Average Calculator
Find the average of any list of numbers, percentages or times with every step, or combine group averages the correct way.
Separate values with commas, spaces or new lines. Times such as 1:32.4 and percentages such as 12% work too. Ctrl + Enter calculates.
Enter each group's average and how many values it has. Leave unused rows empty.
If the total of 495 were shared equally, each of the 6 values would be 82.5.
Where each value sits
4 above the average, 2 below. The gaps above add to +25 and the gaps below to −25, so they cancel: the average is the balance point.
Your calculation
The same steps the calculator runs, with your numbers.
Other types of average for your data
The arithmetic mean above is the usual meaning of average.
The calculator uses every value you enter.
What Is an Average?
An average is a single number that represents a whole set of values. In everyday use, and in this calculator, average means the arithmetic mean: add the values and divide by how many there are. NIST describes the mean as the measure most commonly referred to as the average, and OpenStax notes that the two words are used interchangeably outside technical statistics.
The mean has two useful interpretations. It is the fair share: if the total were split evenly, every value would equal the average. It is also the balance point: the distances of the values above the average add up to exactly the same amount as the distances below it. The number line in the results shows both.
People calculate averages for test scores and grades, monthly spending, temperatures, sales, sports times and survey results. The same arithmetic applies in every case, but percentages, rates, times and group averages each need a little care, covered below.
How to Use the Average Calculator
- Choose List of values and type or paste your numbers. Commas, spaces, semicolons and new lines all work as separators, so you can paste a column from a spreadsheet. Negative numbers and decimals are accepted.
- Add a unit if needed. End values with % to average percentages, or type times as m:ss or h:mm:ss, such as 1:32.4 or 1:05:30. The result comes back in the same format.
- Choose Combine averages when you only know each group's average and size, such as class averages or monthly averages with different numbers of days.
The results show the average with a plain language meaning, a number line with the average and median marked, six tiles (sum, median, minimum, maximum, range and sample standard deviation), the steps with your numbers and a table of alternative averages. In Combine averages mode you see each group's share and how far the simple average of averages would be off.
Average Formula
The average formula divides the sum of the values by the count of values.
In statistics the mean of a sample is written x̄ and the mean of a whole population is written μ. Both use the same formula.
How to Calculate an Average Manually
- Write down every value, including real zeros.
- Count the values to get n.
- Add them. Keep the sign of negative numbers.
- Divide the sum by n and round only at the end.
For the temperatures −3, 2, 5, −1, 4, 7 and 0: the sum is −3 + 2 + 5 − 1 + 4 + 7 + 0 = 14, n = 7, and the average is 14 ÷ 7 = 2 degrees.
For the bills 120.50, 98.75, 143.20 and 110.00: the sum is 472.45 and the average is 472.45 ÷ 4 = 118.1125, or 118.11 rounded to cents.
Types of Average and When to Use Each
The arithmetic mean is the default, but other averages answer different questions. All examples below were computed with the same code as the calculator.
| Type | Formula | Example | Best for |
|---|---|---|---|
| Arithmetic mean | Sum ÷ n | 85, 92, 78, 90, 88, 62 → 82.5 | Most everyday averages |
| Median | Middle value when sorted | 40k, 42k, 45k, 48k, 250k → 45k | Incomes, prices, data with outliers |
| Geometric mean | nth root of the product | Growth +10%, +20%, −5% → 7.84% a year | Growth rates, returns, ratios |
| Harmonic mean | n ÷ Σ(1/x) | 60 and 40 km/h → 48 km/h | Average speed over equal distances |
| Quadratic mean (RMS) | √(Σx² ÷ n) | 3, 4, 5 → 4.08 | Errors, voltages, alternating signals |
| Weighted mean | Σ(w × x) ÷ Σw | Grades by credit hours | Values that count unequally |
| Trimmed mean | Mean after dropping extremes | Scores without 92 and 62 → 85.25 | Judged events, resisting outliers |
For the growth example, the factors 1.10 × 1.20 × 0.95 multiply to 1.254, and the cube root of 1.254 is 1.0784, so the investment grew 7.84% a year on average. The arithmetic mean of 10, 20 and −5 is 8.33%, which overstates the result. For any set of positive values that are not all equal, the harmonic mean is below the geometric mean, which is below the arithmetic mean.
Average of Averages: Combining Groups
When groups have different sizes, the average of their averages is wrong. Weight each group average by its count instead.
The simple average (82 + 76 + 90) ÷ 3 = 82.67 is 1.74 points too high, because the small class with the highest average counts as much as the largest class. The two methods agree only when every group has the same size. The same rule applies to store averages, monthly averages with different numbers of days and survey results from samples of different sizes.
Averaging Percentages and Rates
Percentages based on different totals behave like group averages. Scoring 80% on a 50 question test (40 correct) and 90% on a 150 question test (135 correct) gives 175 out of 200, which is 87.5%, not the simple average of 85%.
Rates such as speed work the same way. Driving 120 km at 60 km/h takes 2 hours and returning at 40 km/h takes 3 hours, so the average speed is 240 ÷ 5 = 48 km/h. Always divide the total quantity by the total time or total base.
Averaging Times
Convert times to a single unit before adding. The lap times 1:32.4, 1:30.8, 1:33.1 and 1:29.9 are 92.4, 90.8, 93.1 and 89.9 seconds. The sum is 366.2 seconds and the average is 91.55 seconds, or 1:31.55.
Adding the minutes and seconds columns separately fails whenever the seconds pass 60. The calculator converts automatically when a value contains a colon, and returns the total, average, median and range as times.
Average vs Median: Which One to Report
The average uses every value, so one extreme value can move it a long way. For the salaries 40,000, 42,000, 45,000, 48,000 and 250,000, the average is 85,000, higher than four of the five salaries. The median, 45,000, describes a typical salary better.
OpenStax recommends the median when data contain outliers, because it depends on the order of the values rather than their size. Use the average when values are roughly symmetric and every unit matters to the total, such as average spending used to set a budget. When the average and median in the results are far apart, look at the number line for an outlier.
Common Mistakes When Calculating an Average
- Leaving out real zeros. A missed assignment scored 0 is a value. Dropping it raises the average.
- Counting blanks as zeros. An empty cell for a day with no data is not 0. Remove it instead.
- Averaging averages of unequal groups. Weight by group size, as shown above.
- Averaging percentages with different bases. Go back to the counts and divide total by total.
- Using the arithmetic mean for speeds or growth. Use total distance over total time, or the geometric mean for growth.
- Rounding too early. Round the final answer only. Rounding each value first can shift the result.
- Using commas inside numbers. In a list, 1,250 reads as two values, 1 and 250. Type 1250.
Related Calculations
The Mean Median Mode Calculator adds the mode, weighted averages, grouped data and the score needed for a target average. The Statistics Calculator gives quartiles, variance and a full summary.
For school, the GPA Calculator and Grade Calculator apply weighted averages to credits and category weights. The Average Return Calculator uses the geometric mean for investments, and the Percent Calculator handles percentage changes.
Frequently Asked Questions
How do you calculate the average?
Add all the values, then divide the total by how many values there are. For the test scores 85, 92, 78, 90, 88 and 62, the sum is 495 and there are 6 scores, so the average is 495 ÷ 6 = 82.5. This is the arithmetic mean, the number every value would equal if the total were shared out evenly. Include zeros that are real values, such as a missed test scored 0, but leave out blanks. Negative numbers count with their sign: −3, 2, 5, −1, 4, 7 and 0 add to 14, giving an average of 2.
What is the difference between mean and average?
In everyday use they mean the same thing: add the values and divide by the count. OpenStax Introductory Statistics notes that the technical term is arithmetic mean, while average can refer to any measure of the center, and NIST describes the mean as the value most commonly referred to as the average. The median and mode are also measures of the center. For 40,000, 42,000, 45,000, 48,000 and 250,000, the mean is 85,000 but the median is 45,000, because one large value pulls the mean up.
How do you find the average of percentages?
If every percentage is based on the same total, add them and divide by the count: 12%, 15%, 9% and 14% average 12.5%. If the totals differ, weight each percentage by its total. Scoring 80% on a 50 question test and 90% on a 150 question test means 40 + 135 = 175 correct out of 200, which is 87.5%, not the simple average of 85%. Use the Combine averages mode with each percentage as the average and each total as the count to get the correct figure.
How do you calculate an average of averages?
Multiply each group's average by its size, add those totals and divide by the combined size. Classes of 30, 25 and 10 students with averages of 82, 76 and 90 give 82 × 30 + 76 × 25 + 90 × 10 = 5,260 points over 65 students, so the combined average is 80.92. Averaging the three averages directly gives 82.67, which is too high because it treats the class of 10 as if it were as large as the class of 30. The simple average only works when every group has the same size.
How do you find the average speed of a round trip?
Divide the total distance by the total time, which for equal distances is the harmonic mean of the speeds. Driving 120 km out at 60 km/h takes 2 hours, and returning at 40 km/h takes 3 hours, so the average speed is 240 km ÷ 5 h = 48 km/h, not 50 km/h. The arithmetic mean overstates it because you spend more time at the slower speed. The harmonic mean formula gives the same result: 2 ÷ (1/60 + 1/40) = 48.
How do you calculate the average time in minutes and seconds?
Convert every time to seconds, average the seconds, then convert back. For lap times of 1:32.4, 1:30.8, 1:33.1 and 1:29.9, the seconds are 92.4, 90.8, 93.1 and 89.9, which add to 366.2. Dividing by 4 gives 91.55 seconds, or 1:31.55. Averaging the minutes and seconds columns separately goes wrong whenever the seconds carry past 60. This calculator accepts times in m:ss or h:mm:ss format directly and shows the average, total and spread in the same format.
Sources & References
- NIST/SEMATECH. e Handbook of Statistical Methods, 1.3.5.1 Measures of Location (mean as the average, median, trimmed mean, midrange). itl.nist.gov
- OpenStax. Introductory Statistics 2e, 2.5 Measures of the Center of the Data (mean and average, median with outliers). openstax.org
- OpenStax. Introductory Business Statistics 2e, 2.5 Geometric Mean (geometric mean for growth rates). openstax.org
- NIST. Dataplot Reference Manual: Harmonic Mean (definition n ÷ Σ(1/x)). itl.nist.gov
Results are for educational purposes. Every number on this page was recomputed with the same code the calculator uses. Methodology reviewed: 2026.