Standard Deviation Calculator
Calculate population or sample standard deviation and variance with detailed statistical summary metrics.
Enter Dataset
Standard Deviation (σ)
14.142
What is the Variance Calculator?
The Variance Calculator is a core statistical tool that measures how far a set of numbers is spread out from their average value. It is the crucial intermediate step required before calculating the Standard Deviation.
How It Works (Formula)
Variance ($s^2$ or $\sigma^2$) is mathematically defined as the average of the squared differences from the Mean. Squaring the differences ensures that negative and positive deviations don't accidentally cancel each other out.
$$ s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1} $$
The equation for finding the variance of a statistical sample.
How to Use It
Enter your dataset into the input field, separating each value with a comma. Select whether your data is a Population or a Sample. The calculator will automatically output the Mean, the Sum of Squares, and the final Variance.