Math

Standard Deviation Calculator

Calculate mean, variance, and standard deviation for a dataset.

Last validated: 2026-02-14

Standard Deviation Calculator computes mean, variance, and standard deviation for a dataset. It is useful in descriptive statistics and quality monitoring tasks. The tool provides fast spread measurements without spreadsheet setup. Use it to compare variability across data samples.

Permalink

Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Dataset Input

Use commas, spaces, or semicolons between values.

Statistics

Count: 8

Mean: 18.00000

Population variance: 24.00000

Population std dev: 4.89898

Sample variance: 27.42857

Sample std dev: 5.23723

How to use this tool

Enter the dataset values in list format.
Run calculation to get mean, variance, and standard deviation.
Compare standard deviation across groups to assess dispersion.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

Values input: 10, 12, 23, 23, 16, 23, 21, 16
Variance population: 24.0
Stddev population: 4.898979485566356
Variance sample: 27.428571428571427
Stddev sample: 5.237229365663817

Expected Outputs

Parsed values 0: 10
Parsed values 1: 12
Parsed values 2: 23
Parsed values 3: 23

Interpretation

Parsed values 0 is 10.0. Use this as a decision input, not as a standalone conclusion.
Parsed values 1 is 12.0. Use this as a decision input, not as a standalone conclusion.
Parsed values 2 is 23.0. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Values input

Variance population

Stddev population

Variance sample

Stddev sample

Scenario B

Values input

Variance population

Stddev population

Variance sample

Stddev sample

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

Formula References

Algebra and arithmetic identities used by the selected formula.
Standard precision arithmetic; rounding shown for readability.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

Explore more versions

Tailored guides for specific audiences, regions, and scenarios.

core