Calculate population standard deviation

Students and analysts use it to measure population spread while checking the mean, variance and standard deviation together.

Calculate the population mean, variance and standard deviation. Everything runs in your browser, so no input is uploaded or stored.

How to use

Enter your values in the input area, separated by spaces, commas or semicolons.
Import a text or CSV file when your numbers are already saved in a document.
Run the calculation to get the population mean, variance and standard deviation.
Check how many values were taken into account before you interpret the figures.

Example

The sample holds a short series of measurements. After calculating, look at the mean to see where the values sit and at the standard deviation to judge how far they spread, since two series can share a mean and behave very differently.

Input

12, 15, 18, 22, 25, 29

Limits and formats

The result is the population standard deviation; if your values are only a sample, the figure shown is not the one a statistician would expect.
Values must be numeric, and an unusual separator can change how your list is read.
A single value cannot describe spread, even though a result may still appear on screen.
Interpreting the spread and spotting an outlier remains your job: the result gives indicators, not an automatic reading.

Where processing happens

The numbers you type or import are processed inside the browser, with no transmission and no storage. That makes the tool convenient for measurements you would rather keep to yourself, and you can run the calculation as often as you need.

Frequently asked questions

Should I use the population or the sample version?

It depends on your data. Use the population version when your values cover the whole group you are studying. If they are only a subset of a larger set, the sample version would fit better, but this tool does not provide it.

Are decimal values supported?

Numbers with a decimal part are fine as long as the separator between values stays unambiguous. Mixing a decimal comma with comma separators confuses the reading, so pick a clear separator between entries.

Why is the variance so much larger than my data?

Variance is expressed in squared units, which makes it look big next to your original values. Its square root, the standard deviation, comes back to the same unit as your measurements.