About Standard Deviation
Standard Deviation measures how far the values in a dataset typically sit from their mean. It takes the mean, squares each value deviation from it, averages those squares, and returns the square root — so the result comes back in the same units as the data, unlike variance, which is left in squared units.
The averaging step is where this tool needs a clear statement. It divides the sum of squared deviations by N, the number of values, which is the population formula. The sample formula divides by N-1 instead, producing a slightly larger figure that corrects for the fact that a sample mean is itself estimated from the data. If your dataset is a sample drawn from a larger population and you intend to estimate that population spread, the N-1 version is the conventional choice, and the value here will read marginally small.
The output is rounded to four decimal places, and the same list can be pasted into the Variance calculator to see the squared figure this one is derived from. Extreme values have a large effect by construction, since deviations are squared before being averaged.
How to use Standard Deviation
- 1 Load the sample into the Numbers box; separators can be commas, spaces or line breaks.
- 2 Read the population standard deviation, shown to four decimal places.
- 3 Paste the same list into the Variance calculator to see the squared quantity it is derived from.
Frequently asked questions
Does it use the population or the sample formula?
The population formula — the sum of squared deviations is divided by the number of values. If you have a sample and want the N-1 estimate of the wider population spread, expect the correct value to be slightly larger than the figure reported here.
What does a standard deviation of zero mean?
That every value is identical, so there is no spread at all. The mean equals every data point. A zero result on data you know varies usually means only one value was parsed — check the count on the average calculator for the same list.
Why square the deviations instead of just averaging them?
Because signed deviations cancel out, and the average would always be zero. Squaring removes the sign, and the square root at the end converts the result back into the original units so it can be compared with the values themselves.
How does it relate to variance?
Variance is this number squared. This tool reports the square root of that same quantity, which is why the two tools agree exactly on the same input and why the standard deviation is easier to interpret — same units as the data.
Free, online, and private
Free to use
Standard Deviation is completely free. There is no account to create, no login, and no hidden charge or usage limit.
Runs online in your browser
It is a free online tool that runs entirely in your browser. Nothing to download or install — open the page and start using it right away.
Your data stays private
All processing happens locally on your device. Your input is never uploaded, stored, or tracked, so it never leaves your browser.
How Standard Deviation behaves in detail
These are the specifics of this implementation — the exact ranges, defaults and fixed settings you are working with.
| Parameter | Value |
|---|---|
| Variance divisor | n — the population form; the output line spells out "Population SD" so the convention is visible |
| Formula | the square root of the mean of the squared deviations from the mean |
| Precision | 4 decimal places |
| Separators recognised | commas and any whitespace, split on /[, s]+/ before the statistics run |
| Empty result | the words "No numbers" when the parse yields nothing |
| Defaults | 10, 12, 23, 23, 16, 23, 21, 16, which returns 4.8990 |
Compiled from the implementation of this tool and checked against it by itoolnet.
What Standard Deviation does not do
Knowing the edges of a tool saves more time than another list of its features. These are the cases where it will not do what you might expect.
- There is no sample form. When the list is a sample drawn from a larger population the divisor should be n − 1, and this page has no toggle for it, so the figure comes back systematically too small with nothing on screen to warn you that the wrong convention was used.
- The variance is not shown alongside the standard deviation, only its square root. Recovering the intermediate value means running the Variance page on the same dataset, which uses the same n divisor and therefore agrees — but the two numbers are never presented together here.
- One value produces 0 rather than a complaint. The mean is that single point, every squared deviation is zero, and the output reads 0.0000, which looks like a measured spread of zero rather than a question that cannot be answered from one observation.
Tested and documented by itoolnet, the team that builds and maintains this site.