Enter the complete dataset.
Statistics Calculator
Standard Deviation Calculator
Calculate mean, population variance and standard deviation, plus sample variance and standard deviation for a numeric dataset.
Instant answer
Formula breakdown
Browser-based
Mobile friendly
Interactive calculator
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Use the example values or replace them with your own. Required validation happens before the calculation.
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Calculated answer
Result
Simple workflow
How to use the Standard Deviation Calculator
Follow these steps to get a reliable result and understand how it was produced.
Find the mean and squared deviations.
Divide by N or n−1, then take the square root.
Understanding the calculation
Standard deviation measures typical spread around the mean. Sample formulas use n−1 to estimate population variability from a sample.
Population σ = √[Σ(x−μ)²/N]; sample s = √[Σ(x−x̄)²/(n−1)]The result panel substitutes your numbers into this relationship and shows the important intermediate values.
Common uses
- Quality control and measurement spread
- Exam and survey data
- Comparing consistency between datasets
Accuracy tips
- Use population SD when the data is the full population.
- Use sample SD when estimating from a sample.
- At least two values are required for sample variance.
Helpful answers
Standard Deviation Calculator FAQs
Important details about formulas, inputs, limitations, and result interpretation.
What does a small standard deviation mean?
Values are clustered relatively close to the mean.
Why are sample and population results different?
The sample formula divides by n−1 to reduce estimation bias.
Can standard deviation be negative?
No. It is a square root of variance and is always non-negative.
Does data order matter?
No. Reordering the same values does not change the result.