Complete IQ Percentile & Rarity Chart
Calculated Distribution for Wechsler (SD15) and Stanford-Binet (SD16).
| IQ Score | 15 SD %-ile | 15 SD Rarity | 16 SD %-ile | 16 SD Rarity |
|---|---|---|---|---|
| 180 | 99.99999% | 1 in 20,696,863 | 99.99997% | 1 in 3,483,046 |
| 175 | 99.99997% | 1 in 3,483,046 | 99.99986% | 1 in 722,337 |
| 170 | 99.99985% | 1 in 652,598 | 99.99939% | 1 in 164,571 |
| 165 | 99.99927% | 1 in 136,074 | 99.99757% | 1 in 41,174 |
| 160Extremely Rare | 99.99683% | 1 in 31,560 | 99.99116% | 1 in 11,307 |
| 159 | 99.99581% | 1 in 23,863 | 99.98867% | 1 in 8,829 |
| 158 | 99.99448% | 1 in 18,120 | 99.98555% | 1 in 6,920 |
| 157 | 99.99276% | 1 in 13,817 | 99.98163% | 1 in 5,443 |
| 156 | 99.99055% | 1 in 10,581 | 99.97673% | 1 in 4,298 |
| 155 | 99.98771% | 1 in 8,137 | 99.97064% | 1 in 3,406 |
| 154 | 99.98409% | 1 in 6,284 | 99.96309% | 1 in 2,709 |
| 153 | 99.97948% | 1 in 4,873 | 99.95376% | 1 in 2,163 |
| 152 | 99.97365% | 1 in 3,795 | 99.94229% | 1 in 1,733 |
| 151 | 99.96630% | 1 in 2,968 | 99.92824% | 1 in 1,394 |
| 150 | 99.95709% | 1 in 2,330 | 99.91109% | 1 in 1,125 |
| 149 | 99.94558% | 1 in 1,838 | 99.89024% | 1 in 911 |
| 148 | 99.93128% | 1 in 1,455 | 99.86500% | 1 in 741 |
| 147 | 99.91358% | 1 in 1,157 | 99.83456% | 1 in 604 |
| 146 | 99.89176% | 1 in 924 | 99.79798% | 1 in 495 |
| 145Genius Level | 99.86500% | 1 in 741 | 99.75420% | 1 in 407 |
| 144 | 99.83232% | 1 in 596 | 99.70202% | 1 in 336 |
| 143 | 99.79258% | 1 in 482 | 99.64005% | 1 in 278 |
| 142 | 99.74448% | 1 in 391 | 99.56675% | 1 in 231 |
| 141 | 99.68651% | 1 in 319 | 99.48039% | 1 in 192 |
| 140 | 99.61696% | 1 in 261 | 99.37903% | 1 in 161 |
| 139 | 99.53388% | 1 in 215 | 99.26054% | 1 in 135 |
| 138 | 99.43508% | 1 in 177 | 99.12255% | 1 in 114 |
| 137 | 99.31811% | 1 in 147 | 98.96250% | 1 in 96 |
| 136 | 99.18025% | 1 in 122 | 98.77756% | 1 in 82 |
| 135 | 99.01847% | 1 in 102 | 98.56470% | 1 in 70 |
| 134 | 98.82947% | 1 in 85 | 98.32068% | 1 in 60 |
| 133 | 98.60966% | 1 in 72 | 98.04200% | 1 in 51 |
| 132 | 98.35514% | 1 in 61 | 97.72499% | 1 in 44 |
| 131 | 98.06173% | 1 in 52 | 97.36579% | 1 in 38 |
| 130Very Superior | 97.72499% | 1 in 44 | 96.96037% | 1 in 33 |
| 129 | 97.34025% | 1 in 38 | 96.50456% | 1 in 29 |
| 128 | 96.90260% | 1 in 32 | 95.99409% | 1 in 25 |
| 127 | 96.40697% | 1 in 28 | 95.42464% | 1 in 22 |
| 126 | 95.84818% | 1 in 24 | 94.79187% | 1 in 19 |
| 125 | 95.22097% | 1 in 21 | 94.09149% | 1 in 17 |
| 124 | 94.52007% | 1 in 18 | 93.31928% | 1 in 15 |
| 123 | 93.74031% | 1 in 16 | 92.47120% | 1 in 13 |
| 122 | 92.87666% | 1 in 14 | 91.54342% | 1 in 12 |
| 121 | 91.92433% | 1 in 12 | 90.53242% | 1 in 11 |
| 120 | 90.87887% | 1 in 11 | 89.43502% | 1 in 9.5 |
| 119 | 89.73627% | 1 in 10 | 88.24847% | 1 in 8.5 |
| 118 | 88.49303% | 1 in 8.7 | 86.97054% | 1 in 7.7 |
| 117 | 87.14628% | 1 in 7.8 | 85.59956% | 1 in 6.9 |
| 116 | 85.69388% | 1 in 7.0 | 84.13447% | 1 in 6.3 |
| 115High Average | 84.13447% | 1 in 6.3 | 82.57493% | 1 in 5.7 |
| 114 | 82.46761% | 1 in 5.7 | 80.92131% | 1 in 5.2 |
| 113 | 80.69377% | 1 in 5.2 | 79.17477% | 1 in 4.8 |
| 112 | 78.81447% | 1 in 4.7 | 77.33727% | 1 in 4.4 |
| 111 | 76.83225% | 1 in 4.3 | 75.41162% | 1 in 4.1 |
| 110 | 74.75075% | 1 in 4.0 | 73.40145% | 1 in 3.8 |
| 109 | 72.57469% | 1 in 3.6 | 71.31123% | 1 in 3.5 |
| 108 | 70.30986% | 1 in 3.4 | 69.14625% | 1 in 3.2 |
| 107 | 67.96308% | 1 in 3.1 | 66.91256% | 1 in 3.0 |
| 106 | 65.54217% | 1 in 2.9 | 64.61697% | 1 in 2.8 |
| 105 | 63.05586% | 1 in 2.7 | 62.26697% | 1 in 2.7 |
| 104 | 60.51370% | 1 in 2.5 | 59.87063% | 1 in 2.5 |
| 103 | 57.92597% | 1 in 2.4 | 57.43657% | 1 in 2.3 |
| 102 | 55.30352% | 1 in 2.2 | 54.97383% | 1 in 2.2 |
| 101 | 52.65765% | 1 in 2.1 | 52.49177% | 1 in 2.1 |
| 100Average (Mean) | 50.00000% | 1 in 2.0 | 50.00000% | 1 in 2.0 |
| 99 | 47.34235% | 1 in 2.1 | 47.50823% | 1 in 2.1 |
| 98 | 44.69648% | 1 in 2.2 | 45.02617% | 1 in 2.2 |
| 97 | 42.07403% | 1 in 2.4 | 42.56343% | 1 in 2.3 |
| 96 | 39.48630% | 1 in 2.5 | 40.12937% | 1 in 2.5 |
| 95 | 36.94414% | 1 in 2.7 | 37.73303% | 1 in 2.7 |
| 94 | 34.45783% | 1 in 2.9 | 35.38303% | 1 in 2.8 |
| 93 | 32.03692% | 1 in 3.1 | 33.08744% | 1 in 3.0 |
| 92 | 29.69014% | 1 in 3.4 | 30.85375% | 1 in 3.2 |
| 91 | 27.42531% | 1 in 3.6 | 28.68877% | 1 in 3.5 |
| 90 | 25.24925% | 1 in 4.0 | 26.59855% | 1 in 3.8 |
| 89 | 23.16775% | 1 in 4.3 | 24.58838% | 1 in 4.1 |
| 88 | 21.18553% | 1 in 4.7 | 22.66273% | 1 in 4.4 |
| 87 | 19.30623% | 1 in 5.2 | 20.82523% | 1 in 4.8 |
| 86 | 17.53239% | 1 in 5.7 | 19.07869% | 1 in 5.2 |
| 85Lower Average | 15.86553% | 1 in 6.3 | 17.42507% | 1 in 5.7 |
| 84 | 14.30612% | 1 in 7.0 | 15.86553% | 1 in 6.3 |
| 83 | 12.85372% | 1 in 7.8 | 14.40044% | 1 in 6.9 |
| 82 | 11.50697% | 1 in 8.7 | 13.02946% | 1 in 7.7 |
| 81 | 10.26373% | 1 in 9.7 | 11.75153% | 1 in 8.5 |
| 80 | 9.12113% | 1 in 11 | 10.56498% | 1 in 9.5 |
| 79 | 8.07567% | 1 in 12 | 9.46758% | 1 in 11 |
| 78 | 7.12334% | 1 in 14 | 8.45658% | 1 in 12 |
| 77 | 6.25969% | 1 in 16 | 7.52880% | 1 in 13 |
| 76 | 5.47993% | 1 in 18 | 6.68072% | 1 in 15 |
| 75 | 4.77903% | 1 in 21 | 5.90851% | 1 in 17 |
| 74 | 4.15182% | 1 in 24 | 5.20813% | 1 in 19 |
| 73 | 3.59303% | 1 in 28 | 4.57536% | 1 in 22 |
| 72 | 3.09740% | 1 in 32 | 4.00591% | 1 in 25 |
| 71 | 2.65975% | 1 in 38 | 3.49544% | 1 in 29 |
| 70Borderline | 2.27501% | 1 in 44 | 3.03963% | 1 in 33 |
| 65 | 0.98153% | 1 in 102 | 1.43530% | 1 in 70 |
| 60 | 0.38304% | 1 in 261 | 0.62097% | 1 in 161 |
| 55 | 0.13500% | 1 in 741 | 0.24580% | 1 in 407 |
| 50 | 0.04291% | 1 in 2,330 | 0.08891% | 1 in 1,125 |
| 45 | 0.01229% | 1 in 8,137 | 0.02936% | 1 in 3,406 |
| 40 | 0.00317% | 1 in 31,560 | 0.00884% | 1 in 11,307 |
Understanding the IQ Distribution Data
The chart above provides a detailed breakdown of Standard Deviations (SD), which are the primary method psychologists use to determine how rare an intelligence score is. An IQ score is not a linear measurement; it is a ranking within the general population based on the Gaussian Normal Distribution (bell curve).
Wechsler (SD 15) vs. Stanford-Binet (SD 16)
It is critical to know which test you took. The Wechsler Adult Intelligence Scale (WAIS) and WISC use a Standard Deviation of 15. The older Stanford-Binet editions (and some high-IQ society admissions) utilize an SD of 16. As you can see in the chart, an IQ of 145 on a Wechsler test is "rarer" than a 145 on a Stanford-Binet test because the curve is tighter.
What do the Percentiles Mean?
The percentile indicates the percentage of the population that scores lower than you. For example, an IQ of 130 (SD 15) is in the 98th percentile. This means that if you are in a room with 100 randomly selected people, you would statistically have a higher IQ than 98 of them.
Rarity (1 in X)
Rarity converts the percentile into a tangible number. If your rarity is "1 in 50," it means that, statistically, you are the highest scorer in a typical bus full of people. If your rarity is "1 in 30,000," you would be the highest scorer in a full sports stadium.
The values presented in this table were calculated using the Standard Normal Cumulative Distribution Function (CDF).If you would like to calculcate yourself, you can use the following forumla.
Formula: $P(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{z} e^{-t^2/2} dt$, where $z = \frac{x - 100}{\sigma}$.
