# Normal CDF Formula

Cumulative density function is one of the methods to describe the distribution of random variables. It defines the probability that the X, a real-valued random variable will take a value less than or equal to x. The page lists the Normal CDF formulas to calculate the cumulative density functions. Cumulative distribution function formula gives you the individual formulas for the calculation of probability function, lower cumulative distribution, and upper cumulative distribution.

# Cumulative Distribution Function Formula

#### Formula:

Probability Function f(x, μ, σ) = 1 / (√ (2 x Π) x a x e(-1 / 2 x ((b - c) / a)2)
Lower cumulative distribution P(x, μ, σ) = -∞x f(x, μ, σ) dt
Upper cumulative distribution Q(x, μ, σ) = x f(x, μ, σ) dt

Where,

a = Standard Deviation σ
b = Percentile x
c = Mean μ

#### Related Calculator:

Cumulative Distribution Function is a non-decreasing and right-continuous function. Use the Normal CDF formula to manually calculate the probability function.