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Standard Deviation — Sample & Population, With Steps

Mean, variance and sample/population standard deviation with the full working shown. Client-side and private.

Free No signup Client-side Privacy friendly Updated

Enter at least one number.

How to use

  1. 1 Paste or type your numbers, separated by commas, spaces or new lines.
  2. 2 Choose Sample (÷ n−1) or Population (÷ n).
  3. 3 Read the mean, variance and standard deviation — expand “Show working” for the steps.

Why use this tool

  • Both sample and population standard deviation, switchable in one click.
  • Shows every deviation and squared deviation so you can follow the maths.
  • Runs entirely in your browser — your data never leaves the page.

Frequently asked questions

What is the difference between sample and population SD?

Population SD divides the sum of squared deviations by n; sample SD divides by n−1 (Bessel’s correction) to better estimate the spread of a wider population from a sample.

Which one should I use?

Use sample (s) when your numbers are a sample drawn from a larger group, and population (σ) when they are the entire group.

What is variance?

Variance is the average of the squared deviations from the mean; standard deviation is its square root, back in the original units.

What is the coefficient of variation?

The standard deviation expressed as a percentage of the mean — useful for comparing the relative spread of different datasets.

What is Standard Deviation Calculator?

A standard deviation calculator measures how spread out a set of numbers is, reporting the mean, variance and standard deviation for either a sample or a whole population.

Features

Sample or population

Sample SD uses n−1 (Bessel's correction); population SD uses n — toggle between them.

Mean, variance & SD

Reports the mean, sum of squares, variance, and standard deviation together.

Free & private

Runs on your device — your data is never uploaded.

Example

Input

2, 4, 6   (sample)

Output

mean = 4 · sample SD (n−1) = 2

Common use cases

  1. 1

    Analyze measurements

    Quantify the spread of a set of experimental or survey values.

  2. 2

    Grades & scores

    See how tightly scores cluster around the average.

  3. 3

    Quality & finance

    Measure variability in process outputs or returns.

Summary

Zerethon's standard deviation calculator computes the mean, variance, and standard deviation of a data set in your browser. It defaults to the sample standard deviation (dividing by n−1, Bessel's correction) and can switch to the population form (dividing by n). Everything runs client-side — nothing is uploaded.

Category
Math
Pricing
Free
Privacy
Browser-based
Signup
Not required

References

Privacy

Your data never leaves your browser unless explicitly stated. Standard Deviation Calculator runs entirely client-side — no server upload, no logging, no tracking of your input.

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