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Standard Deviation Calculator

Spread & variance of your data

Enter a list of numbers to instantly calculate the standard deviation, variance, mean, and range — for either a population or a sample.

Enter at least one number to see the standard deviation.

About the standard deviation calculator

The standard deviation calculator measures how spread out a set of numbers is from the average. A low standard deviation means the values cluster close to the mean; a high standard deviation means they are spread out over a wider range. Enter your numbers separated by commas, spaces, or new lines and the results update instantly.

Choose population standard deviation when your data is the entire group, and sample standard deviation when your data is a sample drawn from a larger population. The difference is the divisor: population divides by N, while sample divides by N − 1 (Bessel's correction) for an unbiased estimate.

The formulas

  • Mean = sum ÷ count
  • Population variance = Σ(x − mean)² ÷ N
  • Sample variance = Σ(x − mean)² ÷ (N − 1)
  • Standard deviation = √variance

How to use the standard deviation calculator

  1. Enter your numbers

    Type or paste a list separated by commas, spaces, or line breaks.

  2. Pick population or sample

    Use population for a full data set, sample for a subset of a larger population.

  3. Read the results

    Standard deviation, variance, mean, and range update instantly.

Frequently asked questions

What is standard deviation?
It is a measure of how spread out numbers are from the mean. A larger value means more spread; a value of zero means all numbers are identical.
When do I use population vs sample?
Use population standard deviation when your data set is the entire group you care about. Use sample standard deviation when your data is a sample from a larger population and you want to estimate the population spread.
Why does sample divide by N − 1?
Dividing by N − 1 (Bessel's correction) gives an unbiased estimate of the population variance when working from a sample.
What separators can I use?
Commas, spaces, and new lines all work. You can mix them in the same input.
Is the standard deviation calculator free?
Yes, it is completely free and requires no account.

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