​Empirical Rule Calculator

Empirical rule or 3 Sigma rule. The empirical rule implies that under the normal deviation we have fixed values of data. Therefore, it is also known as the 68 95, and 99.7 rules as well.

For example, in a normal curve where the data is equally distributed about the mean, we have fixed values for the standard deviation according to the rule. Moving a step forward or backward from the mean of the curve means + or - Sigma(σ) or standard deviation. It may be 1σ, 2σ, or 3σ key points to be noted.

Under this rule, from 1σ or standard deviation, we mean that up to 68% of data fall in the curve. Furthermore, for 2σ, we mean that 95% is false under the curve. Lastly, 3σ means that 99.7% falls in this region.


Formula of ​Empirical Rule Calculator

However, there is no defined formula but you can have a simple equation in order to solve a complicated dataset. i.e.,

x ± standard deviation (either 1σ, 2σ or 3σ)


Visit our Relative Standard Deviation Calculator to know more about the standard deviation.


To make the process easier for you, we can have an illustration with the help of an example. Suppose we have a history of previous school results, having a normal distribution with a mean of 82 but a standard deviation is 6.

Now we have to find the range around the mean including 95% of the grade.

x = 82
σ = 6

From the empirical formula, we find that the standard deviation for 95 falls in 2σ.

Applying the empirical rule in a simple way.

x + 2σ = 82 + 2(6)
82 + 12 = 94


x - 2σ = 82 - 2(6)
82 - 12 = 70

So this is the average number of scores the students can achieve under the mentioned standard deviation about the mean value.

How to use ​Empirical Rule Calculator?

The steps to use ​an empirical rule calculator are as follows:

Step 1: Enter the value of the mean in the first required input.

Step 2: Enter the value of standard deviation in the second required input.

Step 3: The calculator will automatically display an answer on the screen.

Calculator use

By using the empirical rule calculator, you can find the upper and lower limit deviation by simply putting the value of the mean and deviations. In other words, you have to give your graph a written form. Afterward, you have to click on the button in order to get your upper and lower limits. In case you don't have the exact percentage of standard deviation. Simply place your percentage and the algorithm will automatically find the deviation. It is a better way to solve complex statistical equations.