Standard Deviation Calculator

Calculate population and sample standard deviation, variance, mean, median, min, max, and range for a list of comma or space-separated values. Free and instant.

Summary:This Standard Deviation Calculator provides population and sample SD, mean, variance, and median for any set of values.

Data Dataset

Data values (separated by commas, spaces, or newlines)

Statistical metrics

Sample Std Dev (s)None

Population Std Dev (σ)None

Mean (μ)None

MedianNone

Count (N)None

RangeNone

Min / MaxNone

Sample VarianceNone

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Copy this code snippet to add the Standard Deviation Calculator to your blog or website for free. It adjusts dynamically to mobile and desktop screens.

<iframe src="https://hellotools.net/tools/standard-deviation-calculator?embed=true" width="100%" height="650" style="border:none; overflow:hidden;" allowtransparency="true"></iframe>

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How to Use Standard Deviation Calculator

Our Standard Deviation Calculator is a free math utility: 1. Type or paste your dataset of numbers in the text box. 2. Separate numbers with commas, spaces, or line breaks. 3. The tool parses values and computes statistics automatically. 4. Review Mean, Median, Count, Range, Variance, and SD outcomes.

Standard Deviation Calculator Formula / How It Works

This calculator splits input text into individual numbers. It computes the arithmetic mean, then calculates the squared deviation of each number from that mean. It sums these squared values and divides by N (for population) or N-1 (for sample), finally taking the square root.

Formula:Population SD = sqrt(Σ(x - μ)^2 / N); Sample SD = sqrt(Σ(x - μ)^2 / (N - 1))

Example Calculation:

For example, for the dataset [2, 4, 4, 4, 5, 5, 7, 9], the Mean is 5.00, the Population SD is 2.00, and the Sample SD is 2.1381.

Frequently Asked Questions

Population SD (σ) is used when you have the complete dataset of the entire population. Sample SD (s) is used when your data represents a sample selected from a larger population, applying Bessel's correction (N - 1) to account for bias.

Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of the variance.

This tool is highly flexible and accepts numbers separated by commas, spaces, tabs, or newlines.

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