Math

Standard Deviation Calculator

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

Last validated: 2026-02-14

Use this free online Standard Deviation Calculator to compute mean, variance, and standard deviation for a dataset. It is useful for analysis, reporting, coursework, and experiment planning when you need quick statistical evidence without building a spreadsheet. The form focuses on Values and returns Dataset Input, Statistics, so you can move from input to answer without setting up a spreadsheet or custom script. Run one realistic example, adjust the inputs, and compare how the result changes before you copy or share it. Treat the result as a statistical aid: sample quality, independence, distribution assumptions, and context still determine whether the conclusion is valid.

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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 Values for the standard deviation calculator, keeping units, dates, or text format consistent with the form labels.
Confirm sample size, ordering, and distribution assumptions before relying on the calculated result.
Click "Run the tool" and review Dataset Input, Statistics for the primary output.
Check the statistical assumptions and sample context before using the result in a report or decision.

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.

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.

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Standard Deviation Calculator

Input Pattern

Dataset Input

Statistics

How to use this tool

Worked Example

Example Inputs

Expected Outputs

Interpretation

Confidence and limitations

Formula References

Assumptions

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