Standard Deviation Calculator Online
Calculate population and sample standard deviation, variance, mean and sum from a list of numbers. Your data stays on your device.
The Standard Deviation Calculator runs entirely in your browser. The numbers you enter are computed locally and never leave your device.
Open the Statistics Calculator
About Standard Deviation Calculator
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 or newlines 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 or newlines — mixed separators are fine
- 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 or newlines
- Read the mean, sum and count at the top of the results
- Compare population standard deviation against sample standard deviation for your use case
- Expand the steps table to see each value's deviation and squared deviation
- 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 2.14
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. — The Standard Deviation Calculator accepts newline-separated values, so a pasted spreadsheet column works as-is — check for stray text or currency symbols mixed into the cells, which get skipped as non-numeric.
- 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, 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.
- Why is sample standard deviation always slightly larger than population standard deviation?
- Sample standard deviation divides by n − 1 instead of n, which produces a slightly larger value to correct for the tendency of a sample to underestimate the true population variance.
- 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, newlines and semicolons all work, and you can mix them — pasting a column from a spreadsheet or a comma-separated list both parse the same way.
Related tools
All ArrayKit tools