Inverse Normal Distribution Calculator

Calculate X-Value for Given Probability

A value between 0 and 1 (exclusive).
Must be a positive value.

Easily calculate the X-value corresponding to a specific cumulative probability in a normal distribution. Our Inverse Normal Distribution Calculator helps you determine the data point given the mean, standard deviation, and a desired probability.

Formula:

The inverse normal distribution function, often denoted as Φ⁻¹(p, μ, σ), determines the value 'x' below which a given cumulative probability 'p' occurs in a normal distribution.
The underlying relationship is:
X = μ + Z × σ
Where:

  • X is the value (data point) we want to find.
  • μ (mu) is the mean of the distribution.
  • σ (sigma) is the standard deviation of the distribution.
  • Z is the Z-score corresponding to the cumulative probability p in a standard normal distribution (mean=0, std=1).
Our calculator numerically approximates the Z score from the probability p and then applies the formula to find X.

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