CalcArcade.

Standard Deviation Calculator

Paste or type a list of numbers and choose whether it is a whole population or a sample. You get the standard deviation and the main summary statistics.

Your numbers

Result

How we calculate it

First the mean is found. Each value’s distance from the mean is squared and the squares are added. Dividing by n gives the population variance and dividing by n − 1 gives the sample variance. The standard deviation is the square root of the variance.

For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the population variance is 4 and the standard deviation is 2.

Assumptions and limits

  • Use the sample version when your numbers are a subset drawn from a larger group, which is the usual case in surveys and experiments.
  • Standard deviation is in the same units as the data; variance is in squared units.

Frequently asked questions

What is the difference between sample and population standard deviation?

Population uses n in the denominator because you have every member. Sample uses n − 1 (Bessel’s correction) to avoid underestimating the spread of the full population.

What does standard deviation tell me?

It measures how spread out the values are around the mean. A small value means values cluster near the mean.

How many numbers can I enter?

Thousands. Separate them with commas, spaces or new lines.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Numbers (comma, space or new-line separated) = 2, 4, 4, 4, 5, 5, 7, 9; Data type = Population (divide by n).

  • Population standard deviation 2
  • Variance 4
  • Mean 5
  • Median 4.5
  • Count 8
  • Sum 40
  • Minimum 2
  • Maximum 9
  • Range 7

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.