Thirteen rulers stacked on the same bell curve
Each ruler spans −3.5 to +3.5 standard deviations. Ticks show what −3 … +3 SD reads on that scale. The vertical line is your rank; slide any ruler's score above to move it.
Exact rows are linear rescales of one normal curve: value = mean + z × SD (stanines round 2z + 5 and clip at 1 and 9). Matched rows use approximate published means and SDs for each test's own takers; their ticks are only as good as those figures (see references).
Three kinds of "conversion", only one of them exact
Exact rescale
Same test, same norm group, different units. Change the mean and SD and nothing is lost except rounding.
Rank match
Different tests, different people. We line up equal rarity using each test's own takers, which assumes the groups are comparable. They are not quite.
Not convertible
Some numbers cannot be put on the curve at all, or need a correction first.
Same rank is not the score you would actually get
A rank match answers "what is as rare on the SAT as my IQ is among everyone?" It does not predict your SAT. Two tests that correlate at r share a lot, but not all: on average, someone 2.0 SD from the mean on one lands only r × 2.0 SD out on the other, and individuals scatter widely around that.
Frey and Detterman (2004) found SAT scores correlated about .82 with a general factor from the ASVAB; Koenig, Frey and Detterman (2008) reported about .77 for the ACT. Correlations for the GRE, Wonderlic and AFQT below are set to illustrative values; move the slider to test your own assumption.
Your input sits at z = 2.00. With r = 0.82, the average SAT total for people at that rank is z = 1.64: closer to the middle. This is regression to the mean, and it is why rank-matched tables flatter high scorers and undersell low ones.
Each conversion, with its formula and its weak spot
z = (IQ − 100) / 15Exact for any SD-15 test. Use SD 16 or 24 if your report says so.T = 50 + 10zExact; T-scores are common on memory and personality scales, so check what the T measures.stanine = round(2z + 5), 1–9Bands are coarse: 127 and 145 both read stanine 9.scaled = 10 + 3zOne subtest is not a full-scale IQ; composites are normed separately.SAT ≈ 1028 + 200zSAT takers are a selected group, and the 2016 and 2024 redesigns changed the scale.ACT ≈ 19.5 + 5.9zCeiling of 36 compresses the top; state-mandated testing shifts the mean year to year.V+Q ≈ 309 + 15.6zGRE takers are graduates, well above the general average; the match is rank among them.W ≈ 21 + 7.5z12-minute speeded test; widely quoted 'W × 2 + 60' rules are folk shortcuts.AFQT = percentile vs 1997 youthAFQT is already a percentile, but against a 1997 sample of young adults.- Frey, M. C., & Detterman, D. K. (2004). Scholastic Assessment or g? The relationship between the Scholastic Assessment Test and general cognitive ability. Psychological Science, 15(6), 373–378.
- Koenig, K. A., Frey, M. C., & Detterman, D. K. (2008). ACT and general cognitive ability. Intelligence, 36(2), 153–160.
- College Board (2023). SAT Suite of Assessments Annual Report: Total Group. Mean total score used here: 1028.
- ACT, Inc. (2023). The ACT Profile Report: National, Graduating Class 2023. Mean composite used here: 19.5.
- ETS. GRE General Test Interpretive Data (Guide to the Use of Scores). Verbal and Quantitative means and SDs, combined here approximately.
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson. Index scores mean 100 / SD 15; subtest scaled scores mean 10 / SD 3.
- Flynn, J. R. (1987). Massive IQ gains in 14 nations: What IQ tests really measure. Psychological Bulletin, 101(2), 171–191.