IQ Standard Deviation Calculator
Calculate how many standard deviations your IQ score is from the mean and see your exact position on the bell curve. This free tool converts any IQ score to its z-score, percentile rank, and population rarity using the Wechsler (SD = 15) or Cattell (SD = 24) scale.
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Used by WAIS-IV, WISC-V: the most widely administered IQ tests worldwide
Using the Wechsler scale (mean = 100, SD = 15)
Standard Deviation Reference Table
| SD | Wechsler IQ | Cattell IQ |
|---|---|---|
| -3σ | 55 | 28 |
| -2σ | 70 | 52 |
| -1σ | 85 | 76 |
| Mean | 100 | 100 |
| +1σ | 115 | 124 |
| +2σ | 130 | 148 |
| +3σ | 145 | 172 |
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What Is Standard Deviation in IQ Testing?
Standard deviation (SD) is a statistical measure of how spread out values are from the average. In IQ testing, the mean is set at 100, and the standard deviation determines how scores are distributed around that average. A score exactly one SD above the mean falls at the 84th percentile, while one SD below falls at the 16th percentile.
The concept is central to understanding how IQ scores are interpreted. Without knowing the standard deviation of the scale used, an IQ score alone is incomplete information. A score of 130 means something very different on the Wechsler scale (2 SD above the mean, 98th percentile) than it would on a hypothetical scale with SD = 10 (3 SD above, 99.87th percentile).
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The Normal Distribution and IQ
IQ scores are designed to follow a normal (Gaussian) distribution, commonly known as the bell curve. This symmetrical shape means:
- 68.2% of people score within ±1 SD of the mean
- 95.4% score within ±2 SD
- 99.7% score within ±3 SD
This is known as the 68-95-99.7 rule (or the empirical rule). On the Wechsler scale, ±1 SD covers IQ 85–115, ±2 SD covers 70–130, and ±3 SD covers 55–145. Scores beyond ±3 SD are extremely rare, occurring in fewer than 0.3% of the population.
Wechsler vs. Cattell Scales
The two most common IQ scales differ in their standard deviation:
- Wechsler (SD = 15): Used by the WAIS-IV, WISC-V, and most modern IQ tests. This is the most widely used scale worldwide.
- Cattell (SD = 24): Used by the Culture Fair Intelligence Test (CFIT) and some Cattell-Horn-Carroll based assessments. Produces more spread-out scores.
Because the Cattell scale has a wider SD, the same raw cognitive ability produces a higher number on the Cattell scale than on the Wechsler scale. For example, someone at the 98th percentile would score 130 on Wechsler but 148 on Cattell. Both represent exactly 2 standard deviations above the mean.
Common IQ Standard Deviation Benchmarks
Here are the key standard deviation boundaries and what they mean:
- ±1 SD: IQ 85–115 (Wechsler). Average range, 68% of the population
- ±2 SD: IQ 70–130 (Wechsler). 95% of the population falls here
- +2 SD (IQ 130+): Gifted threshold, top 2.3%
- +3 SD (IQ 145+): Profoundly gifted, top 0.13%
- -2 SD (IQ 70): Threshold for intellectual disability assessment
For a complete percentile reference, see our full IQ percentile table or convert any score using our IQ Percentile Calculator. To translate between different IQ scales (Wechsler, Cattell, Stanford-Binet), use the IQ Score Converter. To see how these ranges map to real careers, explore our IQ by Profession tool, or check what any score means in plain language with the IQ Score Meaning tool.
Frequently Asked Questions
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This calculator shows where a score sits on the bell curve. Take the free 15-minute test to place your own.