Calculate sample standard deviation, population standard deviation, variance, mean, and more. Enter any list of numbers instantly. Free and pure client-side.
Enter numbers separated by commas, spaces, or line breaks
This calculator computes both sample and population standard deviation for any set of numbers. Standard deviation measures how spread out numbers are from the mean. A low standard deviation means values tend to be close to the mean, while a high standard deviation means values are spread out over a wider range. It is widely used in statistics, finance, science, quality control, and education. All calculations happen instantly in your browser — no server required.
Population standard deviation (σ) uses all data points from an entire population and divides by N. Sample standard deviation (s) uses a subset of data and divides by N−1 to provide an unbiased estimate of the population parameter. Use population when you have complete data; use sample when working with a subset.
Variance is the average of squared differences from the mean. Standard deviation is simply the square root of variance. While variance is useful mathematically, standard deviation is more intuitive because it uses the same units as the original data.
Yes. This calculator supports any real numbers including negative values, decimals, and scientific notation. Temperature changes, stock returns, and test score deviations are common use cases with negative numbers.
There is no universal "good" value — it depends on context. In quality control, a smaller standard deviation means more consistent products. In investing, a higher standard deviation means higher volatility and risk. Always interpret standard deviation relative to the mean and the specific domain.