Calculate arithmetic mean, weighted average, geometric mean, or harmonic mean. See the formula, your numbers, step-by-step math, and guidance on which type of average to use.
Average Calculator
Choose an average type, enter your values, and click Calculate for instant results.
Arithmetic Mean
Ordinary numerical data, like test scores or temperatures.
Weighted Average
Some values count more, like grades or credit hours.
Geometric Mean
Multiplicative relationships, like growth factors.
Harmonic Mean
Certain rates and ratios, like equal-distance speeds.
Separate numbers with commas, spaces, or one per line. Positive numbers, negative numbers, zero, and decimals are all accepted. Example: 85, 92, 78, 96, 88, 72, 91
ValueWeight
Weights represent relative importance, such as percentages, points, credits, or frequency. Weights do not have to add up to 100; this calculator divides by the total weight automatically. If you intend your weights as percentages, make sure they total 100 for that interpretation.
An average is a value used to summarize or represent a group of numbers. In everyday mathematics, the word "average" most often means the arithmetic mean: add all the values and divide by how many values there are.
For example, suppose the numbers are 2, 4, and 6. Add them: 2 + 4 + 6 = 12. There are 3 values. Divide: 12 ÷ 3 = 4. The arithmetic average is 4.
The arithmetic mean can also be understood as equal sharing. The original values contain a total of 12. If that total were redistributed evenly among three positions, each position would contain 4. That is one reason the mean is useful: it creates a single number that represents the same total spread equally across all observations.
Figure 1
The Arithmetic Mean Shares the Total Equally
2 + 4 + 6
↓
Same Total = 12
↓
444
For 2, 4, and 6, the total is 12. Redistributing that same total of 12 evenly across three positions gives 4, 4, and 4, so Average = 4.
What Is the Average Formula?
For an ordinary arithmetic average: Average = Sum of Values ÷ Number of Values. Using mathematical notation: Mean = Σx / n. The symbol Σ means to add the values. The letter n represents the number of observations.
Suppose the values are 85, 92, 78, 96, 88, 72, 91. Add them: 85 + 92 + 78 + 96 + 88 + 72 + 91 = 602. There are 7 values. Therefore Average = 602 ÷ 7 = 86. The arithmetic mean is 86.
Figure 2
Sum and Count
85 + 92 + 78 + 96 + 88 + 72 + 91
↓
Sum = 602 · Count = 7
↓
602 ÷ 7
↓
Average = 86
Finding the sum and the count first makes the division step easy to check: 602 ÷ 7 = 86.
How Do You Calculate an Average Step by Step?
Use 12, 18, 20, 25, 30.
1Add the numbers: 12 + 18 + 20 + 25 + 30 = 105.
2Count how many values there are. There are 5.
3Divide the sum by the count: 105 ÷ 5 = 21. Therefore Average = 21.
The process can be remembered as: Add, Count, Divide. Do not divide by a value simply because it appears large or because it is the last number in the list. The denominator is the number of observations.
What Is the Difference Between Average and Mean?
In ordinary school mathematics, "average" usually refers to the arithmetic mean. For example: 4, 6, 8. Arithmetic Mean: (4+6+8)/3 = 18/3 = 6.
In more advanced mathematics and statistics, however, there are several kinds of means. This calculator supports arithmetic mean, weighted average, geometric mean, and harmonic mean. That is why "average" can be a broader word than one single formula.
What Is an Arithmetic Mean?
The arithmetic mean is the standard average most people first learn. Formula: Arithmetic Mean = Sum of Values ÷ Number of Values. It is often useful for data that combines additively. Examples may include test scores, daily temperatures, measurements, heights, quantities, or other numerical observations.
Suppose five temperatures are 72, 75, 77, 74, 72. Add: 72+75+77+74+72 = 370. Divide by 5: 370÷5 = 74. The arithmetic mean temperature is 74 degrees. The calculation itself is straightforward, but interpreting the result still depends on what the measurements represent.
When Is the Arithmetic Mean Useful?
The arithmetic mean can be useful when all values should influence the result, the observations are numerical, each observation carries equal importance, and extreme outliers are not making the result misleading for the question being asked.
Example: Scores 82, 84, 86, 88, 90. Mean: 86. The values are fairly balanced around the center, so the arithmetic mean provides an intuitive summary.
How Do Outliers Affect the Average?
Because every value is included in the arithmetic mean, an extreme value can substantially change the result. Consider 10, 11, 11, 12, 13. Sum: 57. Mean: 57÷5 = 11.4.
Now replace 13 with 100. The new data is 10, 11, 11, 12, 100. Sum: 144. Mean: 144÷5 = 28.8. One value dramatically changed the mean.
Figure 3
One Extreme Value Can Pull the Arithmetic Mean
Without Outlier
10, 11, 11, 12, 13
Mean = 11.4
With Outlier
10, 11, 11, 12, 100
Mean = 28.8
Changing one value from 13 to 100 pulls the mean from 11.4 up to 28.8, even though only one of the five numbers changed.
What Is the Difference Between Average and Median?
The arithmetic mean uses every value. The median is the middle value after the data is sorted. Consider 10, 11, 11, 12, 100. Arithmetic Mean: 28.8. Sorted data: 10, 11, 11, 12, 100. Median: 11.
The mean is pulled upward by 100. The median remains near where most of the data lies. Neither measure is automatically "better." They answer different questions. When extreme values are important to the total, the mean may be useful. When you want the middle position in a skewed data set, the median may be more informative. For a calculator that compares these measures directly, use the Mean, Median, Mode and Range Calculator.
Why Can an Average Salary Be Misleading?
Salary data provides a useful example of why the type of average matters. Consider the fictional salaries: $35,000, $40,000, $42,000, $45,000, $500,000. Total: $662,000. Arithmetic Mean: $662,000 ÷ 5 = $132,400. But the median salary is $42,000.
Both results are mathematically correct. They answer different questions. The mean considers the total amount distributed evenly among all five values. The median identifies the middle salary after sorting. The unusually high $500,000 value pulls the arithmetic mean far above most salaries in the list. This is why real-world statistics should be interpreted instead of reporting the word "average" without specifying what measure was used. For a side-by-side comparison of mean and median, the Mean, Median, Mode and Range Calculator can help.
What Is a Weighted Average?
A weighted average is used when some values should influence the final result more than others. Formula: Weighted Average = Σ(value × weight) ÷ Σ(weights).
Suppose three scores are 80, 90, 100. But they have weights 20, 30, 50. Calculate each weighted contribution: 80×20 = 1600. 90×30 = 2700. 100×50 = 5000. Add the weighted values: 1600 + 2700 + 5000 = 9300. Add the weights: 20+30+50 = 100. Divide: 9300÷100 = 93. The weighted average is 93.
Figure 4
Weighted Average Gives Some Values More Influence
80 × 20 = 1600
90 × 30 = 2700
100 × 50 = 5000
↓
Weighted Sum = 9300 · Total Weight = 100
↓
9300 ÷ 100 = 93
Each value is multiplied by its own weight before the values are added together, so the value with the largest weight, 100, pulls the result up the most.
Do Weights Have to Add Up to 100?
No. Weights can represent relative importance instead of percentages. Suppose 80 has weight 2, 90 has weight 3, and 100 has weight 5. Calculate: 80×2 = 160. 90×3 = 270. 100×5 = 500. Weighted Sum: 930. Total Weight: 10. Weighted Average: 930÷10 = 93.
The relative weighting is the same as 20, 30, 50. The weighted average is therefore also 93. Weights represent relative importance, and this calculator divides by the total weight automatically.
Where Are Weighted Averages Used?
Weighted averages appear when different observations do not contribute equally. Examples include course grades, credit hours, weighted scoring systems, product ratings with different sample sizes, certain scientific calculations, and many other situations involving unequal importance.
Average atomic mass provides a classic weighted-average idea because different isotopes may occur in different proportions. Consider a simplified fictional example: Isotope A has mass 10 and abundance 80%. Isotope B has mass 11 and abundance 20%. Weighted Average: 10×0.80 + 11×0.20 = 8 + 2.2 = 10.2. This example is fictional and is included only to demonstrate the weighted-average calculation. If you need to convert values or weights into percentages first, use the Percentage Calculator.
What Is the Geometric Mean?
The geometric mean is calculated by multiplying the values and then taking the nth root, where n is the number of values. Formula: Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n). For this calculator, geometric-mean inputs should be positive values greater than zero.
Consider 2 and 8. Multiply: 2×8 = 16. There are 2 values. Take the square root: √16 = 4. Geometric Mean: 4.
Figure 5
Geometric Mean Uses Multiplication Instead of Addition
2 × 8
↓
16
↓
√16
↓
4
Where the arithmetic mean adds values and divides by the count, the geometric mean multiplies values and takes a root, which matters when values combine multiplicatively.
When Should You Use the Geometric Mean?
The geometric mean is useful when values combine multiplicatively rather than additively. It is commonly associated with growth factors, proportional changes, compound processes, and certain rate comparisons.
Suppose yearly growth factors are 1.10, 0.95, 1.20. Multiply: 1.10×0.95×1.20 = 1.254. There are 3 periods. Take the cube root: 1.254^(1/3) ≈ 1.0787. That corresponds to an equivalent compounded average growth factor of about 1.0787, or approximately 7.87% above 1. This does not mean every individual year changed by exactly 7.87%. It means the constant multiplicative factor that would produce the same overall compounded result is approximately 1.0787. If you want to explore how compounding works over multiple periods in a financial context, the Compound Interest Calculator can help, though this average calculator does not provide investment advice.
Growth Factor Chain
1.10×0.95×1.20≈ 1.0787 per period
The product of the three growth factors is 1.254. Splitting that product evenly across 3 periods geometrically gives an equivalent per-period growth factor of about 1.0787, roughly 7.87% growth per period.
Why Can the Arithmetic Mean Be Misleading for Compounded Growth?
Suppose an investment changes +50% and then -50%. The arithmetic average of the percentage changes is 0%. But the value does not return to its starting point. Start: 100. Increase 50%: new value 150. Then decrease 50%: new value 75. The ending value is 25% below the starting value. This demonstrates why multiplicative changes require careful treatment. Do not automatically average percentage changes arithmetically when the process compounds.
What Is the Harmonic Mean?
The harmonic mean is another type of average. Formula: Harmonic Mean = n ÷ Σ(1/x). It is particularly useful for certain kinds of rates and ratios. For this calculator, harmonic-mean inputs should be positive values greater than zero.
Consider 30 and 60. Calculate the reciprocals: 1/30 and 1/60. Add: 1/30 + 1/60 = 2/60 + 1/60 = 3/60. There are 2 values. Harmonic Mean: 2 ÷ (3/60) = 40.
Why Is the Harmonic Mean Useful for Some Speed Problems?
Suppose you travel 60 miles at 60 mph and then another 60 miles at 30 mph. The arithmetic mean of the speeds would be 45 mph. But that is not the correct average speed for equal distances.
First trip: 60 miles ÷ 60 mph = 1 hour. Second trip: 60 miles ÷ 30 mph = 2 hours. Total Distance: 120 miles. Total Time: 3 hours. Average Speed: 120÷3 = 40 mph. The harmonic mean of 60 and 30 is also 40.
Figure 6
For Equal Distances, the Harmonic Mean Gives the Correct Average Speed
Trip 1
60 miles at 60 mph
Time = 1 hour
Trip 2
60 miles at 30 mph
Time = 2 hours
Total: 120 miles in 3 hours → 120 ÷ 3 = 40 mph (Harmonic Mean = 40 mph, not the 45 mph arithmetic mean)
Which Type of Average Should I Use?
The correct average depends on what your values represent. Use the Arithmetic Mean when values contribute additively and generally carry equal importance. Use a Weighted Average when some values should count more than others. Use the Geometric Mean when values combine multiplicatively, such as certain growth factors. Use the Harmonic Mean for certain rates and ratios, especially equal-distance rate problems.
Figure 7
Four Types of Averages at a Glance
Arithmetic
Σx / n
Add then divide by count
Weighted
Σ(wx)/Σw
Different importance
Geometric
(Πx)^(1/n)
Multiplicative growth
Harmonic
n/Σ(1/x)
Certain rates and ratios
All four measures answer the question "what is a typical value?" but they do so with different math, which is why the right choice depends on what the numbers represent.
Is Average the Same as Mode?
No. The arithmetic mean uses addition and division. Mode identifies the value that occurs most often. Example: 2, 2, 2, 10. Arithmetic Mean: (2+2+2+10)/4 = 16/4 = 4. Mode: 2. For mean, median, mode, and range calculations, use the Mean, Median, Mode and Range Calculator.
Is Average the Same as Range?
No. Average describes a center. Range describes how far the smallest and largest values are apart. Example: 40, 50, 60. Arithmetic Mean: 50. Range: 60-40 = 20. They describe different properties of the data.
Is Average the Same as Standard Deviation?
No. An average describes a center. Standard deviation describes spread around the mean. Consider Data Set A: 49, 50, 51. Mean: 50. Data Set B: 0, 50, 100. Mean: 50. Both have the same arithmetic mean. But their spreads are obviously very different. If you need to measure variation around the mean, use the Standard Deviation Calculator.
When Should I Use the Statistics Calculator?
This page focuses specifically on averages. If you need a broader statistical summary rather than only an average, including measures such as median, mode, range, quartiles, IQR, and other descriptive statistics, use the Statistics Calculator.
How Should You Round an Average?
Do not round intermediate values too early. Suppose 17÷3 = 5.666666... If the final result requires two decimal places, report 5.67. If it requires one decimal place, report 5.7. Keep greater precision during the calculation, then round the final answer. If your answer must be reported to a specific number of decimal places or significant figures, use the Rounding Calculator after calculating the full-precision average.
Visual Lesson: How to Find the Average
If you learn best by watching a worked example, Supercharged Science & Math - Aurora Lipper also provides a visual lesson on how to find the average (mean). Use this only as a supplementary learning resource.
What Are Common Average Calculation Mistakes?
Dividing by the wrong number. The arithmetic mean divides by the number of observations, not by one of the values.
Forgetting a value. Every intended observation must be included in the sum.
Counting a value twice. The sum and count must describe the same data set.
Confusing mean with median. Mean uses arithmetic. Median uses ordered position.
Confusing mean with mode. Mode identifies frequency, not an arithmetic result.
Using arithmetic mean for a weighted problem. Values with different importance require a weighted average.
Using arithmetic mean for compounded growth. Multiplicative processes may require the geometric mean.
Using arithmetic mean for certain rate problems. Some equal-quantity rate problems require the harmonic mean.
Rounding too early. Keep extra precision during intermediate calculations.
Ignoring outliers. Extreme observations can strongly affect the arithmetic mean.
What Should You Leave This Page Knowing?
Do not leave knowing only "My average is 86." Leave knowing:
I understand what an average is.
I know what arithmetic mean means.
I know the basic average formula.
I know to add the values and divide by the count.
I know how to check the sum and count.
I understand how outliers can change the arithmetic mean.
I know the difference between mean and median.
I know why an average salary can differ greatly from a median salary.
I understand what a weighted average is.
I know that weights do not have to total 100 as long as they are used consistently.
I know what a geometric mean is.
I know why geometric mean is useful for multiplicative relationships.
I know what a harmonic mean is.
I understand why equal-distance speed problems can require a harmonic mean.
I know that "average" does not always mean the same formula.
I know when to use the Mean, Median, Mode and Range Calculator.
I know when to use the Statistics Calculator.
I know when standard deviation answers a different question.
I know not to round too early.
And most importantly: I can see how the calculator produced my average. That is what the CalculateThisWay Average Calculator should help someone understand.
Formulas at a Glance
Average Type
Formula
Best Used For
Arithmetic Mean
Σx / n
Ordinary equally weighted numerical data
Weighted Average
Σ(wx) / Σw
Values with different importance
Geometric Mean
(Πx)^(1/n)
Multiplicative relationships and growth factors
Harmonic Mean
n / Σ(1/x)
Certain rates and ratios
Sum
Add all observations
Used to calculate the arithmetic mean
Count
Number of observations
Used in every average formula
Average Examples With Answers
Example 1. Data: 2, 4, 6
Arithmetic Mean: 4
Example 2. Data: 10, 20, 30, 40
Sum: 100Count: 4Average: 25
Example 3. Data: 85, 92, 78, 96, 88, 72, 91
Sum: 602Count: 7Arithmetic Mean: 86
Example 4. Values 80, 90, 100 with weights 20, 30, 50
Weighted Average: 93
Example 5. Values 80, 90, 100 with weights 2, 3, 5
Weighted Average: 93
Example 6. Geometric Mean of 2 and 8
Answer: 4
Example 7. Harmonic Mean of 30 and 60
Answer: 40
Example 8. Temperatures: 72, 75, 77, 74, 72
Arithmetic Mean: 74
Example 9. Salaries: 35,000, 40,000, 42,000, 45,000, 500,000
Arithmetic Mean: 132,400Median: 42,000
Use this example to demonstrate interpretation: the mean and median answer different questions about the same data.
Example 10. Fictional isotope masses: 10 at 80%, 11 at 20%
Weighted Average: 10.2
Try It Yourself
For the numbers 12, 18, 24, 30, find the arithmetic mean.
Hint: add all four numbers first, then divide the total by 4.
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An average is a single value used to represent or summarize a group of numbers. In everyday math it usually means the arithmetic mean, found by adding the values and dividing by how many there are.
What is the average?
The average of a set of numbers is typically the arithmetic mean: add every value, then divide by the count. For 2, 4, and 6, the average is (2+4+6)/3 = 4.
What is average in math?
In mathematics, average can refer to several measures, including the arithmetic mean, weighted average, geometric mean, and harmonic mean. Without more context, average usually means the arithmetic mean.
What is the average formula?
The basic average formula is Average = Sum of Values / Number of Values, often written Mean = Σx / n.
How do you calculate an average?
Add all the values together to get the sum, count how many values there are, then divide the sum by the count.
How do you find the average?
Find the average by adding every number in the list, counting how many numbers you added, and dividing the sum by that count.
How do you calculate mean?
Calculate the mean the same way you calculate an arithmetic average: sum every value and divide by the number of values.
Is average the same as mean?
In ordinary school mathematics, yes, average usually refers to the arithmetic mean. In more advanced statistics, several other types of means also exist.
What is arithmetic mean?
The arithmetic mean is the standard average: the sum of a set of values divided by how many values there are. It is useful for data that combines additively, like test scores or temperatures.
What is a weighted average?
A weighted average gives some values more influence than others. It is calculated as the sum of each value multiplied by its weight, divided by the sum of the weights.
How do you calculate a weighted average?
Multiply each value by its weight, add those products together, then divide by the total of the weights. For values 80, 90, 100 with weights 20, 30, 50, the weighted average is 9300÷100 = 93.
Do weights have to add up to 100?
No. Weights represent relative importance and can be any consistent set of numbers, such as 2, 3, and 5 instead of 20, 30, and 50. The calculator always divides by the total weight automatically.
What is geometric mean?
The geometric mean multiplies a set of positive values together and takes the nth root, where n is the count of values. For 2 and 8, the geometric mean is √(2×8) = √16 = 4.
How do you calculate geometric mean?
Multiply all the values together, then take the nth root of that product, where n is the number of values. This calculator requires every value to be greater than zero.
When should you use geometric mean?
Use the geometric mean when values combine multiplicatively, such as growth factors, proportional changes, or compounding rates, rather than ordinary additive quantities.
What is harmonic mean?
The harmonic mean is the number of values divided by the sum of their reciprocals. For 30 and 60, the harmonic mean is 2÷(1/30+1/60) = 40.
How do you calculate harmonic mean?
Add the reciprocals of every value, then divide the count of values by that sum. This calculator requires every value to be greater than zero.
When should you use harmonic mean?
Use the harmonic mean for certain rates and ratios, especially when averaging rates over equal quantities, such as equal distances traveled at different speeds.
What type of average should I use?
Use the arithmetic mean for ordinary additive data, a weighted average when values carry different importance, the geometric mean for multiplicative relationships, and the harmonic mean for certain rate and ratio problems.
What is the difference between average and median?
The average (arithmetic mean) uses every value in the calculation. The median is the middle value after sorting. An extreme value can pull the mean away from the median.
What is the difference between average and mode?
The average (arithmetic mean) is calculated with addition and division. The mode is simply the value that occurs most often, which may be very different from the mean.
What is the difference between average and range?
The average describes the center of a data set. The range describes how far apart the smallest and largest values are. They answer different questions.
What is the difference between average and standard deviation?
The average describes a center. Standard deviation measures how far values tend to spread out around that center. Two data sets can share the same average but have very different standard deviations.
Can outliers change the average?
Yes. Because the arithmetic mean uses every value, one unusually large or small value can shift it substantially. Changing 13 to 100 in 10, 11, 11, 12, 13 moves the mean from 11.4 to 28.8.
Why can an average salary be misleading?
A single very high or very low salary can pull the arithmetic mean far from where most salaries actually sit, which is why median salary is often reported alongside, or instead of, the mean.
How do you calculate average temperature?
Add each temperature reading together and divide by the number of readings, the same process used for any arithmetic mean.
How is weighted average used for grades?
Course grades often weight assignments differently, such as counting a final exam more than a quiz. Each component is multiplied by its weight, the products are summed, and the total is divided by the sum of the weights.
How does average atomic mass use a weighted average?
Average atomic mass is a weighted average of isotope masses, weighted by how abundant each isotope is, because isotopes of an element do not necessarily occur in equal proportions.
Can an average be a decimal?
Yes. Averages are frequently decimals. The average of 85, 92, 78, 96, 88, 72, and 91 happens to be the whole number 86, but many data sets produce a decimal result.
Can an average be negative?
Yes, if the underlying values are negative or mixed. For -5, 0, and 5, the arithmetic mean is 0.
Can the average be larger than some values?
Yes. The arithmetic mean only needs to represent the whole set, so it is normal for it to be larger than some individual values and smaller than others.
Can the average be smaller than some values?
Yes, for the same reason. The mean sits somewhere between the minimum and maximum of the data, but it does not have to equal any individual value.
Does the average have to be one of the original numbers?
No. The average is calculated from the data but is rarely one of the original numbers itself, except in special cases like a single value or a perfectly symmetric data set.
How do I round an average?
Keep extra precision during the calculation and round only the final answer. For example, 17÷3 = 5.666..., which rounds to 5.67 at two decimal places.
Why is the average speed not always the arithmetic mean of two speeds?
When equal distances are traveled at different speeds, the arithmetic mean of the speeds overstates the true average speed. The harmonic mean gives the correct result, such as 40 mph for 60 mph and 30 mph over equal distances.
Can geometric mean use negative numbers?
Not on this calculator. Geometric Mean mode here requires positive values greater than zero to avoid undefined or complex results.
Can harmonic mean include zero?
No. A zero value makes the reciprocal undefined, so this calculator requires every Harmonic Mean input to be greater than zero.
Arithmetic mean equals the sum of values divided by the count of values.
Weighted average equals the sum of value-weight products divided by the total weight.
Weights may be percentages or relative weights as long as they are used consistently.
Geometric Mean mode on this calculator uses positive values greater than zero and is computed internally using a log-based method for numerical stability.
Harmonic Mean mode on this calculator uses positive values greater than zero.
Arithmetic mean can be sensitive to outliers.
Median is calculated differently and is handled by the Mean, Median, Mode and Range Calculator.
Results retain greater internal precision before display rounding.
The appropriate average depends on the mathematical context.
The calculator does not treat arithmetic mean as universally appropriate for every type of data.
Last reviewed: October 4, 2026
This calculator is provided for general educational and informational purposes only. It is not a substitute for instruction from a qualified teacher or textbook, and it is not financial, medical, or professional advice. Always double-check results that will be used for graded coursework, professional work, or any other high-stakes purpose.