Z-Score Calculator

Calculate z-scores for normal distributions. Free online standard score calculator.

The Z-Score Calculator converts raw scores to standardized z-scores, showing how many standard deviations a value is from the mean. Z-scores are essential for comparing data from different distributions, finding percentiles, and conducting hypothesis tests. Enter a value, mean, and standard deviation to find the z-score.

Common use cases

  • Standardized test interpretation
  • Quality control analysis
  • Comparing across different scales
  • Finding percentile ranks
  • Outlier detection

How to use

  1. Enter the raw score (x)
  2. Enter the population mean (μ)
  3. Enter the standard deviation (σ)
  4. Click calculate for z-score
  5. View the percentile and probability

FAQ

What is a z-score?

Z = (x - μ)/σ, measuring how many standard deviations a value is from the mean.

What does a z-score of 2 mean?

The value is 2 standard deviations above the mean—higher than about 97.7% of values in a normal distribution.

How do I find probability from z-score?

Use a z-table or calculator. Z = 1.96 corresponds to the 97.5th percentile (2.5% in each tail for 95% CI).

Can z-scores be negative?

Yes, negative z-scores indicate values below the mean.