Statistics & Research Tools
Standard Deviation Calculator
Paste a list of numbers to get the standard deviation, variance, mean, median, mode, quartiles and more in one step, for a sample or a whole population.
What standard deviation shows
The standard deviation measures how spread out your values are around the mean. A small value means the data points sit close to the average. A large value means they are widely scattered. It is expressed in the same units as the data, which makes it easier to interpret than the variance. Standard deviation is part of descriptive statistics.
Sample or population?
Use the population formula, dividing by n, only when your data include every member of the group you care about. Use the sample formula, dividing by n − 1, when the data are a sample drawn from a larger population. This is the correct choice in most research projects.
Other statistics in the results
- Variance: the squared standard deviation.
- Standard error: the standard deviation divided by √n, showing how precisely the mean is estimated.
- Quartiles and IQR: describe the middle half of the data and are robust to outliers.
- Coefficient of variation: the standard deviation as a percentage of the mean, useful for comparing spread across different scales.
Worked example
For the values 12, 15, 11, 18, 22, 15, 19, 14, 15, 20 and 17, the mean is 16.18 and the sample standard deviation is 3.37. About two thirds of the values fall within one standard deviation of the mean.
Related analysis services
We can run descriptive statistics and SPSS and STATA analysis on your dataset, with missing data and outlier handling and clear tables, charts and written summaries for your report. See all services or tell us about your project.
Frequently asked questions
Why divide by n − 1 for a sample?
A sample tends to underestimate the spread of the population. Dividing by n − 1 corrects this bias.
What is a good standard deviation?
There is no universal good value. It depends on the scale of the data, so compare it to the mean using the coefficient of variation.
How do I report the mean and standard deviation?
Write them as M = 16.18, SD = 3.37.
Can I paste data from Excel?
Yes. Copy a column from Excel or Google Sheets and paste it into the box. Numbers separated by commas, spaces, tabs or new lines are all accepted.