How to calculate z-score
z = (value − mean) ÷ standard deviation
Worked example. Z-score: 2.
Example inputs — Value: 130; Mean (average): 100; Standard deviation: 15. Starting values are illustrative.
About the 98th percentile (normal distribution)
From George Guju, founder of Calculyn · Educational calculator guidance, not professional advice.
How it works
A z-score says how many standard deviations a value is above or below the mean. On a normal curve, z = 0 is the 50th percentile, z = 1 is about the 84th, z = 2 about the 98th.
Assumptions & limitations
- Percentile assumes a normal distribution.
Formula and assumptions reviewed October 2026 by the Calculyn team. How we build our calculators
Frequently asked questions
Is a high z-score good?
It depends on context — high is great for test scores, but not necessarily for things like error rates.