weights Have to Add Up to 100?

No. Percentages often add to 100 because they represent portions of a complete whole, but the weighted-average formula does not require that particular total. Weights of 20, 30 and 50 have the same relative influence as 2, 3 and 5 or 0.2, 0.3 and 0.5.

What matters is the relationship among the weights. The calculator totals the weights automatically and divides the weighted sum by that actual total.

Weighted Average for Grades

Course grades are a common use for weighted averages because exams, assignments, projects and participation may each contribute different percentages to the final mark. If that is your specific goal, the Grade Calculator provides dedicated grade and assignment features in addition to the general weighted-average calculation available here.

For example, imagine assignments are worth 30% and have an average score of 88, a midterm is worth 25% with a score of 78, and a final exam is worth 45% with a score of 92. A simple average would treat the three numbers equally, which would ignore the course weighting. A weighted calculation correctly gives the final exam the greatest influence.

Weighted Average Using Quantities

Weights can also represent quantities instead of percentages. Suppose a store sells 10 items at $20 each and 90 items at $12 each. It would be incorrect to average $20 and $12 directly and report $16 as the average selling price, because the store sold far more units at $12.

The correct calculation is (20 × 10 + 12 × 90) ÷ 100. That gives an average selling price of $12.80. Quantity acts as the weight because every individual unit contributes to the overall average.

Average Percentage Calculator

If several percentages should count equally, add the percentages and divide by how many there are. For 80%, 90% and 70%, the total is 240%. Divide by three and the average percentage is 80%.

That simple approach is correct only when equal weighting makes sense. Percentages can hide the number of observations behind them, which means two percentages that look similar may represent very different amounts of underlying data.

When You Should Not Simply Average Percentages

Suppose one location has a success rate of 90% based on 1,000 attempts and another has a success rate of 50% based on only 10 attempts. A simple average of 90% and 50% is 70%, but that gives the tiny ten-attempt group exactly as much influence as the thousand-attempt group.

If your goal is the combined success percentage for all attempts, the group sizes should be used as weights. In this example the large group contributes almost all of the underlying observations, so the combined percentage remains much closer to 90% than to 70%.

Use the optional weights field in Average Percentage mode when every percentage corresponds to a known sample size, quantity, credit value or other weighting factor. If you are working with percentage increases, decreases or percentage differences rather than averaging percentages, use the Percentage Calculator.

Mean, Median and Mode

Mean, median and mode are different ways of describing the center or typical value of a data set. People sometimes use the words interchangeably, but mathematically they are not the same calculation.

What Is the Mean?

The arithmetic mean is the standard average described throughout this page. Add all observations and divide the sum by their count. Every value contributes to the mean, which makes it useful but also means unusually high or low observations can move it substantially.

What Is the Median?

The median is the middle value after the numbers have been arranged from smallest to largest. If there is an odd number of observations, the median is the single number in the center. If there is an even number of observations, average the two middle values.

For 3, 7, 10, 12 and 20, the median is 10 because it is the third value in a sorted list of five numbers. For 3, 7, 10 and 12, there are two middle values: 7 and 10. Their average is 8.5, so the median is 8.5.

What Is the Mode?

The mode is the value that appears most frequently. In 2, 2, 3, 5 and 8, the mode is 2. A data set can have more than one mode if multiple values share the highest frequency.

If every number appears only once, this calculator reports “No mode.” That is more informative than choosing an arbitrary value when none occurs more frequently than the others.

What Is the Range?

Range measures the distance between the smallest and largest values. Subtract the minimum from the maximum. If the data are 10, 13, 18 and 25, the range is 25 − 10 = 15.

The range tells you something about spread rather than center. Two data sets can have identical averages but very different ranges, which is one reason the calculator displays both.

Mean vs. Average

In everyday arithmetic, “mean” and “average” usually refer to the same thing: the arithmetic mean. If someone asks for the average of 4, 8 and 12, they generally expect you to add the three values and divide by three.

In more advanced mathematics and statistics, however, the word average can be used more broadly. Mean, median and mode are all ways to describe central tendency, while specialized means such as the geometric mean and harmonic mean are used for certain types of data.

For the ordinary “average calculator” problem, arithmetic mean is the standard method unless the context tells you otherwise.

Arithmetic Mean, Geometric Mean and Harmonic Mean

The arithmetic mean is appropriate when values are added together and each value contributes equally. There are other types of mean that serve different mathematical purposes, and using the wrong one can create a result that looks reasonable but does not represent the situation correctly.

Arithmetic Mean

The arithmetic mean is the familiar sum divided by count. It is commonly used for temperatures, marks, prices, measurements and repeated observations where every value has equal status.

Geometric Mean

The geometric mean multiplies values and then takes the appropriate root. It is often more suitable for multiplicative changes, growth factors and some types of rate data. A simple arithmetic average of annual growth percentages can be misleading when the values compound over time.

Harmonic Mean

The harmonic mean is based on reciprocals and is useful in certain rate calculations. For example, average speed over equal distances can require a harmonic mean rather than simply averaging two speed values. The correct type of average depends on what is being held constant.

The main calculator on this page focuses on arithmetic and weighted averages because those match the broadest everyday search intent. More specialized means should be used only when the structure of the problem calls for them.

How to Combine Averages From Two or More Groups

You cannot always calculate a true combined average by adding group averages together and dividing by the number of groups. That shortcut works only when every group contains the same number of observations.

Suppose Group A has an average of 80 based on 10 observations and Group B has an average of 90 based on 100 observations. Simply averaging 80 and 90 gives 85, but that would pretend the ten-observation group and the hundred-observation group are equally large.

Instead, reconstruct the totals represented by each group:

• Group A: 80 × 10 = 800
• Group B: 90 × 100 = 9,000

The combined total is 9,800 across 110 observations. Divide 9,800 by 110 and the true combined average is approximately 89.09.

This is mathematically the same principle used by a weighted average. The group size is the weight because a group containing more observations must contribute more to the combined result.

Can You Take the Average of Averages?

You can take a simple average of averages when every underlying group contains the same number of observations. If three classes each contain 25 students, the average of the three class averages equals the combined student average because each class contributes the same number of scores.

If the groups are different sizes, a simple average of their averages is generally incorrect. A class of five students should not receive the same influence as a class of 200 students when calculating the combined average for all students.

Use Combine Averages mode when you know both the group averages and the number of observations behind each one. The calculator weights each group by its size automatically.

How to Find a Missing Number From an Average

If you know the desired average and all but one of the values, you can work backward to find the missing value. First determine how many values the completed set will contain. Multiply that final count by the target average to determine the total that the complete set must have.

Next, add all the known values. Subtract their sum from the required total. The difference is the missing number.

Missing Average Value Example

Suppose your known scores are 70, 80 and 90, and you want four scores to have an average of 85. The completed set will contain four scores, so the required total is:

85 × 4 = 340

The known scores total:

70 + 80 + 90 = 240

Subtract the known total from the required total:

340 − 240 = 100

The missing score must be 100 to produce an average of 85. Missing Value mode performs this process automatically.

If the problem is written as an algebraic equation rather than an average problem, the Algebra Calculator can help with broader equation solving.

How Outliers Affect the Average

An outlier is a value that lies far away from most of the other observations. Because the arithmetic mean uses the numerical value of every observation, a very large or very small outlier can move the mean considerably.

Consider 2, 2, 2, 3 and 100. The total is 109 and the mean is 21.8. Yet four of the five values are between 2 and 3, so a mean of 21.8 does not look typical of most observations.

The median tells a different story. When the numbers are sorted, the middle value is 2. The median therefore remains close to the cluster of ordinary observations even though the extreme value of 100 is present.

Neither measure is automatically right or wrong. The mean answers one question and the median answers another. If the total amount represented by all observations matters, the mean may still be important. If you want a central value that is less sensitive to extremes, the median can sometimes be more descriptive.

Why Average and Median Can Be Very Different

The mean and median tend to be fairly close when a data set is balanced without major extremes. They can separate dramatically when the distribution is skewed or contains outliers.

Income is a common conceptual example. A small number of extremely high values can lift the mean while the median remains tied to the value in the middle of the ordered population. This does not make either measure dishonest; they are simply describing different properties of the data.

That is one reason the Mean Median Mode mode reports both values side by side. Seeing the difference can be more informative than relying on the average alone.

Average With Decimals

Decimals require no special formula. Add the decimal values exactly as you would add whole numbers and divide by the number of observations. For 1.25, 2.50 and 3.75, the sum is 7.50 and the average is 2.50.

Do not round each number before averaging unless the problem specifically requires it. Premature rounding can introduce small errors, especially when many observations are involved. It is usually better to calculate with the full values and round only the final result.

How Rounding Changes an Average

Rounding changes the displayed precision of a number. If the exact average is 12.666666…, rounding to two decimal places gives 12.67. Rounding to one decimal place gives 12.7, while rounding to the nearest whole number gives 13.

The decimal selector in this calculator controls the displayed answer and supporting values. Choosing fewer decimal places makes results easier to read, while additional places can be useful for scientific, engineering or financial calculations where more precision is needed.

If you need to perform the individual addition or division steps manually, the Simple Math Calculator can be used for basic arithmetic.

Average and Ratios

An average and a ratio answer different questions. An average summarizes a set of numerical values, while a ratio compares one quantity with another. The two concepts can appear together in the same problem, but they should not be confused.

For example, a business may calculate the average number of customers per day and separately calculate the ratio of online customers to in-store customers. The average describes a typical daily amount; the ratio describes the relationship between two groups.

For direct ratio calculations, simplification or missing ratio terms, use the Ratio Calculator.

Average in School and Education

Students frequently use averages to summarize quiz scores, assignment results and test marks. If five equally important quizzes are scored 70, 80, 90, 85 and 95, their arithmetic average is 84.

Course grading becomes more complicated when quizzes, assignments, projects and exams do not all have the same weight. In that situation, a weighted average is normally required. A final exam worth 40% of a course should have four times as much influence as an assignment worth 10%.

The Average Calculator can perform the underlying weighted calculation, while the dedicated Grade Calculator is more convenient when the values specifically represent school grades.

Average Price

An average price can be calculated in different ways depending on the question. If you simply record five independent prices and each observation is equally important, the arithmetic mean may be appropriate. Add the five prices and divide by five.

If different quantities were purchased at different prices, however, quantity should usually be used as a weight. Buying one item at $100 and 100 items at $10 does not produce a realistic average unit cost of $55. The much larger quantity purchased at $10 should dominate the weighted average.

This distinction is important in inventory, purchasing, manufacturing, sales analysis and any situation where a price applies to multiple units.

Average Cost

Average cost generally means total cost divided by the number of units or observations. If a project costs $5,000 and produces 100 units, the average cost per unit is $50.

When costs vary among batches, the calculation may need to incorporate the quantity produced or purchased in each batch. That turns the problem into a weighted average rather than a simple average of the individual batch prices.

Average Monthly Expense

Average monthly expenses can help smooth out month-to-month changes. Add the expenses from the months you want to analyze and divide by the number of months included.

For example, if electricity bills over six months are $110, $125, $160, $175, $145 and $115, their total is $830. Dividing by six gives an average monthly bill of approximately $138.33.

The average can be useful for budgeting, but remember that seasonal costs may vary substantially. The maximum, minimum and range shown by the calculator help reveal how much the actual bills move around the mean.

Average Sales

A business can calculate average sales per day, week, month, employee, store or customer. The denominator must match the question. If total monthly revenue is $90,000 across 30 days, average daily revenue is $3,000. If the same $90,000 came from 900 orders, average revenue per order is $100.

Both figures are averages, but they measure different things because they divide the same total by different counts. Always define what one observation represents before interpreting the result.

Average Measurement

Repeated measurements are often averaged to reduce the effect of small random variations. Suppose an object is measured five times as 10.1, 10.2, 10.0, 10.1 and 10.2 centimetres. The arithmetic mean provides a single summary measurement of 10.12 centimetres.

Averaging repeated measurements does not automatically correct systematic error. If the measuring device is consistently miscalibrated, every observation may be shifted in the same direction. An average can reduce random variation, but it cannot guarantee that the measurement process itself is accurate.

Average From a Frequency Table

A frequency table lists each value along with the number of times it occurs. Instead of typing the same value repeatedly, you can treat frequency as a weight.

Suppose a score of 5 occurs three times, a score of 6 occurs once, and a score of 7 occurs twice. The total represented by the frequency table is:

(5 × 3) + (6 × 1) + (7 × 2) = 35

The total frequency is 3 + 1 + 2 = 6. Divide 35 by 6 and the mean is approximately 5.83. Weighted Average mode can perform this calculation directly by entering the values 5, 6 and 7 with weights 3, 1 and 2.

Average of Consecutive Numbers

For a sequence of evenly spaced numbers, the average lies exactly halfway between the first and last values. The numbers 10, 11, 12, 13 and 14 have an average of 12. You can find that by performing the normal calculation or by taking the midpoint of 10 and 14.

The same shortcut works for any arithmetic sequence because the values are symmetrically distributed around their center. For example, 20, 25, 30, 35 and 40 have an average of 30.

For unrelated values, use the ordinary sum-divided-by-count method instead of assuming the midpoint of the smallest and largest numbers is the mean.

Average of Fractions

Fractions can also be averaged, but the fractions first need to be added correctly. Once their total is known, divide that sum by the number of fractions. You can convert fractions to decimals before using this calculator if that is more convenient.

For example, the average of 1/2 and 3/4 is found by adding them to get 5/4 and then dividing by 2. The result is 5/8, or 0.625.

Factors can be useful when simplifying whole-number fractions manually. The Factor Calculator can find factors, factor pairs, greatest common factors and prime factorizations when you need them for related math work.

How to Calculate an Average in Excel

Microsoft Excel includes an AVERAGE function. If your values are stored in cells A1 through A10, you can calculate their arithmetic mean with:

Excel ignores empty cells in a range but handles cells containing numerical zero differently because zero is a real number. That distinction can change the result, so check whether a zero represents an actual observation or a placeholder for missing data.

If you need a weighted average in Excel, one common approach is to multiply values by weights using SUMPRODUCT and divide by the total weights. If values are in A1:A5 and corresponding weights are in B1:B5, the calculation can be written as:

How to Calculate an Average in Google Sheets

Google Sheets uses the same basic AVERAGE syntax. If the values are in cells A1 through A10, enter =AVERAGE(A1:A10). For a weighted average, SUMPRODUCT can also multiply each value by its corresponding weight before dividing by the sum of the weights.

An online average calculator can be quicker when you have a temporary list of numbers and do not need to create a spreadsheet. A spreadsheet becomes more useful when the data are already organized in rows and columns or when you need repeated calculations.

Common Mistakes When Calculating an Average

The formula for an arithmetic mean is simple, but several common mistakes can still produce an incorrect result.

• Dividing by the wrong count: The denominator must equal the number of observations included in the sum.
• Ignoring a zero: A genuine zero is still an observation and must be counted.
• Counting a blank as zero: Missing data and an observed value of zero are not the same thing.
• Using a simple average when weights differ: Values with different importance, frequency or quantity may require a weighted average.
• Taking a simple average of unequal group averages: Group size must be considered when combining groups.
• Averaging percentages with different sample sizes: The percentages may need to be weighted by the numbers of observations behind them.
• Rounding too early: Keep full precision during intermediate calculations and round the final result when possible.
• Confusing mean and median: They measure center differently and can produce very different answers when outliers are present.

Why Use an Average Calculator?

For two or three easy numbers, calculating an average mentally may be faster than using a tool. The advantage of a calculator becomes clearer when the list contains many values, decimals, negative numbers, weights or several groups that need to be combined.

This calculator also keeps related information together. Instead of calculating the mean and then performing separate calculations for count, range, median or weighted results, you can enter the data once and see the relevant values in the same result area.

The different modes are also intended to reduce a common problem: applying the ordinary average formula to data that should actually be weighted. By separating simple averages, weighted averages, percentage averages and combined groups, the calculator makes the assumptions behind each answer clearer.

Average Calculator Frequently Asked Questions

Final Thoughts

The ordinary average is one of the simplest calculations in mathematics: add the values and divide by how many values there are. The important part is knowing when that simple formula accurately represents the question you are trying to answer.

If every observation should count equally, use the Average / Mean mode. If some values represent greater importance, frequency or quantity, use Weighted Average. Use Average Percentage when working with percentages, Mean Median Mode when you need a broader statistical summary, Missing Value when you know the target average, and Combine Averages when groups contain different numbers of observations.

By choosing the method that matches the structure of the data, you can avoid common mistakes such as averaging unequal groups as though they were identical or giving a small sample the same influence as a much larger one. The result is an average that is not only mathematically correct, but also appropriate for what your numbers actually represent.