Langford Analytic · Knowledge Base

Standard Normal Z-Score Calculator

Convert a value to a z-score and compute the corresponding standard normal probability. Shows the conversion equation and the result.

Probabilistic & Reliability2 min read
calculatorz-scorestandard normalprobability

Calculator

z = (x - mu) / sigma
P(Z < z) = Phi(z)
P(Z > z) = 1 - Phi(z)

Enter x, mu and sigma to compute z and the probabilities.

Assumptions

  • The variable is normally distributed
  • The z-score is a dimensionless measure of how far x is from the mean in standard-deviation units