Math

Standard Deviation Calculator

Calculate population and sample standard deviation, variance, mean, and other key statistics from a data set.

Using the Standard Deviation Calculator

Standard deviation measures how spread out the values in a dataset are from the average. This tool calculates both Population SD (for entire datasets) and Sample SD (for subsets), helping you quantify the volatility or consistency of your data.

How it Works

Enter your list of numbers.

Choose between "Sample" (standard for research) or "Population" (for total data).

Review the calculated Standard Deviation (σ or s).

Check the "Step-by-Step" section to see the sum of squares and variance derivation.

Technical Formula


                        σ = √[ Σ(x-μ)² / N ]