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Empirical Rule Interval Calculator — result sheet
Calculate one-, two-, and three-standard-deviation intervals and their normal-model coverage percentages.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Intervals are μ±kσ for k=1,2,3 with approximate normal-model coverage 68.27%, 95.45%, and 99.73%.
The calculator separates interval endpoints from the approximate coverage associated with a bell-shaped distribution.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mean — minimum -1000000000000; maximum 1000000000000
- Standard deviation — minimum 0; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Mean | 100 |
| Standard deviation | 15 |
1σ:85–115; 2σ:70–130; 3σ:55–145.
Assumptions and limits
- The empirical-rule percentages are used as normal-model approximations.
- The standard deviation is nonnegative and shares units with the mean.
- A dataset test, skewness check, and formal interval inference are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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