Result
Result reflects the current submitted inputs.
- Risk B
- Reviewed 2026-05-26
- 1 sources
- Population mode uses n; sample mode uses Bessel's correction n - 1.
- At least two values are required for sample standard deviation.
Accuracy notes
- Risk level
- B
- Reviewed
- 2026-05-26
- Sources
- 1
- Primary result
- Standard deviation
Formula logic is kept in a pure calculator module with fixtures, source notes, and page-visible assumptions.
What the result means
Standard deviation describes how far the entered values typically sit from the mean. A larger value means the data is more spread out; compare sample versus population mode before using the result in a report because the denominator changes.
Use the result this way
- Start with Standard deviation, then use supporting outputs for context.
- Verify Values and Data type before copying the result.
- Check the formula, example, and assumptions before reusing the answer.
User job
How to use this calculator
Use Standard Deviation Calculator when you need standard deviation, then use variance and mean to check the context for data review, classwork, quality checks, and quick descriptive summaries.
Best for
- Summarizing a list of values
- Checking spread, center, or sample assumptions
- Reviewing a default example before entering your own values and data type.
Check before relying
- Confirm whether the data is a sample or population and whether outliers should stay in the list.
- Population mode uses n; sample mode uses Bessel's correction n - 1.
- At least two values are required for sample standard deviation.
- Source context: National Institute of Standards and Technology, reviewed 2026-05-26.
Next useful step
- Average CalculatorUse next when your task shifts from Standard Deviation Calculator to Average Calculator.
- Variance CalculatorUse next when your task shifts from Standard Deviation Calculator to Variance Calculator.
- Median CalculatorUse next when your task shifts from Standard Deviation Calculator to Median Calculator.
Formula
Population variance divides the sum of squared deviations by n. Sample variance divides by n - 1. Standard deviation is the square root of variance.
- Population variance divides the sum of squared deviations by n. Sample variance divides by n - 1. Standard deviation is the square root of variance.
- Enter numeric values and choose population or sample. Use sample when the list represents a subset of a larger group.
- Last reviewed: 2026-05-26.
Inputs
Enter numeric values and choose population or sample. Use sample when the list represents a subset of a larger group.
Example
For 2, 4, 4, 4, 5, 5, 7, 9 in population mode, the mean is 5, variance is 4, and standard deviation is 2.
FAQ
What is standard deviation?
Standard deviation measures how far values typically are from the mean, so it helps describe spread rather than center.
Should I use sample or population?
Use population when the list contains every value in the group. Use sample when the list represents a subset.
What is variance?
Variance is the average squared distance from the mean. Standard deviation is the square root of variance.
Why does sample standard deviation divide by n minus 1?
The sample formula uses Bessel's correction to reduce bias when estimating a population from a sample.
What should I verify before using standard deviation calculator?
Verify values and data type, the displayed formula, and the worked example before copying the result into another document or decision.
What is the main output of standard deviation calculator?
Standard deviation is the first value to read. Use the supporting outputs and assumptions to understand why it changed.
Sources
Last reviewed: 2026-05-26
- Reviewed 2026-05-26NIST Engineering Statistics HandbookNational Institute of Standards and Technology. Reference for standard deviation as a measure of spread.
Disclaimer
This statistics calculator is for general analysis and education. It does not replace a full statistical review of study design or sampling method.