These are IQs, their percentiles, and rarity on a 15 SD (e.g. Wechsler) and 16 SD (e.g. Stanford-Binet) scale. They were calculated using the NORMDIST function in Excel. The number of decimal places for the rarity was varied in the hope it might be useful. You can see why presently nobody should be able to get a deviation IQ higher than 195 (or 201 on the 16 SD scale). There are not enough people in the world to ‘beat’. Note that rarities given are of people that have a certain IQ or higher. Some people might find it more useful to know the rarity of people that have a certain IQ or lower. In that case use this example as a guide: If you want to know how many people have IQs of 84 or lower, look at the rarity of people that have an IQ of 116 or higher. (100–84 = 16. 100 + 16 = 116).
The IQ scale — how to interpret an IQ score
IQ tests are designed and updated on a regular basis such that they correspond to the populations they measure in a precise way: a score of 100 is the average score of the population and the distribution of IQ scores has a normal shape with a standard deviation of 15. Therefore, the IQ score is convenient to interpret and work with if you are a statistician, but if you are not into statistics the number itself will likely mean little to you. This is where our IQ percentile calculator can assist you in computing both the percentile of the population you are in and, correspondingly, the rarity of your score.
For example, with an IQ of 125 you will be in the top 5% and only 1 in 20 people selected at random from a large population will have a score equal to or higher than yours. The IQ scale below shows what percentage of the population falls within different ranges of IQ scores, for example 13.6% of people have an IQ score between 115 and 130, by definition.