Sample Standard Deviation Calculator

Work out sample standard deviation instantly with clear inputs, formula shown and shareable results.

About Sample Standard Deviation Calculator

The sample standard deviation divides the sum of squared deviations by n − 1 rather than n. That Bessel correction compensates for using the sample mean instead of the unknown population mean, giving an unbiased variance estimate.

Formulas

Sample standard deviation

s = √[Σ(xᵢ − x̄)² / (n − 1)]

Population standard deviation

σ = √[Σ(xᵢ − μ)² / n]

Worked example

With the default values below, Sample Standard Deviation Calculator returns Standard deviation of 2.13808994. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample data: 2, 4, 4, 4, 5, 5, 7, 9
Divide byone of n − 1 (sample), n (population): n − 1 (sample)

Results

Standard deviation: 2.13808994
Variance: 4.57142857
Mean: 5.00000000
Number of values: 8

Step by step

1Values used
2Sample standard deviation
3Population standard deviation
4Standard deviation= 2.13808994
5Variance= 4.57142857
6Mean= 5.00000000
7Number of values= 8

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For 2, 4, 4, 4, 5, 5, 7, 9?

The mean is 5 and the sample standard deviation is 2.1380899, while the population value is exactly 2.

Which should I use?

Use n − 1 when the data is a sample being used to estimate a wider population, and n only when you have the entire population.