About the Standard Deviation Calculator
Standard Deviation Calculator takes a list of numbers and works out how spread out they are. It gives the standard deviation and variance for a sample (dividing by n − 1) or for a whole population (dividing by n), and alongside them the count, sum, mean, median, mode, smallest and largest value, range and standard error. For lists of up to 30 numbers it shows the working: each value, its distance from the mean and that distance squared. Numbers can be separated by commas, spaces or new lines, and pasting a column from a spreadsheet works. Up to 5,000 numbers are accepted. Everything is calculated in your browser, so your data is not sent anywhere. Results are shown to six decimal places when needed.
Updated September 2026
How to use the Standard Deviation Calculator
- 1Type or paste your numbers into the box, separated by commas, spaces or new lines.
- 2Choose Sample if your numbers are a part of a bigger group, or Population if they are every value in the group.
- 3Read the standard deviation and variance in the big result box.
- 4Look at the other statistics, such as mean, median, mode and range.
- 5Open the working table to check each step, or copy the summary.
What standard deviation tells you
The mean tells you where the centre of a list of numbers is, and the standard deviation tells you how far numbers typically sit from that centre. In many real data sets, such as heights or measurement errors, about two thirds of the values fall within one standard deviation of the mean and about 95 percent within two.
That makes it useful for comparing consistency: the spread of daily sales, the precision of a machine, the variety of exam scores or the risk of an investment. It also helps you spot outliers, which are values many deviations away from the mean.
Sample or population: which to pick
- Population: you have every member of the group, such as all 12 months of last year.
- Sample: your numbers are a subset used to learn about a bigger group, such as a survey of 200 customers.
- If you are unsure, the sample version is the safer choice for most real-life data.
- With large data sets the two answers are very close.
- Textbooks and spreadsheets call these STDEV.S and STDEV.P.
Reading the working table
For up to 30 numbers, the tool shows every step. Column one is your value, column two is the value minus the mean, and column three is that difference squared. The total of the third column, the sum of squares, is divided by n or n − 1 to get the variance. Checking these numbers by hand is a good way to learn the method or to verify homework.
The deviations in the middle column always add up to zero, which is a handy check that the mean is right. If your data has many decimals, small differences in the last digit can come from rounding in the display, since the calculation itself uses full precision.
Related measures and tips
The coefficient of variation is the standard deviation divided by the mean, and it lets you compare spread between data sets with different scales. For a single average, use Average Calculator, and for the position of one value in the group, Z-Score Calculator shows how many standard deviations it lies from the mean.
Do not mix units, and remove text such as currency symbols or thousands separators before pasting. Percentage Calculator and Ratio Calculator help with related everyday maths, and Probability Calculator covers chances of events.
Features
- Sample (n − 1) and population (n) standard deviation
- Variance, mean, median, mode, range and sum
- Standard error of the mean
- Step-by-step working for up to 30 numbers
- Accepts commas, spaces and new lines
- Handles decimals, negatives and up to 5,000 values
- Runs in your browser
Frequently asked questions
How do you calculate standard deviation?
Find the mean of the numbers, subtract the mean from each number and square the result, add up the squares, divide by n − 1 for a sample (or n for a population) to get the variance, and take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the squares add up to 32, the population variance is 4 and the standard deviation is 2.
What is the difference between sample and population standard deviation?
Use the population version when your numbers are the whole group, such as all the test scores in one class you are describing. Use the sample version when your numbers are a smaller part of a larger group, such as 30 people surveyed out of a city. The sample formula divides by n − 1, which corrects for the fact that a sample tends to understate the spread of the whole group.
What does a high or low standard deviation mean?
A low standard deviation means the numbers are close to the mean, and a high one means they are spread out. Two classes can both average 70 on a test, but if one has a standard deviation of 3 and the other 15, the second class has much more varied results.
What is the difference between variance and standard deviation?
Variance is the average squared distance from the mean, and the standard deviation is its square root. The standard deviation is in the same units as your data, so it is easier to interpret, while the variance is used in many formulas.
Why does the sample standard deviation need two numbers?
The sample formula divides by n − 1, which is zero when there is only one number. With a single value there is no spread to measure. Add a second number, or switch to Population, where one value gives a standard deviation of 0.
What is standard error?
Standard error of the mean is the sample standard deviation divided by the square root of the number of values. It tells you how precisely the sample mean estimates the mean of the whole group, and it gets smaller as you add more data.