Z-Score Calculator — Standard Score & Percentile
Enter a value, mean, and standard deviation to instantly find the z-score (how many standard deviations from the mean) and its percentile under a normal distribution.
📊 Enter Your Values
📊 Result
Disclaimer: This tool performs standard mathematical calculations for educational and reference purposes. Always double-check results independently for graded coursework, exams, or safety-critical applications.
What a Z-Score Measures
A z-score (also called a standard score) converts a raw value into a measurement of how many standard deviations it sits away from the mean of its data set. A z-score of 0 means the value is exactly average. A z-score of +2 means the value is two standard deviations above the mean, while −1.5 means it's one and a half standard deviations below average. Because z-scores strip away the original units, they let you compare values from completely different scales — test scores, heights, temperatures — on the same standardized footing.
From Z-Score to Percentile
Once you have a z-score, you can translate it into a percentile by assuming the underlying data follows a normal (bell-curve) distribution. The percentile tells you roughly what share of the distribution falls below your value. This calculator uses a well-known rational polynomial approximation of the standard normal cumulative distribution function (CDF) to compute that percentile directly in your browser, without needing lookup tables.
Worked Example
Suppose a student scores x = 85 on a test where the class mean is μ = 75 and the standard deviation is σ = 10.
- Step 1: z = (x − μ) / σ = (85 − 75) / 10 = 1.0
- Step 2: A z-score of 1.0 falls at roughly the 84th percentile under a standard normal distribution — meaning the student scored better than about 84% of a normally distributed population.