A z-score (standard score) measures how many standard deviations a value is above or below the mean of its distribution. A z-score of 0 is the mean; +1 is one standard deviation above; -1 is one below.

What is a percentile rank?

A percentile rank tells you what percentage of scores in a reference group fall at or below a given value. The 75th percentile means 75% of the group scored at or below that point.

How accurate is this conversion?

The tool uses a rational approximation of the inverse normal CDF accurate to about 5 significant figures — the same precision used in most statistics textbooks and software.

Does this only work for normally distributed data?

Yes. The z-score ↔ percentile relationship assumes a standard normal distribution. Real-world test scores may deviate slightly, but the standard normal is the accepted reference model for most standardized tests.

What z-score is the 99th percentile?

The 99th percentile corresponds to a z-score of approximately 2.326. The 95th percentile is about 1.645, and the 90th percentile is about 1.282.

Percentile To Z Score

Name: Percentile To Z Score
Availability: InStock
Author: Nham Vu

Convert any percentile rank to a z-score, or any z-score to a percentile rank, using the standard normal distribution.

Conversion Settings

Direction

Percentile Rank (0–100)

Enter a value between 0.001 and 99.999

Quick Examples

Standard Normal Distribution

z = −3z = −2z = −1 z = 0 z = +1z = +2z = +3

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Summary

Convert any percentile rank to a z-score, or any z-score to a percentile rank, using the standard normal distribution.

How it works

Choose a conversion direction: Percentile → Z-Score or Z-Score → Percentile.
Enter your value in the input field.
The tool applies the inverse standard normal CDF (for percentile → z) or the standard normal CDF (for z → percentile).
Results appear instantly with a visual marker on the bell curve.
Use the examples panel to explore common academic test benchmarks.

Use cases

Interpret SAT, ACT, GRE, or IQ test scores relative to a population.
Convert a class percentile rank to a z-score for statistical analysis.
Determine what percentile a given standard score falls in.
Compare scores across different standardized tests using z-scores.
Check where a data point sits within a normally distributed dataset.
Teach or study normal distribution concepts in statistics courses.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu