What standard deviation measures
It is the typical distance of a value from the mean. A small figure means the numbers sit close to the average; a large one means they are spread out.
It is the square root of the variance, which is why the answer is in the same units as your data.
Sample or population
The sample version divides by one less than the count. Use it when your numbers are a sample of something larger.
The population version divides by the count itself. Use it when the list is the whole group you care about.
Worked example
For 4, 8, 15, 16, 23, 42 the mean is 18. The sample standard deviation is 13.4907 and the population version is 12.3153.
The sample figure is always slightly larger, because dividing by five instead of six gives a bigger variance.
Inputs for the standard deviation calculator
Your numbers
Separate the numbers with commas, spaces or new lines. A pasted spreadsheet column works as it is.
CALCULATOR QUESTIONS
Standard deviation calculator questions
How do I calculate standard deviation?
Find the mean, subtract it from each value and square the result, average those squares, then take the square root.
Which version should I use?
Use the sample version when the list is part of a larger set, and the population version when it is the whole set.
What does a standard deviation of zero mean?
Every value is identical to the mean, so there is no spread at all.
Why are the two figures different?
They divide the squared distances by different counts: one less than the number of values for the sample version, the full count for the population.