NumberTally Standard Deviation Calculator
Find out how spread out your data is. Paste a list of numbers — separated by commas, spaces, or line breaks — and instantly get the count, mean, population and sample standard deviation, both variances, and a histogram.
Separate with commas, spaces, or line breaks.
Advanced options
Population vs sample: which one do you need?
Population standard deviation (σ) describes every member of a complete group — divide by N. Sample standard deviation (s) estimates the spread of a larger population from a subset — divide by n−1 (Bessel's correction), which corrects the downward bias of small samples. The comparison box below shows both side by side.
Reading the histogram
The bars show how your values cluster. A tight cluster near the mean gives a small SD; values spread far from the mean push it up. The dashed line marks the mean — roughly two-thirds of bell-shaped data falls within one SD of it.
Frequently Asked Questions
What does standard deviation measure?
The typical distance of data points from the mean. A low SD means values cluster tightly; a high SD means they spread out.
What is the difference between population and sample standard deviation?
Population SD divides by N (the whole group); sample SD divides by n−1 to correct for bias when estimating a larger population from a sample.
When should I use sample instead of population standard deviation?
Use sample SD when your data is a subset drawn from something bigger (a survey, an experiment). Use population SD when you have every value that exists.
What is a good standard deviation?
There is no universal "good" — it depends on the units. Compare it to the mean: an SD of 2 on a mean of 100 is tiny; on a mean of 3 it is huge.
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.