IQ Percentile Calculator
Enter your IQ score to instantly see your percentile rank - the share of the population you scored higher than - plus your rarity as a "1 in X" figure. Switch to the reverse mode to find the IQ that corresponds to any target percentile. Supports both SD 15 (Wechsler, Stanford-Binet 5) and SD 16 (Cattell) test scales.
Formula
Worked example
An IQ of 120 on an SD 15 test: z = (120 - 100) / 15 = 1.333. Applying the normal CDF gives P(Z < 1.333) = 0.9088, so the 90.88th percentile. The top 9.12% of people score 120 or above, a rarity of about 1 in 11.
What is an IQ percentile?
An IQ score is a standardized measure of cognitive performance relative to a reference population. Because IQ is scaled so that the average is always 100, the raw number only gains meaning when compared to others. A percentile rank does exactly that: an IQ at the 90th percentile means the person scored higher than 90 percent of the population and lower than the top 10 percent. Percentiles make cross-test comparisons intuitive because they are on a 0 to 100 scale regardless of which test or scale was used.
How the calculation works
IQ scores follow a normal (bell-curve) distribution with a mean of 100. The standard deviation varies by test: 15 for the Wechsler scales (WAIS, WISC, WPPSI), the Stanford-Binet 5, and most modern tests; 16 for the older Cattell Culture Fair. The percentile is the cumulative distribution function (CDF) of the standard normal evaluated at the z-score z = (IQ - 100) / SD. The "1 in X" rarity figure is the reciprocal of the proportion scoring at or above that level, giving an intuitive sense of how uncommon a score is in the general population.
IQ classification systems
Different test publishers use different label bands. The Wechsler Adult Intelligence Scale (WAIS-IV) defines Average as 90-109 (25th-73rd percentile), High Average as 110-119 (75th-91st), Superior as 120-129 (91st-97th), and Very Superior as 130 or above (98th percentile and beyond). The Stanford-Binet Fifth Edition uses similar cut points but different label wording. All systems agree that the middle 50 percent of people (roughly IQ 90-110) fall within the Average band, and fewer than 2.3 percent score above 130 or below 70. The calculator above uses the Wechsler-derived labels as a widely accepted convention, but always refer to the specific classification guide for your test.
Limitations and measurement error
No IQ score is exact. Every standardized test has a standard error of measurement (SEM), typically 3-5 points for modern instruments, meaning a score of 115 represents a true score likely somewhere between 110 and 120. Score inflation over time (the Flynn Effect) means that an older test norm may overestimate your percentile relative to today's population. A single IQ test also captures a snapshot of one session: fatigue, anxiety, language barriers, and test familiarity all affect results. For high-stakes decisions - gifted program placement, disability accommodations, neuropsychological assessment - a comprehensive evaluation by a licensed psychologist is essential and no online calculator is a substitute.
IQ score to percentile chart
| IQ Score | Percentile | Rarity (1 in X) | Classification |
|---|---|---|---|
| 70 | 2.28% | ~1 in 44 | Borderline |
| 80 | 9.12% | ~1 in 11 | Low Average |
| 85 | 15.87% | ~1 in 6 | Low Average |
| 90 | 25.25% | ~1 in 4 | Average |
| 100 | 50.00% | ~1 in 2 | Average |
| 110 | 74.75% | ~1 in 4 | High Average |
| 115 | 84.13% | ~1 in 6 | High Average |
| 120 | 90.88% | ~1 in 11 | Superior |
| 125 | 95.22% | ~1 in 21 | Superior |
| 130 | 97.72% | ~1 in 44 | Very Superior |
| 135 | 99.07% | ~1 in 108 | Very Superior |
| 140 | 99.62% | ~1 in 261 | Gifted |
| 145 | 99.87% | ~1 in 741 | Highly Gifted |
| 160 | 99.997% | ~1 in 31,574 | Exceptionally Gifted |
Percentile ranks for common IQ scores using the standard SD 15 normal distribution (mean = 100). Rarity is the approximate "1 in X" for each score or above.
Frequently asked questions
What percentile is an IQ of 130?
An IQ of 130 on an SD 15 test falls at approximately the 97.72nd percentile, meaning about 97.7 percent of people score below 130. Only about 2.3 percent of the population score 130 or above, a rarity of roughly 1 in 44. On an SD 16 test the same score falls a little lower - around the 97.0th percentile.
What is the difference between SD 15 and SD 16?
Most modern tests, including the Wechsler scales and the Stanford-Binet 5, use a standard deviation of 15. The Cattell Culture Fair Intelligence Test uses SD 16. The same raw percentile corresponds to a slightly different IQ number depending on which scale you use. If you scored 145 on an SD 16 test, that is about the 99.85th percentile; on an SD 15 test a score of 145 corresponds to the 99.87th percentile. If you are unsure which scale your test uses, check the test manual or the score report.
Can I use this calculator to check if I qualify for Mensa?
Mensa International accepts members who score at or above the 98th percentile on a qualifying IQ or other standardized cognitive test. On an SD 15 scale this corresponds to an IQ of approximately 131. However, Mensa requires the test to have been administered by a licensed examiner using an approved instrument; online tests do not qualify. Use this calculator to estimate where your score falls, then check Mensa's list of accepted tests in your country.
Why does my percentile seem higher than I expected?
The normal distribution is not uniform: scores near the mean are densely packed, so a modest jump in IQ points translates to a big jump in percentile. Moving from IQ 100 (50th percentile) to IQ 115 covers the 50th to the 84th percentile - 34 percentage points from just one standard deviation. But moving from the 98th to the 99th percentile requires roughly IQ 131 to 137, a gap of 6 points for just one percentile. This compression at the tails makes very high or very low percentiles particularly sensitive to small score differences.
Is a high IQ percentile the same as being smart?
Not exactly. IQ tests primarily measure general cognitive ability - the capacity for reasoning, pattern recognition, and problem-solving under standardized conditions. They correlate strongly with academic achievement and many real-world outcomes, but they do not fully capture creativity, emotional intelligence, wisdom, or domain expertise. A very high percentile is a meaningful data point, but it is one part of a broader picture of human ability.
How do I convert a percentile back to an IQ score?
Switch the mode selector at the top of the calculator to "Percentile to IQ score" and enter your target percentile. The calculator applies the inverse of the normal CDF to find the z-score and then converts it back: IQ = 100 + z x SD. For example, the 95th percentile corresponds to z = 1.645, so IQ = 100 + 1.645 x 15 = 124.7.