Standard Score (Z-Score) Calculator

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

The formula is Z = (X − μ) / σ, where X is the raw score, μ (mu) is the population mean, and σ (sigma) is the standard deviation. For example, if your score is 75, the mean is 65, and the SD is 10, your Z-score is (75 − 65) / 10 = 1.0.

A Z-score of 1.0 means the raw score is exactly one standard deviation above the mean. In a normal distribution, this corresponds to approximately the 84th percentile — meaning the score is higher than about 84% of all scores.

A Z-score tells you how far a score is from the mean in standard deviation units, while a percentile tells you what percentage of the population scored at or below that value. They convey related but different information — a Z-score of 0 equals the 50th percentile.

Yes. A negative Z-score simply means the raw score is below the mean. For instance, a Z-score of −1.5 means the value is 1.5 standard deviations below the mean, placing it at approximately the 6.7th percentile.

Whether a Z-score is 'good' depends on context. In academic testing, higher is typically better. In medical screenings, scores far from 0 (in either direction) may indicate abnormality. Most values in a normal distribution fall between −3 and +3.

It represents the area under the normal distribution curve between two Z-score values — essentially the proportion of the population expected to fall within that range. For example, between Z = −1 and Z = 1 lies approximately 68.27% of all values.

Z-scores are most meaningful when the underlying data follows a normal (bell-curve) distribution. While you can compute a Z-score for any dataset, the probability and percentile interpretations rely on the assumption of normality to be accurate.