Enter a Z-score, a percentile or a T-score and instantly get all five: Z, percentile, T, IQ and stanine. Free, for psychometrics and norms.
A Z-score tells you how many standard deviations a person is from the mean of their reference group: Z = (X − M) / SD. Z = 0 is exactly the mean; Z = 1.5 is one and a half standard deviations above it; Z = −2 is two below. It lets you compare scores from tests on different scales (a memory test scored 0 to 30 and an anxiety scale scored 20 to 80) and place someone within the norms of their population.
| Z | Percentile | T (M = 50, SD = 10) | IQ (M = 100, SD = 15) | Stanine |
|---|---|---|---|---|
| -2.0 | 2.3 | 30 | 70 | 1 |
| -1.5 | 6.7 | 35 | 78 | 2 |
| -1.0 | 15.9 | 40 | 85 | 3 |
| -0.5 | 30.9 | 45 | 93 | 4 |
| 0.0 | 50.0 | 50 | 100 | 5 |
| 0.5 | 69.1 | 55 | 108 | 6 |
| 1.0 | 84.1 | 60 | 115 | 7 |
| 1.5 | 93.3 | 65 | 123 | 8 |
| 2.0 | 97.7 | 70 | 130 | 9 |
Percentile = Φ(Z)·100; T = 50 + 10·Z; IQ = 100 + 15·Z; stanine = round(2·Z + 5), between 1 and 9. All of them assume a normal distribution.
The 84th percentile does not mean "got 84% of the questions right": it means the score is higher than that of 84% of the norm group. And the Z-to-percentile conversion is only exact when scores are normally distributed in that group. On strongly skewed clinical scales (depressive symptoms in the general population, where almost everyone scores low), the theoretical normal percentile and the real percentile of the norms can differ a lot. There the empirical percentile from the test manual wins, or the one you compute from your own data with the norms table generator.
The T-score in this tool is the usual scale of psychological norms: mean 50 and standard deviation 10 (T = 50 + 10·Z). Many clinical inventories use it so that all their scales read the same way. It has nothing to do with the t statistic of a hypothesis test, even though they share the letter: if what you need is a critical value of t, it is in the t, z, chi-square and F tables.
On an attention test with a norm mean of 50 and a standard deviation of 8, a person scores 62. Their Z-score is (62 − 50) / 8 = 1.5. With the converter: 93.3rd percentile, T = 65, IQ-scale equivalent 123 and stanine 8. In a report you could write "the attention score (Z = 1.50) falls at the 93rd percentile of the norms".
Yes: choose "Percentile" and enter a value between 0 and 100, excluding the ends. The tool uses the inverse of the normal distribution (probit) and returns all five equivalents.
A nine-band scale, from 1 to 9, with mean 5 and standard deviation 2, designed to report results as whole numbers: 1 to 3 below average, 4 to 6 average, 7 to 9 above average.
Because above Z ≈ 3.3 the theoretical percentile, rounded to one decimal, would read 100, and nobody scores above 100% of a population. The tool says it is above 99.9 instead of rounding to an impossible value.
If you use it in your thesis or in a paper, cite it so that readers of your Methods section know how the calculation was done.
Ciudad-Fernández, V. (2026). Z-score, percentile and T-score converter [Web application]. Ciudad Science. Retrieved October 18, 2026, from https://analisisdedatospsicologia.com/en/tools/z-score-converter
For your Methods section: Z-scores were converted into percentiles, T-scores and stanines, assuming a normal distribution, with the Ciudad Science Z-score, percentile and T-score converter (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026conversorz,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{Z-score, percentile and T-score converter}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/tools/z-score-converter},
urldate = {2026-10-18},
note = {Accessed 2026-10-18},
}