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Empirical Rule Bands — result sheet
68-95-99.7% intervals from mean and standard deviation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Bands: mean +/- k x sd for k = 1, 2, 3.
One, two, and three standard deviations about the mean capture about 68%, 95%, and 99.7% of normal data.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mean — minimum -1000000000; maximum 1000000000
- Standard deviation — Must be positive.; minimum 1.0E-12; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Mean | 100 |
| Standard deviation | 15 |
68% (85, 115); 95% (70, 130); 99.7% (55, 145).
Assumptions and limits
- Approximately normal distribution; positive standard deviation.
- Rule of thumb, not an exact probability table.
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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