Percentile, NCE, Stanine, T-Score & Standard Score Converter
Convert between the score scales used on standardised tests: percentile rank, normal curve equivalent (NCE), stanine, z-score, T-score (mean 50, SD 10), deviation IQ / standard score (mean 100, SD 15) and scaled score (mean 10, SD 3), with descriptive categories and the caveats about averaging percentiles.
How it works
z = Φ⁻¹(percentile ÷ 100); NCE = 50 + 21.06z; T = 50 + 10z; standard score = 100 + 15z; scaled = 10 + 3z; stanine = round(2z + 5) clipped to 1–9
Standardised tests report the same underlying position in the norm group on several scales, all derived from the normal curve. Percentile ranks are easiest to explain but are not equal-interval — the gap between the 50th and 60th percentiles is a quarter of a standard deviation, between the 90th and 99th nearly a full one — so they cannot be averaged or subtracted; normal curve equivalents were invented for federal programme evaluation to fix exactly that, matching percentiles at 1, 50 and 99 but spaced evenly between. T-scores, deviation IQs (mean 100, SD 15), scaled subtest scores (mean 10, SD 3) and the nine-band stanine are linear transformations of z, differing only in their convenient means and spreads, and each test manual attaches descriptive labels to ranges of them.
Worked example
A percentile rank of 84 is one standard deviation above the mean: z = 1.0, NCE 71, T-score 60, standard score 115 (high average), scaled score 13, stanine 7 (above average). A percentile of 98 — only 14 points higher — is z = 2.05, standard score 131, stanine 9.
Frequently asked questions
Why did my child's percentile change a lot when the standard score barely moved?
Near the mean, one standard-score point is about 2.5 percentile points; a move from 100 to 105 is the 50th to the 63rd percentile. In the tails the reverse holds. Judge change in standard scores or NCEs.
What is a grade-equivalent score?
The grade level at which the median student earns that raw score — not the grade at which the child can work. A 3rd grader with a GE of 5.2 scored as the average 5th grader would on 3rd-grade material. Use percentiles or standard scores for placement.
Related calculators
Classical test theory formulas as taught in educational measurement courses (Crocker & Algina, AERA/APA/NCME Standards). They describe a test's statistics for one group of examinees; interpret scores with the test publisher's norms and a qualified educator or psychologist.