🔔 Normal Distribution Calculator
Enter the mean and standard deviation of a normal distribution along with a value (or range) to calculate the probability and Z-score.
What is the Normal Distribution?
The normal (bell-curve) distribution describes many real-world measurements — heights, test scores, measurement errors — that cluster symmetrically around an average value. It is defined entirely by its mean (μ) and standard deviation (σ).
The Formula
This calculator converts your value(s) into Z-scores, Z = (X − μ) / σ, and uses the standard normal cumulative distribution function (via the error function) to find the probability of landing below, above, or between values. A Z-score tells you how many standard deviations a value is from the mean.
- Choose “between” and fill in both X1 and X2 to get the probability of a range.
- Standard deviation must be greater than zero.
Provided for general statistical education and planning purposes, not as professional or medical advice.