IQ Scale Chart: Normal Distribution and Score Conversions

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The standard IQ scale is defined by a normal Gaussian distribution with a mean of 100 and a standard deviation of 15 points. This comprehensive scale chart maps every score from 55 to 145 to its exact mathematical percentile, standard deviation z-score, and population rarity.

The normal distribution bell curve

In psychometrics, intelligence scores follow a bell curve where the highest density of scores occurs at the population center (100). Below is a vector representation of the standard deviation zones:

100 (Mean) 85 (-1σ) 115 (+1σ) 70 (-2σ) 130 (+2σ)
Gaussian Normal Distribution (Mean = 100, SD = 15)

Detailed conversion table (55 to 145)

IQ Score Standard Deviation (z) Exact Percentile Rarity Representation
145+3.00 SD99.87th percentile1 in 740 (Top 0.13%)
140+2.67 SD99.62nd percentile1 in 261 (Top 0.38%)
135+2.33 SD99.02nd percentile1 in 102 (Top 0.98%)
130+2.00 SD97.72nd percentile1 in 44 (Top 2.28% - Mensa)
125+1.67 SD95.22nd percentile1 in 21 (Top 4.78%)
120+1.33 SD90.88th percentile1 in 11 (Top 9.12%)
115+1.00 SD84.13th percentile1 in 6.3 (Top 15.87%)
110+0.67 SD74.75th percentile1 in 4.0 (Top 25.25%)
105+0.33 SD63.06th percentile1 in 2.7 (Top 36.94%)
1000.00 SD50.00th percentile1 in 2.0 (Exact Population Median)
95-0.33 SD36.94th percentileBottom 36.94%
90-0.67 SD25.25th percentileBottom 25.25%
85-1.00 SD15.87th percentileBottom 15.87%
80-1.33 SD9.12th percentileBottom 9.12%
75-1.67 SD4.78th percentileBottom 4.78%
70-2.00 SD2.28th percentileBottom 2.28%
65-2.33 SD0.98th percentileBottom 0.98%
60-2.67 SD0.38th percentileBottom 0.38%
55-3.00 SD0.13th percentileBottom 0.13%

How to calculate your exact percentile

If your score falls between the 5-point increments in this table, you can calculate the exact mathematical placement using our real-time interactive IQ percentile calculator, or read our overview of the high IQ genius range.

Frequently Asked Questions

Why is 100 always the center of the IQ scale?
Standardisation norming groups periodically recalibrate the raw score translations so that the mean of the representative general population is defined as 100.
What is the difference between SD 15 and SD 16?
Wechsler tests use SD 15 (where 130 is the 98th percentile). Older Stanford-Binet tests used SD 16 (where 132 is the 98th percentile). Both represent the same relative population standing.

🔗 Related Research & Cognitive Analyses

IQ Percentile Calculator & Normal Curve Convert any deviation IQ into exact population percentiles with interactive distribution. What is the Average IQ Score? Global normative baselines, the Flynn Effect, and population standard distributions. High IQ & Genius Score Criteria Mensa qualifying standards (130+) and cognitive characteristics of the top 2%. Historical Minds & Cognitive Matching Discover how Einstein, Da Vinci, Tesla, and Curie compare on cognitive trait scales. Pattern Recognition & Matrix Reasoning Understanding non-verbal fluid intelligence and spatial problem solving.

📚 Scientific References & Authoritative Citations

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