# Cumulative Distribution Function for a Standard Normal Distribution

**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:

`z`

= a value for which you want to calculate the CDF of the standard normal distribution

## Example valid values:

`z`

= 1.96

## Output:

- The probability that Z will be less than or equal to the given value of
.*z*

## Data validation

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

## Summary

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