Standard Deviation Calculator
Paste or type your numbers. You get the sample and population standard deviation and variance, the mean, the standard error and a table showing how each value is worked in.
Separate numbers with commas, spaces or new lines.
Worked examples
A classic data set
2, 4, 4, 4, 5, 5, 7, 9
Population SD 2, sample SD 2.138
The mean is 5 and the squared differences add to 32.
The variance
2, 4, 4, 4, 5, 5, 7, 9
Population variance 4, sample variance 4.571
32 ÷ 8 and 32 ÷ 7.
About Standard Deviation Calculator
The standard deviation measures how far the values in a list typically are from their mean. A small value means the numbers sit close together, and a large one means they are spread out. To work it out, find the mean, take it from each value, square those differences, add them up, divide, and take the square root. The squared result before the root is the variance. It is the most common measure of spread in science, finance and quality control.
There are two versions. If your numbers are every value in the group you care about, divide by n, the number of values: that gives the population standard deviation. If they are a sample from a larger group, divide by n - 1, which corrects for samples being less spread than the whole group. For 2, 4, 4, 4, 5, 5, 7, 9 the population value is exactly 2 and the sample value is about 2.138. The page shows both, highlights the one you pick, and lists the difference and the square for each value so the working is clear.
How to use Standard Deviation Calculator
- Type or paste your numbers, separated by commas, spaces or new lines.
- Choose sample or population standard deviation.
- Read the standard deviation, variance and mean in the large boxes.
- Follow the working steps and the table of differences from the mean.
Common uses
- Statistics homework and coursework
- Measuring consistency in test marks or lab readings
- Quality control of sizes and weights
- Comparing the spread of two data sets
Frequently asked questions
Should I use the sample or the population standard deviation?
Use the population version if your numbers are the whole group, such as every pupil in a class. Use the sample version if they are only part of a larger group, which is the usual case for surveys and experiments.
What is variance?
It is the square of the standard deviation: the average squared distance from the mean. It is useful in formulas, but the standard deviation is in the same units as your data, so it is easier to read.
What does a standard deviation of zero mean?
Every value is the same, so there is no spread at all.
What is the standard error?
It is the sample standard deviation divided by the square root of the number of values. It shows how much the mean itself would vary from sample to sample.
What is the coefficient of variation?
It is the standard deviation as a percentage of the mean. It lets you compare the spread of data sets measured in different units.