# Standard Deviation Calculator

The following is a free online tool to calculate the standard deviation, variance, mean, sum, and confidence range for given numbers. The value used to calculate the confidence range is the sample standard deviation value.

Please provide numbers separated by comma to calculate.

## Standard Deviation

The following is the definition of the standard definition σ, also called **population standard deviation** if the entire population can be measured, where µ is the expectation, x_{i} is one sample value, and N is the total number of samples. σ^{2} is called variance.

One can find the standard deviation of an entire population in cases where every member of a population is sampled. In most cases, this cannot be done. The standard deviation σ is estimated by examining a random sample taken from the population.

## Sample Standard Deviation

The most common estimator for σ used is an adjusted version, the sample standard deviation, denoted by "s" and defined as follows. s^{2} is the sample standard variance.