𝑧 Statistics Calculator

Z-Score Calculator

Calculate the z-score (standard score) of a data point, find the corresponding percentile and probability from the normal distribution table, and convert between raw scores and z-scores.

Calculate Z-Score

Raw score (x)

Population Mean (μ)

Population Std Deviation (σ)

Enter raw score (or z), mean, and σ

z = (x − μ) / σ — measures how many standard deviations a point is from the mean.

Z-Score Percentile Reference

Z-score	Percentile	Description
−2.0	2.3%	Far below average
−1.0	15.9%	Below average
0.0	50.0%	Average
+1.0	84.1%	Above average
+2.0	97.7%	Far above average

Frequently Asked Questions

What is a z-score?

A z-score (standard score) measures how many standard deviations an observation is above or below the mean: z = (x − μ) / σ. A z-score of 0 is exactly average; +1 is one SD above average.

How do I find the percentile from a z-score?

Percentile = CDF(z) × 100%. The normal distribution CDF gives the probability that a random value falls at or below z. For example, z=1.645 corresponds to the 95th percentile.