Statistics Calculators

Empirical Rule Calculator (68-95-99.7)

Calculate the value ranges covered by 1, 2 and 3 standard deviations from the mean, per the empirical (68-95-99.7) rule.

68% range — lower (μ − 1σ) —

68% range — upper (μ + 1σ) —

95% range — lower (μ − 2σ) —

95% range — upper (μ + 2σ) —

99.7% range — lower (μ − 3σ) —

99.7% range — upper (μ + 3σ) —

About the Empirical Rule Calculator (68-95-99.7)

The empirical rule (also called the 68-95-99.7 rule) describes how data is distributed in a normal distribution: about 68% of values fall within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.

Formula: 68% range = μ ± 1σ · 95% range = μ ± 2σ · 99.7% range = μ ± 3σ

This rule offers a quick way to gauge how typical or extreme a value is without doing a full z-score lookup, and is widely used in quality control and standardized testing to flag unusual results.