Inverse Normal Distribution Calculator
Find the x-value that corresponds to a given cumulative probability on a normal distribution — the inverse of a standard normal (z) table lookup.
What the inverse normal distribution gives you
While a normal CDF calculator tells you the probability of being below a certain value, the inverse normal distribution (quantile function) does the opposite: given a probability, it tells you the value on the distribution below which that proportion of data falls.
How this calculator works
Enter the cumulative probability you want (for example 0.95 for the 95th percentile), along with the mean and standard deviation of your distribution. The calculator uses a well-established rational approximation (Acklam’s algorithm) to find the standard normal z-score for that probability, accurate to roughly nine decimal places, then converts it into your distribution’s actual value using x = mean + z x standard deviation.
This is the same calculation behind finding exam cutoff scores, confidence interval bounds, and process control limits. Provided for general educational and planning purposes.