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

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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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 standard deviation (σ) is used when your data represents the entire group you are studying — divide by N. Sample standard deviation (s) is used when your data is a sample from a larger population — divide by N–1 (Bessel's correction). Use sample SD for most real-world data analysis.

Enter your numbers separated by commas or spaces (e.g., 10, 20, 30, 40). The calculator automatically computes the mean, variance, and standard deviation for both population and sample formulas.

A low standard deviation means your data points are clustered close to the mean — low variability. A high standard deviation means data is spread widely — high variability. For example, test scores with SD = 2 are very consistent; SD = 20 indicates a wide range of performance.

Yes. It uses standard statistical formulas with double-precision arithmetic. Results match those produced by Excel STDEV/STDEVP functions or statistical software for the same dataset.

Yes. You can enter any number of values. For very large datasets, paste your comma-separated values directly into the input field. The calculator processes all values instantly in your browser with no data sent to any server.

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