Statistics Calculator

Z-Score Calculator

Calculate z-scores, find values from z-scores, and look up probabilities from the standard normal distribution.

Value (x)

Mean (μ)

Std Dev (σ)

Learning Guide

What is a Z-Score?

A z-score (also called a standard score) tells you how many standard deviations a data point is from the mean. It allows comparison of values from different normal distributions.

Z-Score Formula

z = (x - μ) / σ

Where x is the value, μ is the mean, and σ is the standard deviation.

Interpreting Z-Scores

z = 0: Value equals the mean
z > 0: Value is above the mean
z < 0: Value is below the mean
|z| > 2: Value is unusual (outside 95%)
|z| > 3: Value is very unusual (outside 99.7%)

Common Z-Scores

Percentile	Z-Score
50th	0.00
84th	1.00
95th	1.645
97.5th	1.96
99th	2.33

Applications

Standardized test scores (SAT, GRE)
Quality control limits
Hypothesis testing
Comparing different datasets