How to Calculate a Z-Score (2026)

A z-score (also called a standard score) tells you how many standard deviations a value is above or below the mean of its dataset. It converts raw data points into a common scale, making it possible to compare values from completely different distributions — for example, comparing a test score in one class against a score in another. Use the Z-Score Calculator to compute this instantly.

The Formula

The z-score formula is: z = (x − μ) / σ, where x is the raw value, μ is the population mean, and σ is the standard deviation. For sample data, replace μ with the sample mean (x̄) and σ with the sample standard deviation (s). A positive z-score means the value is above average; negative means below. A z-score of 0 means the value equals the mean exactly.

Example: if a class has a mean exam score of 72 and a standard deviation of 8, a student who scored 88 has a z-score of (88 − 72) / 8 = +2.0. They are two standard deviations above average.

Z-Score Interpretation Reference

Z-scores map directly onto the normal distribution. This table shows what percentage of a normally distributed population falls below a given z-score — useful for understanding where a value ranks.

When to Use Z-Scores

Z-scores are used any time you need to compare values measured on different scales or from different groups. Common applications include standardising test scores across exams with different difficulty levels, identifying outliers in datasets (values beyond ±3 are typically flagged), grading on a curve, comparing lab results against reference ranges in medicine, and normalising features before running machine learning algorithms. Z-scores only produce meaningful results when the underlying data is approximately normally distributed — they are less useful for heavily skewed distributions.

Use the Z-Score Calculator to do this instantly.