Z-Score Calculator

About the Z-Score Calculator

A Z-score (standard score) measures how many standard deviations a data point is from the population mean. Z-scores standardise different datasets onto the same scale, making it possible to compare test results from different exams, heights between populations of different average sizes, or financial returns across different asset classes. Our Z-score calculator converts raw scores to Z-scores and provides the corresponding percentile rank.

How It Works

Z = (X − μ) / σ, where X is the raw score, μ is the population mean, and σ is the standard deviation. A Z-score of 0 means exactly average. Z = 1 means 1 standard deviation above average (84th percentile). Z = 2 means 2 SDs above average (97.7th percentile). Z = −1.5 means 1.5 SDs below average (6.7th percentile). The standard normal distribution has μ = 0 and σ = 1.

Tips & Best Practices

• ✓Z-scores above 2 or below −2 are statistically unusual (only ~5% of data in a normal distribution).
• ✓Z > 3 or Z < −3 are extreme outliers (0.3% of data) and often worth investigating.
• ✓Z-scores enable comparison of scores from tests with different scales — useful for college admissions.
• ✓IQ scores: mean = 100, SD = 15. IQ 130 has Z = (130−100)/15 = 2.0 (98th percentile).
• ✓Excel: STANDARDIZE(x, mean, SD) calculates Z-score; NORM.DIST() converts to percentile.

Who Uses This Calculator

Psychology researchers comparing test scores, college admissions officers comparing students from different schools, financial analysts measuring portfolio performance relative to benchmarks, and students interpreting their exam grades relative to class performance all rely on Z-scores.