Normal Distribution Calculator
Calculate probability below, between and above entered bounds for a normal model with visible z-scores.
What would you like to do next?
Measure probability across a normal-model interval
Enter a mean, positive standard deviation and lower and upper bounds. The calculator standardizes both bounds, evaluates the cumulative normal model and reports probability below the lower bound, between the bounds and above the upper bound. The displayed z-scores keep the transformation visible and let students or analysts compare the result with a standard normal table.
Verify the model before interpreting its probability
A computed normal probability does not prove that the source population or measurement process is normally distributed. Skew, heavy tails, truncation, discrete outcomes and dependent observations can make the model unsuitable. Inspect the data and collection design, document why a normal approximation is reasonable, and use a method aligned with the actual sampling process when the assumptions do not hold.
Frequently asked questions
What units should the bounds use?
Use the same units as the mean and standard deviation.
Can the standard deviation be zero?
No. A probability distribution calculation requires a positive standard deviation.
Does this test data for normality?
No. It evaluates a normal model that the user has chosen.