Please enter a valid IQ score (40-200).
Most scores fall between 55 (0.1st pct) and 145 (99.9th pct)
Nearly all modern IQ tests use SD 15
💡 Population mean: IQ 100 = 50th percentile by definition. IQ 115 = 84th percentile. IQ 130 = 97.7th percentile.
IQ Percentile Rank
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⚠️ Disclaimer: IQ scores are statistical estimates with measurement error (typically ±5 points). This calculator uses the theoretical normal distribution. Actual test percentiles may vary slightly by test edition, norming sample, and year of administration. IQ is one measure of cognitive ability, not a comprehensive assessment of human potential.
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Sources & Methodology
Percentile calculations use the standard normal distribution CDF (mean 100, SD 15) as specified by the Wechsler Adult Intelligence Scale (WAIS) and Wechsler Intelligence Scale for Children (WISC).
Pearson — Wechsler Adult Intelligence Scale (WAIS)
Standard reference for mean 100, SD 15 IQ scoring and classification system used by most modern cognitive assessments
Khan Academy — Normal Distribution
Normal distribution CDF methodology used to convert z-scores to cumulative probabilities
Methodology: z-score = (IQ - 100) / SD. Percentile = CDF(z) x 100, where CDF is the standard normal cumulative distribution function approximated using the error function: CDF(z) = 0.5 x (1 + erf(z / sqrt(2))). erf approximated using Abramowitz and Stegun formula 7.1.26 with maximum error <1.5e-7. Rarity = 1 / (1 - percentile/100) if above average, or 1 / (percentile/100) if below average.
⏱ Last reviewed: April 2026
IQ Percentile Calculator — How It Works in 2026
IQ scores are designed to follow a normal distribution with a mean (average) of 100 and a standard deviation of 15 on most modern tests. This means about 68% of the population scores between 85 and 115 (within one standard deviation), about 95% score between 70 and 130 (within two SDs), and about 99.7% score between 55 and 145 (within three SDs). Converting a score to a percentile uses the normal distribution's cumulative distribution function.
The Formula
z = (IQ − 100) / 15
Percentile = CDF(z) × 100 | where CDF is the standard normal cumulative distribution function
Example: IQ 130 → z = (130-100)/15 = 2.0 → CDF(2.0) = 97.72nd percentile
Example: IQ 130 → z = (130-100)/15 = 2.0 → CDF(2.0) = 97.72nd percentile
IQ Score Reference Table (SD 15)
| IQ Score | z-score | Percentile | Rarity | Wechsler Classification |
|---|---|---|---|---|
| 70 | -2.00 | 2.3rd | 1 in 44 | Extremely Low |
| 85 | -1.00 | 15.9th | 1 in 6.3 | Low Average |
| 100 | 0.00 | 50.0th | Average | Average |
| 115 | +1.00 | 84.1st | 1 in 6.3 above | High Average |
| 120 | +1.33 | 90.9th | 1 in 11 | Superior |
| 130 | +2.00 | 97.7th | 1 in 44 | Very Superior |
| 145 | +3.00 | 99.87th | 1 in 741 | Very Superior |
| 160 | +4.00 | 99.997th | 1 in 31,560 | Very Superior |
Wechsler IQ Classification System
The Wechsler scales (WAIS-IV for adults, WISC-V for children) use these classifications based on SD 15. Below 70 (Extremely Low) corresponds to the 1st–2nd percentile range. 70–79 (Borderline) is the 2nd–9th percentile. 80–89 (Low Average) is the 9th–25th. 90–109 (Average) is the 25th–73rd. 110–119 (High Average) is the 75th–90th. 120–129 (Superior) is the 91st–97th. 130 and above (Very Superior) is the 98th percentile and above.
The Flynn Effect and IQ Norming
IQ tests are periodically renormed to maintain the population mean at 100. Raw cognitive test scores have risen approximately 3 IQ points per decade globally — a phenomenon called the Flynn Effect, documented by James Flynn in 1984. This means a score from an older test edition may not correspond to the same percentile on the current edition. When interpreting IQ scores, always confirm which edition and year of norming was used.
💡 Measurement precision: All IQ tests have a Standard Error of Measurement (SEM) typically around 3–5 points. A score of 130 might represent a true score anywhere from roughly 125 to 135. Percentile ranges rather than single percentiles are more accurate when interpreting individual scores.
Frequently Asked Questions
IQ 130 is approximately the 97.7th percentile (z = +2.0). About 97.7% of the population scores below 130, and roughly 1 in 44 people score 130 or higher. This is the approximate threshold for Mensa membership (top 2%).
IQ 120 is approximately the 90.9th percentile. About 1 in 11 people score 120 or higher. Wechsler classification: Superior (91st-97th percentile range).
IQ 115 is exactly the 84.1st percentile (z = +1.0 on SD 15). This is the High Average range. About 1 in 6 people score 115 or above.
IQ 100 is the population mean by definition, corresponding to the 50th percentile. Tests are renormed periodically to maintain this. About 50% of people score above 100 and 50% below.
Compute z = (IQ - 100) / 15 (or SD of your test). Find the cumulative area under the standard normal curve to the left of z using the CDF. That area, expressed as a percentage, is the percentile. IQ 130: z = 2.0, CDF(2.0) = 97.72%.
Approximately IQ 130 or above (97.7th percentile) is the top 2.3%. Mensa, the high IQ society, accepts the top 2% on a recognised IQ test, corresponding roughly to IQ 130+.
Approximately IQ 135 or above is the top 1% (99th percentile). IQ 145 is roughly the top 0.13% (about 1 in 741 people).
Default is SD 15, used by the Wechsler WAIS and WISC and most modern IQ tests. You can also select SD 16 (older Stanford-Binet editions) or SD 24 (Cattell Culture Fair). Percentiles differ between SD values for the same raw IQ score.
Below 70: Extremely Low (1-2nd pct). 70-79: Borderline (2-9th). 80-89: Low Average (9-25th). 90-109: Average (25-73rd). 110-119: High Average (75-90th). 120-129: Superior (91-97th). 130+: Very Superior (98th pct and above).
The Flynn Effect is the observed rise in raw IQ test scores over time, averaging about 3 points per decade globally. Tests are renormed periodically to keep the mean at 100. A score from an older test edition may correspond to a higher percentile than the same score on a recently normed test.
IQ scores are relatively stable in adults but more variable in children. Factors affecting IQ include education, early environment, nutrition, and health. Intensive early childhood programmes can produce meaningful gains in young children. Traumatic brain injury can lower IQ scores.
IQ tests measure a range of cognitive abilities: verbal reasoning, working memory, perceptual speed, and fluid intelligence. IQ correlates with academic achievement and job performance but does not measure creativity, emotional intelligence, practical skills, or wisdom. It is one predictor of cognitive potential, not a complete measure of human ability.
IQ 145 corresponds to the 99.87th percentile (z = +3.0 on SD 15). About 1 in 741 people in the general population score at this level. This is considered the entry threshold for many ultra-high IQ societies.
Definitions vary. Common thresholds: 130+ is often termed gifted (top 2.3%). Some educational programmes use 125+ (top 5%). Mensa uses top 2% (roughly 130+). Highly gifted is often defined as 145+ (top 0.13%). Profoundly gifted is sometimes defined as 160+ (top 0.003%).
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