# Standard Deviation Calculator

> Calculate population or sample standard deviation.

Page: https://freecalculator.tech/tools/standard-deviation-calculator
Last reviewed: 2026-10-23

## How do I calculate standard deviation?

Standard deviation is the square root of the average squared distance from the mean, divided by the count for a population or by one less for a sample.

## Formula

Standard deviation is the square root of the average squared distance from the mean; sample variance divides by n−1.

- Methodology type: scientific equation.
- Methodology: NIST measures of scale. Population variance divides squared deviations by n; sample variance by n − 1. Standard deviation is its square root.
- Standard deviation is the square root of the average squared distance from the mean; sample variance divides by n−1.
- Inputs used: Values, Data type.
- Edge handling: Values is required..

## Inputs

- Values
- Data type

## Worked example: Population deviation of 2,4,4,4,5,5,7,9

The mean is 5 and population standard deviation is 2.
1. Start with Values: 2,4,4,4,5,5,7,9, Data type: population.
2. Apply the method: Standard deviation is the square root of the average squared distance from the mean; sample variance divides by n−1.
3. The mean is 5 and population standard deviation is 2.

## Common questions

### How do I calculate standard deviation?

Standard deviation is the square root of the average squared distance from the mean, divided by the count for a population or by one less for a sample. Check the formula, example, and limitations on this page before using the result for a real math decision.

### Which mode should I use?

Use population for the complete group and sample for observations representing a larger group. Check the formula, example, and limitations on this page before using the result for a real math decision.

### Can values be negative?

Yes. Negative and decimal values are supported.

### Where is variance shown?

The breakdown shows variance using the same population or sample denominator selected for standard deviation. Check the formula, example, and limitations on this page before using the result for a real math decision.

### How do I use the Standard Deviation Calculator?

Enter the required values for Values, Data type. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Standard Deviation Calculator use?

Standard deviation is the square root of the average squared distance from the mean; sample variance divides by n−1. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

## Limitations and assumptions

- Complete population or independent representative sample assumed according to selected mode.
- No weighted, clustered or robust variance estimator.
- For education and operational analysis only. No diagnosis, treatment recommendations, prescribing, dosing instructions, or reimbursement entitlement. Scientific calculations require appropriate laboratory verification; operational estimates do not replace local clinical, safety or financial policies.
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this standard deviation calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- NIST — https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm

## Cite this page

- APA: Free Calculator. (2026, October 23). Standard Deviation Calculator. https://freecalculator.tech/tools/standard-deviation-calculator
- MLA: "Standard Deviation Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/standard-deviation-calculator.
- Link: Standard Deviation Calculator — Free Calculator, https://freecalculator.tech/tools/standard-deviation-calculator