What does an IQ of 158 mean?

The Very Superior band: 130 and above

Very Superior is the top label on the WAIS-IV scale (Wikipedia: IQ classification). It starts at 130, exactly two standard deviations above the mean, and has no upper limit. From the normal curve, about 2.5% of people score in it, so it covers roughly the top 2%.

Because the band is open at the top, the label hides big differences. A 131 is about 1 in 52 people; a 150 is about 1 in 2,300. 158 sits at about 1 in 18,000. Two people with the same label can be far apart on the curve, which is why the number and its range say more than the word.

Scores out here are also the hardest to pin down. Each extra point rests on a few of the hardest items, and every test has a ceiling: once you answer almost everything correctly, it has little left to separate you from people who scored higher. A careful report shows a wider confidence range at this level than near the middle.

Where 158 sits inside the band

158 is 28 points above the floor of the Very Superior band (130). Of the people who score in this band, about 100% score below 158, so it is near the top of the group that shares its label.

Clinical IQ scores carry measurement error of around plus or minus 5 points at 95% (Wechsler, 2008). A measured 158 is consistent with a true score anywhere from 153 to 163, which is the 99.98 to 99.999 percentile. That whole range stays inside the Very Superior band, so the label is the most stable part of the result. A short online test has a wider range than a clinical one, so read any single number as the middle of a span.

158 and the Mensa line

Mensa accepts people who score at or above the 98th percentile on an approved, supervised standardized test (Mensa International). On a scale with standard deviation 15 that is about 131; Mensa UK quotes 148 on Cattell III B and 132 on the Culture Fair test, both the 98th percentile on those scales (Mensa UK). 158 is 27 points above that line on such a test. An online estimate, including IQ Octopus, cannot be used to apply. See what IQ you need for Mensa.

What an IQ of 158 does and does not predict

A very high score means you reasoned quickly and accurately on hard, unfamiliar puzzles. It does not guarantee results in school or work, and plenty of people with lower scores outperform people with higher ones.

Across large groups, the links are real. General intelligence at age 11 correlated 0.81 with exam results at 16 in about 70,000 English children (Deary, Strand, Smith & Fernandes, 2007), a review of 85 years of workplace research put the link with job performance at 0.51 (Schmidt & Hunter, 1998), and a 2007 meta-analysis found correlations of about 0.56 with education and 0.23 with income (Strenze, 2007). Those describe tendencies across many people. None of them let anyone predict an individual life from one number. The guide to what IQ predicts explains what a correlation of that size means.

Same score, different tests

Older Stanford-Binet forms used a standard deviation of 16, and the Cattell Culture Fair III scale uses 24 (Wikipedia: IQ classification). The same percentile as 158 on a standard-deviation-15 test reads as about 162 on the first and 193 on the second, so check which scale a number is on before comparing scores from different tests.

Nearby scores

IQ 157 · IQ 159 · every score on the IQ chart · IQ percentile calculator · the seven classification bands