Z-Score Calculator
with Probability and Percentile

What Is a Z-Score and How Is It Calculated?

A z-score (also called a standard score) measures how many standard deviations a value is above or below the population mean. The formula is z = (x − μ) / σ, where x is the raw value, μ is the population mean, and σ is the standard deviation. A z-score of 0 means the value equals the mean. A z-score of 1.0 means the value is one standard deviation above the mean.

Z-scores are used to compare values from different distributions, find probabilities using the standard normal table, and calculate percentile ranks. They appear in standardized test score reporting, quality control, and any analysis that requires comparing a value to its reference population.

What the Calculator Outputs

Z-Score

The standardized score showing how many SDs the value is from the mean. Positive z-scores are above the mean; negative z-scores are below.

Probability

The area under the normal curve below (or above) the z-score — this is the probability that a randomly selected value from the distribution falls at or below the given value.

Percentile Rank

The percentage of values in the distribution that fall at or below the given score. A percentile of 84.13 means 84.13% of values are lower.

When to Use Z-Scores

• Comparing scores from tests with different scales or means
• Finding the probability a value falls within a range
• Identifying outliers (values with |z| > 3 are unusual)
• Converting raw scores to percentiles for reporting