Enter the standard deviation and mean of your data set into the calculator to determine the values that fall within the empirical rule.

Empirical Rule Formula

The following equation is used to calculate the total values of data within the 3 sets of the empirical rule.

  • 68% of data within 1 standard deviation
  • 95% of data within 2 standard deviations
  • 99.7% of data within 3 standard deviations

Empirical Rule Definition

The empirical rule is the analysis of a data set to determine which values of data fall within 3 subsets of data. These subsets are 68%, 95%, and 99.7% of data. So for example, if a data set has a mean of 5 and a standard deviation of 1, then 68% of the data would fall between 4 and 6. (5-1= 4 and 5+1 = 6).

Empirical Rule Example

How to calculate the empirical rule?

  1. First, determine the standard deviation.

    Calculate the average value of the standard deviation of the data set.

  2. Next, determine the empirical rule values.

    Using the formula above, calculate the empirical rule values.


What is the empirical rule?

The empirical rule states that 68% of data lies within 1 standard deviation, 95% of data lies within 2 standard deviations, and 99.7% of data lies within 3 standard deviations.