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 Standard Deviation Calculator?
The Standard Deviation Calculator measures data dispersion. It tells you exactly how "spread out" the numbers in your dataset are relative to the average. A low standard deviation means the data is tightly clustered; a high one indicates high volatility.
How It Works (Formula)
The algorithm computes the arithmetic mean. Then, it subtracts the mean from every single data point, squares the result (to remove negatives), averages those squared differences (yielding the Variance), and finally takes the square root.
$$ s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}} $$
The formula for Sample Standard Deviation.
How to Use It
Enter your dataset into the input field, with numbers separated by commas. Select whether your data represents an entire "Population" or just a "Sample" (which alters the denominator). Click calculate to view the variance and standard deviation.