How to use the empirical rule calculator
Find how much of a normal distribution lies within a number of standard deviations of the mean. Enter number of standard deviations in the field above; the share within k standard deviations (normal), share outside are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “68 95 99.7 rule”, “share within standard deviations”, “empirical rule calculator”, “calculate empirical rule”, “find share within k standard deviations”.
Formula
Variables
- k — Number of standard deviations
Worked example
With number of standard deviations = 2, the calculator gives share within k standard deviations (normal) ≈ 95.44999 %; share outside ≈ 4.550013 %.
Frequently asked questions
What is the empirical rule calculator used for?
Find how much of a normal distribution lies within a number of standard deviations of the mean. It helps with questions such as “68 95 99.7 rule”, “share within standard deviations”, “empirical rule calculator”.
What is the formula for the empirical rule calculation?
Share within k standard deviations (normal) (%) = 100 × (2 × ncdf(k)-1). Share outside (%) = 100-[Share within k standard deviations (normal)]. Here k is number of standard deviations.
What inputs do I need for the empirical rule (68-95-99.7) calculator?
You need number of standard deviations. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the empirical rule calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the empirical rule result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.