Empirical Rule Calculator
Use our empirical rule calculator to calculate empirical rule ranges instantly from a mean and standard deviation. Includes the empirical rule formula, examples, and when the empirical rule can be used. (Note: the empirical rule is different from calculating empirical formula in chemistry.)
What is the Empirical Rule?
The empirical rule (also called the 68–95–99.7 rule) describes how data is distributed in a normal (bell-shaped) distribution. It estimates what percent of data falls within 1, 2, and 3 standard deviations of the mean.
If you want to calculate empirical rule values, the rule says: about 68% of data falls within ±1 standard deviation of the mean, about 95% within ±2, and about 99.7% within ±3.
Important: many people search “calculate empirical formula” or “calculate empirical formula from percent composition.” That refers to chemistry (empirical formula). This empirical rule calculator is for statistics and distributions.
Empirical Rule Formula
To find the ranges for the empirical rule, add and subtract 1, 2, and 3 standard deviations from the mean.
Lower = μ - σ, Upper = μ + σ.
Lower = μ - 2σ, Upper = μ + 2σ.
Lower = μ - 3σ, Upper = μ + 3σ.
These are the three empirical rule ranges for mean 4 and standard deviation 6.
That’s exactly what an empirical rule calculator does.
How to Calculate Empirical Rule
- 1
Enter the mean (μ).
- 2
Enter the standard deviation (σ).
- 3
The calculator finds μ ± 1σ for the 68% range.
- 4
It also finds μ ± 2σ (95%) and μ ± 3σ (99.7%).
Frequently Asked Questions
It’s the 68–95–99.7 rule for normal distributions: ~68% within 1σ, ~95% within 2σ, and ~99.7% within 3σ of the mean.
Compute the ranges: μ±σ, μ±2σ, and μ±3σ.
When the data is approximately normally distributed (bell-shaped and symmetric). It’s an estimate, not an exact rule for non-normal data.
Yes—enter mean and standard deviation and the calculator outputs the 68%, 95%, and 99.7% ranges.
That’s a chemistry topic (empirical formula). This page is about the statistical empirical rule.
No. For chemistry, an empirical formula calculator without percentage or from percent composition uses element moles and ratios. This calculator is for statistical distributions.
All values are the same, so the 68%, 95%, and 99.7% ranges are all equal to the mean.