Free Standard Deviation Calculator
Sample and population standard deviation and variance.
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Result
Sample standard deviation
1.0954
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Short answer
Sample and population standard deviation and variance.
What is the Standard Deviation Calculator?
Sample and population standard deviation and variance.
How does the Standard Deviation Calculator work?
Enter the inputs above and read the result.
Formula
Variables
μPopulation meanx̄Sample mean
Explanation
Sample variance divides by n−1 (Bessel's correction) to give an unbiased estimate from a sample.
Examples
Applications
Advantages
Limitations
Common mistakes
Tips
Related concepts
The Standard Deviation Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding Standard Deviation
Sample and population standard deviation and variance. Within math calculators, standard deviation belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.
Learning how standard deviation is calculated
Sample variance divides by n−1 (Bessel's correction) to give an unbiased estimate from a sample. Working through the variables one at a time — μ, x̄ — makes the result reproducible by hand and easier to sanity-check.
Using standard deviation to make a decision
Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How standard deviation compares with related measures
distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
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