Normal Distribution Calculator
For a normally distributed variable X ~ N(μ, σ), this calculator finds the probability of landing below or above a value x. It converts x to a z-score and evaluates the cumulative distribution function Φ(z).
Frequently asked questions
What is the cumulative probability?
P(X ≤ x) is the area under the normal curve to the left of x — the chance of a value at or below x.
How accurate is the result?
The cumulative probability uses a high-accuracy approximation of the error function, correct to several decimal places.
What is the standard normal distribution?
It is the normal distribution with mean 0 and standard deviation 1; any normal variable can be standardized to it.