Standard Deviation
Calculate standard deviation and variance
How to use Standard Deviation
- 1Enter your data set as a list of numbers separated by commas.
- 2Choose whether it is a population or a sample.
- 3Read the result: the calculator shows the standard deviation and the variance.
What Is Standard Deviation?
σ = √( Σ(xᵢ − μ)² / N ) (population)Standard deviation measures how spread out the values in a data set are around the mean. A small value means the numbers are clustered closely together, while a large value means they vary widely.
Use it to compare consistency between groups, assess risk in finance, or understand variation in test scores and scientific measurements.
Frequently asked questions
Population or sample — which should I pick?
Use population when you have every member of the group (e.g. all students in a class). Use sample when your data is only a subset and you want to estimate the whole population.
Why is the sample standard deviation larger?
The sample formula divides by n−1 instead of n, which corrects the bias from estimating the mean from the same data, giving a slightly larger, more honest spread.
What unit is the result in?
The standard deviation always uses the same unit as your original data, which makes it easy to interpret alongside the mean.