Normal Distribution Calculator

Enter mean μ =
Enter standard deviation       σ =

Probability Density Function

p(x) = \(\frac{1}{\sqrt{2\pi\sigma^2}}e^\frac{-(x-\mu)^2}{2\sigma^2}\)

Cumulative Distribution Function

F(a) = \(P(x\leq a)\) = \(\int_{-\infty}^{a}p(x)\;dx\)
1 - F(a) = \(P(x > a)\) = \(\int_{a}^{\infty}p(x)\;dx\)
1 - F()
F(b) - F(a) = \(P(a \leq x \leq b)\) = \(\int_{a}^{b}p(x)\;dx\)
F() - F()

This calculator gives the probability that a random variable with normal distribution and given mean and standard deviation produces a given value, or value within the specified range.