Why IQ scores aren’t all on the same scale
Every modern IQ score is a deviation IQ: it tells you where you sit on a bell curve relative to your age group, expressed as a number centred on 100. But the spread of that bell curve — the standard deviation — was never standardised across all tests, and that’s where the confusion starts.
- SD 15 — the modern standard. The Wechsler scales (WAIS, WISC), the current Stanford–Binet (SB5), and essentially every online test use this. When people say “IQ 130 is the top 2%,” they mean SD 15.
- SD 16 — the old Stanford–Binet. The Form L-M Stanford–Binet (Terman & Merrill, 1960) used a slightly wider scale. A “132” on that test is the same rarity as a “130” on a Wechsler.
- SD 24 — Cattell. Cattell’s Culture Fair tests use a much wider scale. A score of 148 on a Cattell test is about the 98th percentile — the same place a 130 sits on the standard scale. This is why “my IQ is 148” so often turns out to mean “130, on an unusual scale.”
The SD-15 vs SD-16 vs SD-24 problem (the “148” story)
Two people can both be at the 98th percentile and walk away with the numbers 130, 133, and 149 — identical rarity, three very different-sounding scores. None is “wrong”; they’re measured against differently-sized rulers. The only fair way to compare scores from different tests is to convert them to a common scale or, better, to a percentile — which is exactly what this tool does.
Percentile and rarity
The percentile is the share of people who score at or below your point on the curve; the rarity (“1 in N”) is just the other side of that — how many people you’d need to gather before you’d expect one to match or beat your score. A few familiar landmarks on the standard SD-15 scale:
| IQ (SD 15) | Percentile | Rarity |
|---|---|---|
| 100 | 50th | 1 in 2 |
| 115 | ~84th | ~1 in 6 |
| 120 | ~91st | ~1 in 11 |
| 130 | ~98th | ~1 in 44 |
| 145 | ~99.9th | ~1 in 740 |
| 160 | ~99.997th | ~1 in 31,000 |
Beyond about 145 these figures should be read as “extremely rare” rather than literal counts — real test norms don’t have enough people in the tails for the numbers to be precise, and the underlying distribution stops being neatly normal.
How this converter works (and its limits)
It does one thing, exactly: it finds the percentile your score corresponds to on its own scale, then reads off the score that lands on the same percentile on each other scale. Mathematically that’s a z-score conversion through the normal distribution.
- It assumes the score is a deviation IQ centred on 100 with the standard deviation you select. Ratio IQs from very old tests don’t fit this model.
- It doesn’t adjust for norm year. Raw performance has drifted upward over decades (the Flynn effect), so a 1960 score and a 2020 score on the same scale aren’t strictly equivalent even though the numbers match.
- It doesn’t show measurement error. Any single test result carries a band of roughly ±5 points; treat the converted numbers the same way.
- It’s a converter, not a test. It can’t tell you your IQ — only what a given number would be on another scale.
If you want an actual score — on the standard SD-15 scale, with a domain-by-domain breakdown — take the full IQ test. For more on what the bands mean, see IQ classification ranges, and on what the number does and doesn’t predict, what your IQ score actually means.
References
- Wechsler, D. (2008/2014). WAIS-IV / WISC-V Technical and Interpretive Manuals. Pearson. (Mean 100, SD 15.)
- Terman, L. M., & Merrill, M. A. (1960). Stanford–Binet Intelligence Scale: Manual for the Third Revision, Form L-M. Houghton Mifflin. (SD 16.)
- Cattell, R. B., & Cattell, A. K. S. (1973). Measuring Intelligence with the Culture Fair Tests. IPAT. (SD 24.)
- Wechsler, D. (1939). The Measurement of Adult Intelligence. Williams & Wilkins. (Introduced the deviation IQ.)