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Standard Deviation Calculator

Calculate population and sample standard deviation and variance from a list of numbers. Free online tool showing the mean, count and formula steps.

Enter at least one number to calculate the standard deviation.

  • Population and sample standard deviation
  • Population and sample variance
  • Shows count, mean and sum of squared deviations
  • Formula and step-by-step working displayed
  • Accepts comma, space and newline separated input
  • 100% private — data never leaves your browser

How to use the Standard Deviation Calculator

  1. 1

    Paste or type your numbers, separated by commas, spaces or new lines.

  2. 2

    Read the count and mean that appear at the top.

  3. 3

    Compare the population and sample standard deviation and variance.

  4. 4

    Review the formula and worked steps below to see how it was calculated.

  5. 5

    Click Copy to grab the results.

About the Standard Deviation Calculator

The ByteTools Standard Deviation Calculator measures how spread out a set of numbers is. Paste your data and it returns the count, mean, variance and standard deviation for both the population and a sample, so you can pick the right one for your statistics work.

It is aimed at students, researchers and analysts who need a quick, reliable dispersion measure. The population version divides by N, while the sample version divides by N − 1 (Bessel's correction) — both are shown side by side with the formula and steps.

Every value is processed in your browser with JavaScript. Nothing is uploaded, so the tool is private, instant and works offline. Copy the full breakdown with one click.

Frequently asked questions

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 covers the whole group. Sample standard deviation divides by N − 1 to correct for bias when your data is a sample of a larger population.

How do you calculate standard deviation step by step?

Find the mean, subtract it from each value and square the result, add those squared deviations, divide by N (population) or N − 1 (sample) to get the variance, then take the square root. The tool shows each of these steps.

What is variance?

Variance is the average of the squared deviations from the mean, and standard deviation is its square root. Variance is in squared units, so standard deviation is usually preferred because it is in the same units as the data.

Why does sample standard deviation divide by N minus 1?

Dividing by N − 1, known as Bessel's correction, compensates for the fact that a sample tends to underestimate the true spread of the whole population. It produces a less biased estimate when you only have part of the data.

How many numbers do I need?

Population standard deviation needs at least one value. Sample standard deviation needs at least two, because dividing by N − 1 is undefined for a single value. The calculator flags this when it applies.

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