IQ Percentile Calculator
Convert an IQ score to its percentile (and back) on the three classic IQ scales — Wechsler, Stanford-Binet, and Cattell — with z-score, rarity, and the WAIS-IV classification table.
WAIS-IV classification table (Wechsler scale)
| IQ range | Classification | % of population | At / above this band |
|---|---|---|---|
| Below 70 | Extremely Low | 2.28% | 2.28% |
| 70–79 | Borderline | 6.85% | 9.12% |
| 80–89 | Low Average | 16.13% | 25.25% |
| 90–109 | Average | 49.50% | 74.75% |
| 110–119 | High Average | 16.13% | 90.88% |
| 120–129 | Superior | 6.85% | 97.72% |
| 130 and above | Very Superior | 2.28% | 100.00% |
Band shares and cumulative percentiles are computed from the normal distribution (mean 100, SD 15). The classification labels follow the WAIS-IV descriptive system.
Quick benchmarks
How it works
IQ = 100 + z × SD ← z = Φ⁻¹(percentile / 100)
IQ scores are deviation scores: by construction they follow a normal (bell-curve) distribution with a mean of 100. The percentile is the area under that curve up to your score — i.e. the share of the norming population that scores at or below it. Φ is the standard normal CDF.
The three scales
- Wechsler (WAIS/WISC) — mean 100, SD 15. The most common modern scale.
- Stanford-Binet (classic) — mean 100, SD 16. The classic SB deviation scale (Form L-M). Note: the current SB5 edition (2003) uses SD 15 like Wechsler.
- Cattell Culture Fair — mean 100, SD 24. A wider scale, so the same percentile maps to a more extreme-looking number.
The same percentile is the same rarity on every scale: the 97.7250th percentile (z = +2) is IQ 130 on Wechsler, 132 on Stanford-Binet, and 148 on Cattell — which is why Mensa's cutoffs are 130 / 132 / 148.
Frequently asked questions
What percentile is an IQ of 130?
On the Wechsler scale (mean 100, SD 15), IQ 130 is exactly z = +2.0, which is the 97.7250th percentile — about 1 in 44 people score higher. Wechsler classifies 130 and above as Very Superior. The same percentile is IQ 132 on the classic Stanford-Binet scale (SD 16) and IQ 148 on the Cattell scale (SD 24).
What percentile is an IQ of 115?
IQ 115 on the Wechsler scale is z = +1.0, the 84.1345th percentile — roughly 1 in 6 people score higher. Wechsler classifies 110–119 as High Average.
What percentile is an IQ of 100?
IQ 100 is the mean of every scale, so it is always exactly the 50.0000th percentile: half the norming population scores above it and half below.
What percentile is an IQ of 70?
IQ 70 on the Wechsler scale is z = −2.0, the 2.2750th percentile — about 1 in 44 people score lower. Wechsler classifies 70–79 as Borderline and below 70 as Extremely Low.
What IQ score do I need for the 98th percentile?
On the Wechsler scale the 98th percentile is IQ 130.81 (z ≈ +2.05). High-IQ societies use nearby round cutoffs at z = +2.0: Mensa accepts 130 (Wechsler), 132 (Stanford-Binet) or 148 (Cattell), all the 97.7250th percentile.
How do the Wechsler, Stanford-Binet, and Cattell scales differ?
All three use a mean of 100 but different standard deviations: Wechsler SD 15, classic Stanford-Binet SD 16, Cattell Culture Fair SD 24. The same percentile is therefore a different-looking number on each scale — the 97.7250th percentile (z = +2) is 130 / 132 / 148 respectively. Note: the current Stanford-Binet 5th edition (2003) uses SD 15 like Wechsler; this calculator's Stanford-Binet option is the classic SD-16 scale.
What do the Wechsler classification labels mean?
The WAIS-IV descriptive bands are: 130 and above Very Superior, 120–129 Superior, 110–119 High Average, 90–109 Average, 80–89 Low Average, 70–79 Borderline, below 70 Extremely Low. They are descriptive labels for ranges of a normed test score, not diagnoses — see the classification table tab for each band's share of the population.
Does a higher percentile mean someone is more intelligent?
Not exactly. A percentile is a relative position in the test's norming sample — it says how someone scored compared with the people the test was standardized on, not an absolute amount of intelligence. Two people at the 90th percentile on different tests did not necessarily demonstrate the same ability.
Why does my online IQ test give a different percentile?
Most online tests are not professionally normed: their samples are self-selected, unproctored, and sometimes scored against made-up distributions. Only a test administered and scored under standardized conditions by a qualified professional produces a valid IQ score and percentile.
What is the Flynn effect?
Average raw scores on IQ tests have risen about 3 points per decade over the 20th century. A percentile computed against old norms therefore flatters the result — the same raw performance is a lower percentile against current norms. Serious comparisons always use the test's own current norm tables.
How is the percentile calculated?
First the z-score: z = (IQ − 100) / SD. Then the percentile = Φ(z) × 100, where Φ is the standard normal cumulative distribution function. The inverse direction solves z = Φ⁻¹(percentile/100), then IQ = 100 + z × SD. This page evaluates Φ with the Abramowitz and Stegun 7.1.26 approximation (error below 1.5×10⁻⁷) and inverts it by bisection.
Which nrtechstudio tool should I use for related math?
Use this IQ Percentile Calculator for IQ ↔ percentile on the three IQ scales. Use our Normal Distribution Calculator for general normal probabilities with any mean/SD, our Standard Normal Distribution Calculator for z-table lookups, our Z-Score Calculator for plain standardization, and our Percentile Calculator for percentiles of ordinary datasets.