Z-Score Calculator

A z-score measures how many standard deviations a value is from the mean. A percentile is the percentage of the distribution that falls below that value. They're directly linked for normally distributed data — a z-score of 0 is always the 50th percentile — but they measure different things: distance from centre versus rank within the distribution.

The z-score arithmetic (subtracting the mean, dividing by the standard deviation) is valid for any data. However, the percentile shown here specifically assumes the underlying distribution is approximately normal — for strongly skewed data, treat the percentile as an approximation, or use the data's actual empirical percentile instead.

Yes — use 'Z-score → Value' mode, entering the z-score that corresponds to your target percentile (for example, z ≈ 1.645 for the 95th percentile, or z ≈ 1.96 for the 97.5th percentile). Common percentile-to-z conversions are listed in any standard normal table.

A z-score is meaningless without both. The mean sets the reference point (zero on the z-scale); the standard deviation sets the scale (what one unit of 'z' represents). The same raw value can have a very different z-score depending on how spread out the surrounding population actually is.