Standard Deviation Calculator
Compute the standard deviation and variance of a data set (both sample and population).
Reviewed October 7, 2026 Runs in your browser — inputs are never stored
Sample standard deviation
13.4907
- Population SD
- 12.3153
- Mean
- 18
- Sample variance
- 182
- Population variance
- 151.6667
For roughly normal data, about 68% of values fall within one standard deviation of the mean and 95% within two. The marker shows the mean.
- More than 2 SD below
- 1–2 SD below
- Within 1 SD (~68%)
- 1–2 SD above
- More than 2 SD above
This tool performs standard mathematical operations for educational and reference purposes. Always double-check results for critical academic or professional work.
About the Standard Deviation Calculator
The standard deviation calculator measures how spread out a set of numbers is. It returns the mean, the variance and the standard deviation, for both a population (dividing by n) and a sample (dividing by n − 1). Use the population figures when your data includes every member of the group you care about, and the sample figures when your data is a sample used to estimate a larger group. A small standard deviation means values cluster near the mean; a large one means they are widely spread.
How to use it
- 1Type or paste your data, separated by commas or spaces.
- 2Press Calculate.
- 3Read the population or sample standard deviation, depending on your data.
Worked example
for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5. The population standard deviation is exactly 2 and the sample standard deviation is about 2.14.
How it works
Formulas
Variance is the average squared distance from the mean. Population divides by n; sample divides by n−1. Standard deviation is the square root of variance.
Who it is for
Students, researchers, quality engineers and anyone analysing variation in data.
Why it helps
An average alone hides how consistent the data is; standard deviation measures that consistency.
Common use cases
- Measuring how consistent test scores or measurements are
- Checking statistics homework
- Comparing the variability of two data sets
Common mistakes to avoid
- Using the population formula on a sample, which understates variability.
- Including units or text in the list of numbers.
Frequently asked questions
A:Use sample (n−1) when your data is a sample of a larger group; use population (n) when it is the entire group.
A:A higher standard deviation means the values are more spread out from the mean.
Reviewed for accuracy · Last updated October 7, 2026
Calculations use standard, well-established mathematical identities and algorithms with no approximation beyond normal floating-point precision.
CalcWisee Editorial Team
Calculator development and formula review
CalcWisee is an independent site founded by Ayman. Every calculator is built from a published formula or official definition, tested against hand-worked examples before it goes live, and corrected promptly when a reader reports an issue to ayman@calcwisee.com.
Expertise: Financial mathematics, Health and fitness formulas, Applied mathematics, Unit conversion standards
References & sources
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