Cumulative Distribution Function for a Standard Normal Distribution

Output: Press calculate

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Formula:Φ(z) = 0.5 * (1 + erf(z / √2))

Introduction to the Standard Normal Distribution CDF Calculator

The cumulative distribution function (CDF) for a standard normal distribution calculates the probability that a standard normal random variable Z will be less than or equal to a given value z. The standard normal distribution has a mean of 0 and a standard deviation of 1. The CDF is represented as Φ(z), and it is related to the error function (erf), which is used in this JavaScript function to approximate the result.

Parameter usage:

Example valid values:


Data validation

The parameter z must be a number. The function will return an error message if the input is not a number.


This calculator provides the cumulative probability for a given z-score in the standard normal distribution using the error function to approximate the integral of the probability density function.

Tags: Statistics, Probability, Normal Distribution, Cdf, Score