Math
Standard Deviation Calculator
Mean, variance, and standard deviation from any list of numbers — sample or population.
Choose "Sample" if your numbers are a subset of a larger group; choose "Population" if they're the entire group.
Standard deviation
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Enter a list of numbers
Mean
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Variance
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Count
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Frequently asked questions
What does standard deviation actually tell you?
It measures how spread out your numbers are from the average. A small standard deviation means values cluster tightly around the mean; a large one means they're spread wide, with some far from typical.
Should I use sample or population standard deviation?
Use "Population" when your numbers are the entire group you care about — every student in one class, for instance. Use "Sample" when your numbers are a subset used to estimate a larger group — a survey of 200 people out of a city's population. Sample standard deviation divides by one less than the count, which corrects for that extra uncertainty.
How is standard deviation related to variance?
Standard deviation is simply the square root of variance. Variance is useful mathematically but is in squared units (like "dollars squared"), which is hard to interpret — taking the square root brings it back to the original units, which is why standard deviation is the number most people actually look at.