Math & Statistics · Browser · Free

Standard Deviation Calculator

In Mode, pick Population and sample standard deviation or Discrete random variable standard deviation, enter Data values as text, and press Calculate.

Two modes in one form

Pick Population and sample standard deviation to work from a list of data values. Pressing Calculate returns the population standard deviation, the sample standard deviation, the population variance, the sample variance and the mean.

Pick Discrete random variable standard deviation to give each data value its own probability or weight. The cards then show the standard deviation, the variance and the mean.

The form computes only when the button is pressed. Results appear in cards below the button. Copy writes a result and its unit to the clipboard. Clear resets the form. Everything runs in the browser and nothing is uploaded.

Reading the results

Entering 3, 2, 9, 4 returns a population standard deviation of 2.69258240356725, a sample standard deviation of 3.10912635102961, a population variance of 7.25, a sample variance of 9.66666666666667 and a mean of 4.5.

Results are printed in full, so some come out as long decimals while others are exact, like a sample standard deviation of 2 for the data values 1, 3, 5.

The formula

The tool reports the standard deviation (σ) as the square root of the variance, which is how the worked example for the data values 1, 3, 5 reads: σ = √(2.66666666666667) ≈ 1.63299316185545.

The discrete mode follows the same relation. With data values 1, 2, 3 and probabilities 0.2, 0.5, 0.3 it shows σ = √(0.49) = 0.7, alongside a variance of 0.49 and a mean of 2.1.