Normal Distribution Calculator
Compute cumulative probability using the Gaussian distribution.
💡 Enter mean, standard deviation, and a value. The calculator returns P(X ≤ x).
Internally converts the value to a Z-score and applies the cumulative distribution function (CDF).
Example 1
Example 2 (Extreme Value)
Formula
The error function (erf) approximates the cumulative probability.
What does this calculator do?
It computes cumulative probability under a normal distribution using mean and standard deviation.
When should you use normal distribution?
Normal distribution models natural phenomena, measurement errors, test scores, and financial variables.
Frequently Asked Questions
What is a normal distribution?
A symmetric, bell-shaped probability distribution.
Is this related to Z-score?
Yes. The calculator converts the value to a Z-score before computing probability.
Can probabilities exceed 1?
No. Probabilities always range between 0 and 1.
Can I calculate probability between two values?
Not yet. This version calculates P(X ≤ x). A range version can be added later.