About standard deviation
Standard deviation measures how spread out a set of numbers is around the mean — a low value means the data is clustered, a high value means it is spread out. This calculator gives the population and sample standard deviation, the variance and the mean, with the underlying sum of squared differences, all in your browser.
How Standard Deviation works
How to calculate standard deviation
- Enter your numbers.
- Choose whether the data is a sample or the whole population.
- Read the standard deviation, variance and supporting steps.
The formula
Standard deviation is the square root of the variance. Variance is the average of the squared differences from the mean — divided by n for a population, or by n−1 for a sample (Bessel’s correction).
Why it matters
Standard deviation puts the spread of your data in the same units as the data itself, which makes it easy to interpret and compare.
Common uses
- Measure the spread of a data set
- Compute sample or population SD
- Find the variance and mean
- Compare consistency between groups
- Analyse test scores or measurements
- Check statistics homework
- Support quality-control analysis
- Summarise data dispersion
Frequently asked questions
How do I calculate standard deviation?
Find the mean, square each difference from it, average those, and take the square root. This tool does it for you.
Sample or population — which do I pick?
Sample (n−1) if your data is a subset of a larger group; population (n) if it is every value.
What is variance?
The average of the squared differences from the mean; standard deviation is its square root.
Why divide by n−1 for a sample?
It corrects bias when estimating a population from a sample (Bessel’s correction).
Is my data uploaded?
No — it is calculated entirely in your browser.
Can it handle large data sets?
Yes — paste as many numbers as you like.
Does it show the steps?
Yes — it shows the mean, sum of squared differences and variance.
Is it free?
Yes — completely free with no sign-up.