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Standard Deviation Calculator

Sample and population standard deviation with every step shown.

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Working

xx − mean(x − mean)²

Sample standard deviation

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Variance—
Mean—
Count—
Sum of squared deviations—
The other method—

Empirical rule

For a normal distribution.

68% within ±1σ—
95% within ±2σ—
99.7% within ±3σ—

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Quick Tool Overview

The Standard Deviation Calculator returns standard deviation and variance in both sample and population forms, with a working table showing each value, its deviation from the mean and that deviation squared. The table is the point: it makes obvious what standard deviation actually measures.

What it does
Calculates standard deviation and variance with full working
You give it
A data set and a choice of sample or population
You get back
The result, a step table, empirical rule ranges and z-scores
Best for
Statistics homework, quality control and test score analysis
Calculators Free, unlimited use No sign-up Runs in your browser

About the Standard Deviation Calculator

Paste your data to get the standard deviation and variance in both the sample and population forms, with a working table showing each value, its deviation from the mean, and that deviation squared.

The step-by-step table is the point. Standard deviation is usually taught as a formula to memorise, but seeing the squared deviations laid out makes it obvious what it measures: the typical distance of a value from the mean. The empirical rule ranges are shown alongside, covering roughly 68, 95 and 99.7 percent of a normal distribution within one, two and three standard deviations, and a z-score panel converts any value into how many deviations from the mean it sits.

Key features of the Standard Deviation Calculator

Every step laid out

Each value, its deviation from the mean and the squared deviation are tabulated rather than hidden inside a formula.

Sample and population side by side

The n versus n−1 divisor is applied both ways so you can see the difference it makes.

Empirical rule ranges

Roughly 68, 95 and 99.7 percent of a normal distribution within one, two and three deviations, calculated for your data.

Z-score panel

Convert any value into how many standard deviations from the mean it sits.

Variance reported too

The squared measure is given alongside, since some coursework asks for it directly.

How to use the Standard Deviation Calculator

  1. 1

    Enter your data set

    Paste numbers separated by commas, spaces or line breaks.

  2. 2

    Choose sample or population

    Both are calculated, but the one you select is highlighted with its formula.

  3. 3

    Follow the working

    The table shows every deviation and squared deviation, then the sum, the variance and the square root.

Frequently asked questions

The sample version divides by n minus 1 rather than n. That correction, called Bessel's correction, compensates for a sample understating the true spread of the population it came from.

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