What a z-score tells you
A z-score, or standard score, rewrites a value in terms of standard deviations from the mean. A z of 0 sits exactly at the mean; +1.5 is one-and-a-half standard deviations above it; −2 is two below. Because it strips out the original units, you can compare values from completely different scales — a maths mark against an English mark, for instance.
Z-score and percentile
If the data is roughly normally distributed, the z-score maps to a percentile. This tool estimates the area below the z-score using the standard normal distribution, so a z of about +1.28 lands near the 90th percentile.
Frequently asked questions
Can a z-score be negative?
Yes. A negative z-score simply means the value is below the mean; a positive one means it's above.
Why is the percentile only an estimate?
The percentile assumes a normal (bell-shaped) distribution. If your data is heavily skewed, treat it as an approximation.
What if the standard deviation is zero?
A z-score can't be computed when σ is 0, because every value equals the mean and there's no spread to divide by.