Standard Deviation Calculator

How to use this standard deviation calculator

1. Enter your numbers, separated by commas, spaces or new lines, in the box above.
2. The tool ignores any non-numeric text, so you can paste straight from a spreadsheet or document.
3. Read the count, mean, standard deviation and variance, they recalculate instantly with every keystroke.

Nothing is submitted or stored: your data never leaves your device, so you can analyse private figures with confidence.

Population vs sample standard deviation

Both figures start the same way. First you find the mean (the average) of your numbers. Then you take each value, subtract the mean, and square the result. The variance is the average of those squared differences from the mean, and the standard deviation is the square root of the variance, which puts the answer back into the same units as your original data.

The one difference is what you divide by. Population standard deviation divides the total of the squared differences by N, the full count of values. Sample standard deviation divides byN - 1 instead. That smaller divisor makes the sample figure slightly larger, correcting for the way a sample tends to underestimate the spread of the whole population it was drawn from.

In short: use the sample version when your numbers are a sample of a bigger group (the usual case), and the population version only when your data already covers the entire group you care about.

Note: this tool reports the sample variance (dividing by N - 1) alongside both standard deviations. With a single value the spread is zero, so the sample figures show "-" because N - 1 would be zero.

Frequently asked questions