What is the Empirical Rule?

Also known as the 68-95-99.7 rule. It states that for a normal distribution, nearly all data falls within 3 standard deviations of the mean.

What are the percentages?

68% within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs.

Only for symmetric, bell-shaped (normal) distributions.

Empirical Rule Calculator

Calculate ranges for 68%, 95%, and 99.7% of data in a normal distribution.

Mean (μ)

Average value

Standard Deviation (σ)

Spread of data

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Normal Curve Regions

68% (±1σ)

85 to 115

Approximately 68% of the data falls within this range.

95% (±2σ)

70 to 130

Approximately 95% of the data falls within this range.

99.7% (±3σ)

55 to 145

Approximately 99.7% of the data falls within this range.

Frequently Asked Questions

About the Empirical Rule

What it calculates

This empirical rule solves mathematical and statistical problems using standard formulas. 68-95-99.7 rule ranges.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Empirical Rule.

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