How to use the standard deviation calculator
Paste your numbers into the box – they can be separated by commas, spaces, semicolons or line breaks, so you can copy a column straight from a spreadsheet. Then choose whether the data is a sample or the entire population. The calculator shows the standard deviation together with the count, sum, mean, median, variance, minimum, maximum, range, standard error of the mean and coefficient of variation.
What standard deviation tells you
Standard deviation measures how spread out values are around their average. A small standard deviation means the numbers cluster tightly around the mean; a large one means they are widely scattered. In a roughly normal (bell-shaped) distribution, about 68% of values fall within one standard deviation of the mean and about 95% within two.
Sample versus population
If your data includes every member of the group you care about – for example, the test scores of every student in one class – use the population formula, which divides by n. If the data is a sample used to estimate a larger group, use the sample formula, which divides by n − 1. This "Bessel's correction" compensates for the fact that a sample tends to underestimate the true spread.
Step by step
- Find the mean by adding all values and dividing by how many there are.
- Subtract the mean from each value and square the result.
- Add up the squared differences.
- Divide by n (population) or n − 1 (sample) to get the variance.
- Take the square root to get the standard deviation.
Related statistics
The standard error of the mean (SD ÷ √n) shows how precisely the sample mean estimates the population mean. The coefficient of variation (SD ÷ mean) expresses spread as a percentage, which lets you compare variability between data sets with different units or scales.
Frequently asked questions
When should I use sample standard deviation?
Use it whenever your data is a subset drawn from a larger group and you want to estimate that group’s spread. This is the most common case in research.
What is the difference between variance and standard deviation?
Variance is the average squared deviation from the mean. Standard deviation is its square root, which brings it back to the same units as the data.
Can standard deviation be negative?
No. It is a square root of a sum of squares, so it is always zero or positive. Zero means every value is identical.
How many numbers can I enter?
There is no fixed limit; thousands of values work fine because everything is calculated in your browser.
Last reviewed 2026-10-27. This standard deviation calculator is provided for general information; verify important decisions with a qualified professional.