Z-Score Calculator
Calculate a z-score from a value, mean and standard deviation, or from a pasted data set, with percentile, tail areas and two-tailed p-value.
A z-score tells you how many standard deviations a value lies above or below the mean. It puts scores from different tests, scales or units on the same footing, and with a normal distribution it converts straight into a percentile. Type a value with its mean and standard deviation, or paste a whole data set to standardise every value at once.
How to use this tool
- Enter the value you want to standardise.
- Enter the mean and standard deviation, or paste your raw data instead.
- For pasted data, choose sample SD (most data) or population SD (the complete group).
- Read the z-score, the percentile and the tail areas.
Formula
z = (x − μ) / σ
x is the value, μ the mean and σ the standard deviation. With sample data use x̄ and s in their place. The percentile is Φ(z), the area under the standard normal curve to the left of z; the right tail is 1 − Φ(z) and the two-tailed p-value is 2 × min(Φ(z), 1 − Φ(z)).
Example
An exam has a mean of 70 and a standard deviation of 10, and you scored 85. Then z = (85 − 70) / 10 = 1.5. From the normal curve, Φ(1.5) ≈ 0.9332, so the score sits at about the 93.32nd percentile: roughly 6.68% of test-takers scored higher, and the two-tailed p-value is 0.1336.
Frequently asked questions
What does a negative z-score mean?
The value is below the mean. A z-score of -1 is one standard deviation below average, which is about the 15.87th percentile in a normal distribution.
What is a good z-score?
It depends on the context. About 68% of normal data lies between -1 and 1, 95% between -1.96 and 1.96, and 99.7% between -3 and 3, so values beyond ±2 or ±3 are usually treated as unusual.
Should I use sample or population standard deviation?
Use the sample version (n − 1) when your numbers are a sample from a bigger group, which is the usual case. Use the population version only when the data covers everyone you care about.
Is the percentile valid for any data?
The z-score itself is valid for any data, but turning it into a percentile assumes a roughly normal (bell-shaped) distribution.
Last updated: 2026-10-30