# Standard Deviation Calculator

> Calculate population or sample standard deviation, variance, mean, sum, standard error, and margin of error.

Page: https://askcalculators.com/calculator/standard-deviation-calculator/
Definition: https://askcalculators.com/calculator/standard-deviation-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/standard-deviation-calculator/schema.json
Version: 2.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/standard-deviation-calculator/?values=10%2C+12%2C+23%2C+23%2C+16%2C+23%2C+21%2C+16&sample=0&confidenceLevel=95

## Inputs
- values: Numbers; type=text; required; default=10, 12, 23, 23, 16, 23, 21, 16
- sample: Treat the values as a sample; type=checkbox; optional; default=false
- confidenceLevel: Confidence level for margin of error; type=select; required; default=95; values=80|90|95|98|99

## Outputs
- standardDeviation: Standard deviation; format=number; primary
- variance: Variance; format=number
- mean: Mean; format=number
- sum: Sum; format=number
- count: Count; format=integer
- standardError: Standard error; format=number
- marginOfError: Margin of error; format=number

## Formula
Population: σ = √[Σ(x − μ)²/n]; sample: s = √[Σ(x − x̄)²/(n − 1)]; margin = z·s/√n.

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.