Standard Deviation Calculator

Standard Deviation Calculator takes a list of numbers and returns how spread out they are, along with the rest of the summary statistics you normally want at the same time.

Standard deviation measures typical distance from the mean. A small one means the values cluster; a large one means they scatter. It is the square root of the variance, and variance is the mean of the squared differences from the mean. The squaring is what makes distances above and below count the same, and the square root at the end is what puts the answer back into the original units so it can be compared with the data.

The population and sample versions differ in one place: the sample version divides by n-1 rather than n. This is Bessel's correction, and it exists because a sample's own mean sits slightly closer to its own values than the true mean does, which makes the spread look smaller than it is. Dividing by n-1 compensates. Use the sample version when your numbers are a sample of something larger, which is almost always. Both are shown here, so you need not decide before seeing them.

The working is shown step by step: every value, its difference from the mean, and that difference squared. For coursework that is usually the part being marked, and for real data it is the quickest way to spot the one outlier that is distorting everything.

Everything is worked out inside your browser. Nothing you enter is uploaded, logged or stored, which matters for the financial calculators in particular: the figures you put into them are nobody else's business.

• Both population and sample standard deviation
• Variance, mean, median, mode and range
• Quartiles and the interquartile range
• Full working shown value by value
• Accepts commas, spaces, tabs or new lines
• Flags values more than two standard deviations out
• Runs in your browser; your data stays with you

The standard deviation calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

• Statistics coursework where the working has to be shown
• Checking how consistent a set of measurements is
• Finding the outlier in a list of results
• Summarising survey or test scores
• Comparing the spread of two data sets