Standard Deviation Calculator
Find the mean, variance and standard deviation of a list of numbers.
Results are provided for general informational use. Verify important financial, health or legal figures before relying on them.
About this Standard Deviation Calculator
The Standard Deviation Calculator measures how spread out a list of numbers is from the mean. Choose population or sample mode depending on whether your numbers represent an entire group or a sample drawn from a larger group.
For related tasks, try Average Calculator, GPA Calculator or Percentage Change Calculator.
How the calculation works
Variance is the average of squared differences from the mean. Population variance divides by n; sample variance divides by n−1. Standard deviation is the square root of variance.
How to use it
- Paste or type numbers separated by spaces, commas or new lines.
- Choose population or sample standard deviation.
- Calculate to see the mean, variance and standard deviation.
Practical example
For the numbers 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5 and the population standard deviation is 2.
Frequently asked questions
Population or sample: which should I choose?
Use population if your data is the entire group of interest; use sample if your data is a subset used to estimate a larger population.
Why does sample standard deviation divide by n−1?
This correction, called Bessel's correction, produces a less biased estimate of the population standard deviation from a sample.
Are negative numbers supported?
Yes.
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