📉 Empirical Rule Calculator
Apply the 68-95-99.7 empirical rule to find where most of your normally distributed data should fall.
What the empirical rule states
The empirical rule, also called the 68-95-99.7 rule, describes how data is distributed in a normal (bell-curve) distribution. It states that about 68% of values fall within one standard deviation of the mean, about 95% fall within two standard deviations, and about 99.7% fall within three standard deviations.
How this calculator works
Enter your data’s mean and standard deviation. The calculator adds and subtracts one, two, and three standard deviations from the mean to show the exact numeric ranges that should contain roughly 68%, 95%, and 99.7% of your data, assuming the data is approximately normally distributed.
This rule only applies to data that is roughly bell-shaped. For data with a different or unknown shape, Chebyshev’s theorem provides a more conservative but universally valid bound. This tool is intended for general statistics education.