Empirical Rule Calculator (68-95-99.7)
Turn a mean and standard deviation into the 68%, 95% and 99.7% intervals.
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ⓘ Live results
Results
- 68% of values fall between
- 85 and 115
- 95% of values fall between
- 70 and 130
- 99.7% of values fall between
- 55 and 145
| Interval | Range | Approx. share |
|---|---|---|
| μ ± 1σ | 85 to 115 | 68.27% |
| μ ± 2σ | 70 to 130 | 95.45% |
| μ ± 3σ | 55 to 145 | 99.73% |
Quick answer
The empirical rule says that for a normal distribution about 68% of values fall within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.
μ ± 1σ ≈ 68%, μ ± 2σ ≈ 95%, μ ± 3σ ≈ 99.7%
How to use the Empirical Rule Calculator
- 1Enter the mean and standard deviation of your normally distributed data.
- 2Optionally add a single value to get its z-score and percentile.
- 3Read the three empirical-rule intervals.
Frequently asked questions
What is the 68-95-99.7 rule?
It is a shortcut for normal distributions: roughly 68% of observations lie within one standard deviation of the mean, 95% within two, and 99.7% within three.
When does the empirical rule not apply?
It assumes an approximately bell-shaped distribution. For skewed or heavy-tailed data use Chebyshev's inequality or the actual distribution instead.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
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Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.