Our free z-score calculator computes the standard score (z-score) from a raw value, population mean, and standard deviation. It also converts z-scores to percentiles and probabilities using the standard normal distribution. Use it for statistics, exam scores, quality control, and hypothesis testing.
Input your raw score or observation (x).
Enter the population mean (μ) and standard deviation (σ).
See your z-score, percentile rank, and probability.
Understand what your z-score means relative to the distribution.
The z-score measures how many standard deviations a value is from the mean. A z-score of 0 means the value equals the mean. Positive z-scores are above the mean; negative z-scores are below. The percentile is the cumulative probability P(Z < z) from the standard normal distribution.
z = (x − μ) / σ
z = 0 means you're exactly at the mean
z = ±1 covers ~68% of a normal distribution
z = ±2 covers ~95% of a normal distribution
z = ±3 covers ~99.7% of a normal distribution (the 68-95-99.7 rule)
A z-score above 2.0 means you're in the top ~2.3% of the distribution
Use negative z-scores when the value is below the mean
Calculate z-scores, convert to percentiles, and find probability values using our free z-score calculator. Works with exam scores, quality control data, scientific measurements, and any normally distributed dataset.
The z-score formula is z = (x − μ) / σ, where x is your raw value, μ is the mean, and σ is the standard deviation. Enter these three values into the calculator to get the z-score instantly, along with the corresponding percentile and probability.
Convert any z-score to a percentile rank using the cumulative standard normal distribution. A z-score of 0 = 50th percentile (the mean). A z-score of 1.0 = 84th percentile. A z-score of 1.96 = 97.5th percentile (used in 95% confidence intervals).
Z-scores follow the standard normal distribution (mean=0, SD=1). The 68-95-99.7 rule states that 68% of data falls within z=±1, 95% within z=±2, and 99.7% within z=±3. Our calculator visualizes your z-score on the normal distribution curve.
Data sourced from trusted institutions
All formulas verified against official standards.