Z-Score Calculator

A Z-score, also called a standard score, measures how many standard deviations a data point is from the population mean. A Z-score of 0 means the value equals the mean, a positive Z-score means it is above the mean, and a negative Z-score means it is below the mean.

The Z-score formula is: Z = (x − μ) / σ, where x is the raw data point, μ is the population mean, and σ is the population standard deviation. The result expresses the distance from the mean in units of standard deviation.

A Z-score of 1.0 means the data point is exactly one standard deviation above the population mean. This corresponds roughly to the 84th percentile, meaning about 84% of the population scores below that value.

Yes. A negative Z-score simply means the data point falls below the population mean. For example, a Z-score of −1.5 means the value is 1.5 standard deviations below the mean.

There is no universally 'good' Z-score — it depends on context. In many applications, Z-scores between −2 and +2 are considered typical (covering ~95% of the population). Values beyond ±2 or ±3 are often flagged as unusual or extreme outliers.

The percentile rank is derived from the cumulative distribution function (CDF) of the standard normal distribution applied to the Z-score. It tells you the percentage of the population that falls at or below the given data point.

A population Z-score uses the population mean (μ) and population standard deviation (σ). A sample Z-score (or t-score for small samples) uses the sample mean and sample standard deviation. When the population parameters are known, use the Z-score formula directly.

The 'Probability Below' value (P < x) is the probability that a randomly selected member of the population has a value less than your data point. 'Probability Above' (P > x) is the complementary probability, equal to 1 minus P < x. Together they sum to 1.