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IQ scale converter
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The short answer
The same standing prints as a different number on each IQ scale. Two standard deviations above average is 130 on an SD 15 scale (Wechsler, Stanford-Binet 5), 132 on SD 16 (the 1960 Stanford-Binet, CogAT) and 148 on SD 24, the spread American Mensa's Cattell cutoff implies. To convert, keep the z score: (IQ − 100) ÷ SD.
Converter · same standing, three scales
Range 40 to 175.
| SD 15 | 130 |
|---|---|
| SD 16 | 132 |
| SD 24 | 148 |
| Percentile | 97.7 |
| z score | 2.00 |
Same standing on every scale: SD 15 130, SD 16 132, SD 24 148, Percentile 97.7, z score 2.00.
Want a number of your own to convert? The IQ Octopus test reports an estimated IQ on the SD 15 scale.
Which tests use which scale
Every modern deviation IQ has a mean of 100. What differs is the standard deviation, the size of one step away from average. Here is what we can document for each spread, and how firmly.
| SD | Tests | How we know |
|---|---|---|
| 15 | Wechsler scales (WAIS, WISC, WPPSI), Stanford-Binet Fifth Edition | Stated by the publishers: mean 100, SD 15. (Wechsler, 2008)(PRO-ED: SB5) |
| 16 | 1960 Stanford-Binet (Form L-M), CogAT SAS, NNAT3 NAI | Stated by Roid (2004) for Form L-M, by Riverside for the CogAT and by Pearson for the NNAT3. (Roid, 2004)(Riverside: CogAT score descriptions)(Pearson: NNAT3) |
| 24 | Cattell (as listed by American Mensa) | Implied, not published: American Mensa's Cattell cutoff of 148 sits two SDs above 100 only if the SD is 24. (American Mensa: qualifying scores) |
The SD 24 row is the weakest link: it is inferred from a cutoff, not printed in a manual we could read. We label it that way in the converter.
The conversion table
Each row is one standing. Read across to see the number it prints on each scale; the percentile is the same on all three because it is computed from the z score (NIST/SEMATECH e-Handbook, normal data).
| SD 15 | SD 16 | SD 24 | Percentile |
|---|---|---|---|
| 115 | 116 | 124 | 84.1 |
| 120 | 121 | 132 | 90.9 |
| 125 | 127 | 140 | 95.2 |
| 130 | 132 | 148 | 97.7 |
| 135 | 137 | 156 | 99 |
| 140 | 143 | 164 | 99.6 |
| 145 | 148 | 172 | 99.9 |
The method
A deviation IQ is a z score in disguise. Wechsler built his tables from each age group's mean and standard deviation, so an IQ says how far you sit from people your own age (Wechsler, 1944). Converting is two steps: z = (IQ − 100) ÷ SD on the old scale, then 100 + z × SD on the new one. A 132 on SD 16 is z = 2.0, which is 130 on SD 15 and 148 on SD 24.
That arithmetic is why American Mensa can list 130 on the Stanford-Binet 5, 132 on the older Stanford-Binet and 148 on the Cattell as one threshold (American Mensa: qualifying scores). To check a score against those cutoffs directly, use the Mensa qualifying score checker. If you have a percentile instead of a score, the percentile to IQ converter starts from there.
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Sources
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.
- Wechsler, D. (1944). The Measurement of Adult Intelligence, 3rd ed. Williams & Wilkins (first edition April 1939). Internet Archive scan. archive.org/details/in.ernet.dli.2015.58005
- Roid, G. H. Stanford-Binet Intelligence Scales, Fifth Edition (SB5), PRO-ED product page. 2003. proedinc.com/products-13290.html
- Roid, G. H. (2004). Essentials of Stanford-Binet Intelligence Scales (SB5) Assessment. Wiley. Chapter 1, Overview of the SB5 and its history (publisher excerpt). catalogimages.wiley.com/images/db/pdf/0471224049.excerpt.pdf
- Riverside Insights DataManager help. CogAT score descriptions. info.riversideinsights.com/datamanager-onlinehelp/cogat-score-descriptions
- Pearson. Naglieri Nonverbal Ability Test, Third Edition (NNAT3), product page. www.pearsonassessments.com/store/en/usd/p/100001822.html
- American Mensa. Qualifying test scores. www.us.mensa.org/join/testscores/qualifying-test-scores/
- NIST/SEMATECH e-Handbook of Statistical Methods, section 6.5.1, "What do we mean by Normal data?" National Institute of Standards and Technology. www.itl.nist.gov/div898/handbook/pmc/section5/pmc51.htm