Calculated Distribution for Wechsler (SD15) and Stanford-Binet (SD16). Need to find your baseline? Take our free IQ test online to get your instant score.
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.
Methodology:
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 $z = \frac{x - 100}{\sigma}$.
