Empirical Rule Calculator

Calculate data distribution percentages within 1, 2, and 3 standard deviations from the mean

Input Parameters

Mean (μ)

Standard Deviation (σ)

Data Range (Optional)

Minimum Value

Maximum Value

The Empirical Rule states that for a normal distribution:

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

Results & Distribution

Within 1 Standard Deviation

68%

μ ± σ: 40 to 60

Within 2 Standard Deviations

95%

μ ± 2σ: 30 to 70

Within 3 Standard Deviations

99.7%

μ ± 3σ: 20 to 80

μ-3σ

μ-2σ

μ

μ+2σ

μ+3σ

0.15% 2.35% 13.5% 34% 34% 13.5% 2.35% 0.15%

1

Calculate range for 1 standard deviation: Mean ± Standard Deviation

2

Calculate range for 2 standard deviations: Mean ± (2 × Standard Deviation)

3

Calculate range for 3 standard deviations: Mean ± (3 × Standard Deviation)

Empirical Rule

Also known as the 68-95-99.7 rule, it describes how data is distributed in a normal distribution.

Easy Calculation

Simply enter the mean and standard deviation to get instant results for data distribution.

Visualization

See the distribution of data across standard deviations with our intuitive chart.

Educational

Learn how the empirical rule works with step-by-step calculations and explanations.

Empirical Rule Calculator © 2023 | A tool for understanding normal distribution

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