Statistics Calculators

Inverse Normal Distribution Calculator

Calculate the value (x) and z-score corresponding to a given cumulative probability in a normal distribution — the inverse of the normal CDF.

Z-score —

Value (x) —

About the Inverse Normal Distribution Calculator

The inverse normal distribution (quantile function) answers the reverse of the usual normal distribution question: instead of finding the probability below a value, it finds the value that corresponds to a given cumulative probability.

Formula: x = μ + z × σ, where z is found from a rational approximation of the inverse standard normal CDF for the given probability

This calculator uses a high-accuracy numerical approximation (Acklam's algorithm) to invert the normal CDF. It's commonly used to find critical values for confidence intervals, percentile cutoffs, and control limits.