Standard Deviation Calculator
Last updated: July 2026
Calculate population and sample standard deviation.
Population standard deviation
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- Sample standard deviation: —
- Mean: —
On this page
Quick summary: Calculate population and sample standard deviation. Enter the requested values, calculate, review the result, and compare more than one realistic scenario before making a decision.
Read the complete guide
What this calculator does
The Standard Deviation Calculator measures how spread out numerical values are around their mean. A smaller standard deviation indicates values are more tightly clustered, while a larger value indicates greater dispersion.
How to use the calculator step by step
Enter the numerical dataset in the format requested. Choose population or sample standard deviation if the calculator provides that option.
How the calculation works
The calculation finds the mean, measures each value's deviation from that mean, squares those deviations, averages them using the appropriate denominator, and takes the square root.
Worked example and scenario testing
The dataset 10, 10, 10 has a standard deviation of zero because every value equals the mean. A dataset such as 5, 10, 15 has a larger standard deviation because the values are more spread out.
How to interpret your result
Standard deviation is expressed in the same unit as the original data, unlike variance, which uses squared units.
Accuracy, assumptions, and limitations
Standard deviation alone does not describe skewness, outliers, multimodal distributions, or whether the data are normally distributed.
Common mistakes to avoid
Do not use the population formula for a sample without considering the correct denominator. Also check the dataset for entry errors and extreme outliers.
Privacy and browser-based calculations
Only numerical data are required. Avoid pasting confidential records when anonymous values are sufficient.