Skip to content
Collabs Tool
CalculatorsRuns in your browser

Standard Deviation Calculator (Sample & Population)

Sample and population standard deviation, variance and mean for a data set.

Input
No upload needed — instant
Privacy
Nothing is uploaded
Cost
Free · no sign-up · no watermark

Loading tool…

The tool is loading its code on your device. This happens once and is cached for later visits.

Processed entirely on your device

Everything you type or paste is handled by JavaScript running in this tab. No request is sent, nothing is logged and nothing is stored. Close the page and it is gone.

Overview

About the Standard Deviation Calculator (Sample & Population)

Enter a data set to get the sample and population standard deviation, both variances, the mean and the sum of squared deviations, with every step shown.

Standard deviation is the standard way to describe how much a set of numbers varies. Enter your data and this calculator returns the sample and population standard deviation, both variances and the mean, with the intermediate sums shown.

The formula

mean      x̄ = Σx ÷ n
variance  s² = Σ(x − x̄)² ÷ (n − 1)   [sample]
          σ² = Σ(x − x̄)² ÷ n         [population]
std dev   s  = √s² ,  σ = √σ²

The only difference between the two versions is the divisor: n − 1 for a sample, n for a whole population.

Reading the number

For roughly bell-shaped data, about 68% of values fall within one standard deviation of the mean and 95% within two. That makes it a quick way to judge whether a value is typical or an outlier.

Private and instant

Your data set is processed entirely in the browser and is never uploaded.

Step by step

How to use the Standard Deviation Calculator (Sample & Population)

  1. Enter at least two numbers, separated by commas, spaces or new lines.

  2. Read the sample and population standard deviation and both variances.

  3. Check the mean, sum of squared deviations and the divisors in the breakdown.

Why use it

Benefits and common use cases

What this tool is good for, and what it deliberately does not try to do.

Sample and population

Both standard deviations and both variances are shown side by side, so you never have to guess which formula a task wants.

Shows the working

The mean, the sum of squared deviations and the n and n − 1 divisors are all listed, so the result is easy to verify by hand.

Explains n − 1

A plain note tells you when to use Bessel's correction, which is the part most people get wrong.

Questions

Frequently asked questions

Short, honest answers about quality, limits and privacy.

What does standard deviation measure?

How spread out the numbers are around the mean. A small standard deviation means values cluster near the average; a large one means they are widely scattered. It is in the same units as the data, unlike the variance.

When do I use sample versus population?

Use the sample formula (divide by n − 1) when your data is a sample from a bigger population — almost always in practice. Use the population formula (divide by n) only when you have every member of the group.

Why divide by n − 1?

Bessel's correction. Using the sample mean underestimates the true spread, and dividing by n − 1 instead of n removes that bias, giving a better estimate of the population variance.