The Standard Deviation Calculator finds the mean, variance and standard deviation of a data set, computing both the population version (divides by n) and the sample version (divides by n − 1) so you can pick the one that matches your data. Paste numbers separated by commas, spaces, tabs, semicolons or new lines and it instantly returns the count, sum, mean, population and sample variance, and population and sample standard deviation, alongside a step-by-step table of each value's deviation from the mean and its squared deviation. It is useful for students checking homework, analysts summarizing a sample, and anyone who needs to gauge how spread out a set of measurements is. Everything runs locally in your browser — the numbers you enter are never uploaded.
Features
Enter numbers separated by commas, spaces, tabs, semicolons or new lines, in any mix
Computes count, sum and mean alongside variance and standard deviation
Shows both population standard deviation (÷ n) and sample standard deviation (÷ n − 1)
Step-by-step table of each value's deviation and squared deviation from the mean
Handles negative numbers and decimals
One-click copy of a plain-text summary of every result
Clear message when there is only one value (sample stats need at least two)
Runs entirely in your browser with nothing uploaded
How to use the Standard Deviation Calculator
Type or paste your numbers into the data set field, separated by commas, spaces, tabs, semicolons or new lines
Read the mean, sum and count at the top of the results
Compare population standard deviation against sample standard deviation for your use case
Look over the steps table below the results for each value's deviation and squared deviation (it lists the first 50 values)
Copy the summary for your notes or report
Example
Input
2,4,4,4,5,5,7,9
Output
Mean 5 · Pop SD 2 · Sample SD 2.1381
Population SD divides by n = 8 and sample SD by n − 1 = 7; results are rounded to 4 decimal places.
Common errors & troubleshooting
Sample standard deviation shows 'Need ≥ 2 values'. — Sample standard deviation divides by n − 1, so it needs at least two numbers. With a single value, only the population statistics (which are 0 for one point) apply.
Result looks wrong after pasting a column copied from a spreadsheet. — A pasted column works as-is, because new lines separate values. Anything that is not a plain number, such as $5 or 5%, is skipped, and a thousands separator splits a value: 1,000 is read as 1 and 0. Format the cells as plain numbers like 1000 before copying.
Not sure whether to use population or sample standard deviation. — Use population standard deviation when your numbers are the entire group you care about; use sample standard deviation when they are a subset drawn from a larger population you are estimating.
Standard deviation seems too small compared to the range of the data. — Standard deviation measures typical spread around the mean, not the full range — a few outliers pull the mean but a majority of clustered values keep the standard deviation modest.
Frequently asked questions
What does the Standard Deviation Calculator return?
It returns the count, sum and mean of your data set, plus population and sample variance and standard deviation, rounded to 4 decimal places, along with a table showing each value's deviation and squared deviation from the mean.
What is the difference between population and sample standard deviation?
Population standard deviation divides the sum of squared deviations by n and is used when your data is the entire group. Sample standard deviation divides by n − 1 (Bessel's correction) and is used when your data is a sample estimating a larger population.
Can the standard deviation calculator handle negative numbers?
Yes. Negative numbers, decimals and mixed positive/negative data sets are all supported — the calculator parses each token and skips anything that is not a valid number.
Is sample standard deviation always larger than population standard deviation?
Yes, whenever the values differ. Sample standard deviation divides by n − 1 instead of n to correct a sample's tendency to underestimate the spread of the whole population, which makes it larger by a factor of √(n/(n − 1)): about 41% for two values, about 5% for ten, and less as n grows. When every value is the same, both are 0.
Does the Standard Deviation Calculator upload my numbers anywhere?
No. The Standard Deviation Calculator runs entirely in your browser. The numbers you type or paste are never sent to a server and stay on your device.
What separators can I use between numbers?
Commas, spaces, tabs, semicolons and new lines all work, and you can mix them, so a column pasted from a spreadsheet and a comma-separated list parse the same way. Leave out thousands separators: 1,000 is read as two values, 1 and 0, so type 1000.