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Scientific Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

Standard Deviation Calculator

You can calculate the mean, variance and standard deviation of a list of numbers in your browser, see both the population and sample values, and follow the working step by step.

Runs in your browserFree · No sign-up · No watermark
NUMBERS → MEAN & SDRuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
NUMBERS → MEAN & SD
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Scientific Tools

About Standard Deviation Calculator

Standard deviation is the usual number for how spread out a set of measurements is, but it comes in two versions that differ by a single denominator. Dividing by n describes a complete population; dividing by n − 1 estimates the spread of a larger population from a sample. Using the wrong one is a common reason two reports disagree.

This calculator takes a pasted list of numbers and returns the count, sum, mean, median, range, both variances and both standard deviations, with every intermediate value shown. A short note explains which result to report, and a table lists each value with its deviation from the mean so the arithmetic can be checked.

What this tool does

The details that matter when you use Standard Deviation Calculator for real work.

  • Population and sample side by side

    See σ and s together, with the n and n − 1 denominators and both variances, so the difference is visible rather than buried in a formula.

  • Working shown line by line

    The step section lists the mean, the sum of squared deviations and each division instead of showing only the final answer.

  • Deviation table

    Each value is listed with x − mean and (x − mean)², which is exactly the input to the variance calculation.

  • Paste any list

    Commas, spaces, tabs and newlines all separate values, and up to 2,000 numbers are accepted in one run.

  • Guidance on which SD to report

    A plain-language note covers the sample and population cases, so a report or assignment does not quote the wrong figure.

How to use Standard Deviation Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Paste the values

    Enter the numbers, separating them with commas, spaces, tabs or newlines; one value per line also works.

  2. 02

    Read the count and mean

    The summary shows n, the sum, the mean, median, minimum, maximum and range so the data can be sanity-checked first.

  3. 03

    Compare σ and s

    Both standard deviations are listed with their variances; the top result shows the sample value when it is available.

  4. 04

    Follow the working

    The step-by-step section substitutes your numbers into the variance formula and shows each division and square root.

  5. 05

    Report the right one

    Use the sample SD for data drawn from a larger population and the population SD only for a complete population.

How this tool works

Works with
NUMBERS → MEAN & SD
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • The calculation uses the arithmetic mean, so a single extreme value can dominate the standard deviation.
  • Results are rounded for display to six decimal places, and very large offsets between values can introduce small floating-point differences.
  • Up to 2,000 values are accepted per run; longer lists need to be split.

Privacy and file handling

The numbers you paste are parsed and calculated with plain JavaScript inside your browser tab. Nothing is uploaded, logged or stored, and no request is made to a server while you work. Closing the page clears the input.

Read the full privacy policy

Standard Deviation Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
What is the difference between population and sample standard deviation?
The population version divides the squared deviations by n; the sample version divides by n − 1. The sample version is slightly larger and is used when your values estimate a wider population rather than covering it completely.
Why does the sample standard deviation divide by n − 1?
Dividing by n − 1 corrects for the fact that a sample mean is itself estimated from the sample, which makes deviations around it slightly smaller than they would be around the true mean. The adjustment is called Bessel's correction.
Which standard deviation should I report?
Report the sample standard deviation (n − 1) when the numbers are a sample from a larger population, which is the common case in coursework and lab reports. Use the population value only when the list is the entire population you care about.
Can I calculate standard deviation with one value?
One value has no spread: the population standard deviation is 0, and the sample standard deviation is undefined because it would divide by n − 1 = 0. The calculator shows the population value and explains why the sample one is unavailable.
Does the calculator use the mean or the median in the formula?
Standard deviation is built around the arithmetic mean: each value's deviation from the mean is squared, then averaged. That is why one outlier can inflate the result, while the median and interquartile range are more resistant to extreme values.
What happens if my data contains extreme values?
The result is still computed correctly, but a large outlier can dominate the sum of squared deviations and inflate the standard deviation. Check the deviation table to see which values contribute most; a median-based measure may describe the centre better.
How are the results rounded for display?
Results are shown with up to six decimal places and trailing zeros are trimmed, while the calculations keep full floating-point precision. Treat the last shown digit as display rounding rather than a limit of the method.
Are my numbers uploaded anywhere?
No. The list is parsed and calculated with plain JavaScript in your browser; nothing is uploaded, stored or logged, and closing the page clears the input.

Background reading

Format guides that explain the trade-offs behind Standard Deviation Calculator.