Standard Deviation Calculator

Calculate sample and population standard deviation, variance, mean, variance steps, and confidence interval limits instantly.

Calculate from Raw Numbers

Enter a set of numbers separated by commas, spaces, or newlines.

Data Set (Numbers):

Confidence Interval Level (%):

Calculate from Frequency Table

Enter pairs of (Value, Frequency) separated by comma or tab per row.

Values & Frequencies (Value, Frequency):

How to Calculate Standard Deviation

Standard deviation measures the amount of variation or dispersion of a set of values relative to its mean.

Sample Standard Deviation ($s$): Used when the data represents a sample drawn from a larger population ($n - 1$ degrees of freedom).
Population Standard Deviation ($\sigma$): Used when the data set contains the entire population ($N$ degrees of freedom).

Frequently Asked Questions (FAQs)

Sample standard deviation divides the sum of squared differences by $n - 1$ (Bessel's correction), whereas population standard deviation divides by $N$.

Variance is simply the square of the Standard Deviation ($s^2$ or $\sigma^2$).

Use Sample Standard Deviation when your data represents only a subset of a larger population. Use Population Standard Deviation only when your dataset includes every member of the population.

Yes. In addition to standard deviation, this calculator also computes the mean, variance, sample size, confidence interval, and other statistical values based on your input.

You can enter raw numbers separated by commas, spaces, or new lines, or use the frequency table option by providing value-frequency pairs for grouped data.