Convert an IQ score to percentile rank, rarity, z-score, and broad band, or reverse a percentile into an IQ cutoff using selectable SD 15, SD 16.
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IQ percentile calculator with rarity, z-score, and reverse lookup Convert an IQ score to percentile rank on a selected IQ scale, or work backward from a target percentile to the approximate IQ cutoff. The default uses mean 100 and standard deviation 15, the common public reference for Wechsler-style scores.
Quick checks
Conversion direction
Most common public reference scale for IQ percentile lookups.
Result
98th percentile
IQ 130 is at about the 98th percentile on the SD 15 (Wechsler-style) scale.
97.72%
At or below this score
2.28%
Estimated share higher
2
Z-score
Very Superior
Broad band
1 in 44 people score higher IQ 130 is 2 standard deviations above the mean on an SD 15 scale. Percentile output is a distribution estimate, not a diagnosis or proof of eligibility for any program.
Reference points on the selected IQ scale
These rows show how the same normal-curve positions translate into IQ scores when the standard deviation changes.
Position
IQ score
Percentile
Above
-3 SD
55
0.13%
99.87%
-2 SD
70
2.28%
97.72%
-1 SD
85
15.87%
84.13%
Mean
100
50%
50%
+1 SD
115
84.13%
15.87%
+2 SD
130
97.72%
2.28%
+3 SD
145
99.87%
0.13%
How to read the number
An IQ percentile rank means the estimated share of the reference population at or below that score. It does not mean percent correct, and it does not prove that an online practice score was professionally administered or validly normed.
For high-score questions such as Mensa eligibility, use the percentile idea as context only. Official organizations evaluate approved tests, administration conditions, and score reports rather than a standalone online conversion.
IQ percentile calculator guide: IQ score chart, rarity, z-score, and reverse lookup
An IQ percentile calculator converts an IQ score into a percentile ranking that shows where the score falls relative to a reference population.
How IQ scores map to percentiles
IQ scores are usually interpreted as standard scores centred at a mean of 100. On the most familiar public scale, each 15-point move represents one standard deviation from the mean: 85 is one standard deviation below average, 115 is one standard deviation above average, and 130 is two standard deviations above average.
The percentile is calculated using the cumulative distribution function (CDF) of the normal distribution. A score of 115 corresponds to roughly the 84th percentile, meaning the score is higher than about 84 out of every 100 people under that model. A score of 130 reaches approximately the 98th percentile on the SD 15 scale.
z = (IQ − 100) / SD
The z-score measures how many standard deviations the IQ score is from the mean.
percentile = Φ(z) × 100
Φ(z) is the standard normal cumulative distribution function.
Use the right IQ scale before comparing scores
A common competitor-page weakness is treating every IQ number as if it uses the same standard deviation. That is misleading. An IQ of 130 on an SD 15 scale is two standard deviations above the mean and about the 98th percentile. The same raw number on an SD 24 Cattell-style scale is only about 1.25 standard deviations above the mean and lands closer to the 89th percentile.
That is why the calculator lets you choose SD 15, SD 16, or SD 24. The percentile is tied to the z-score, not the raw IQ number alone. If your score report names a scale or standard deviation, use that setting rather than assuming the default.
What percentile is 130 IQ, and why people focus on the top 2%
A score of 130 on the common mean-100, standard-deviation-15 scale is about two standard deviations above average and lands around the 98th percentile. That is why searches such as 130 IQ percentile, top 2 percent IQ, Mensa IQ requirement, and IQ rarity calculator often overlap.
The phrase top 2 percent describes a percentile threshold, not one universal raw score. Mensa and similar organizations evaluate approved tests and administration conditions. A standalone online conversion can show why 130 on SD 15 is near the top-2% reference point, but it cannot prove eligibility.
Reverse lookup: what IQ is a given percentile?
Some users start with a percentile rather than an IQ score. For example, the 88th percentile on the SD 15 scale is around IQ 118. The 95th percentile is around IQ 125, and the 98th percentile is around IQ 131. Those values come from the inverse normal distribution: find the z-score for the target percentile, then convert it back to the IQ scale.
Reverse lookup is especially useful when a score report, gifted-program note, or search result gives only a percentile. It also makes scale differences visible: the same percentile maps to a higher raw score when the standard deviation is wider.
IQ = 100 + z × SD
Use this after finding the z-score that corresponds to the target percentile.
Reading an IQ percentile chart
An IQ percentile chart is a set of landmarks on the bell curve. On SD 15, the common checkpoints are about IQ 70 at the 2nd percentile, IQ 85 at the 16th percentile, IQ 100 at the 50th percentile, IQ 115 at the 84th percentile, IQ 130 at the 98th percentile, and IQ 145 near the 99.9th percentile.
The chart is not linear in rarity. Moving from IQ 100 to 115 shifts from the median to about the 84th percentile, while moving from 130 to 145 compresses into a much smaller upper-tail slice. That is why the result includes both percentile and estimated share higher.
Standard IQ classifications
Psychologists and educational reports often use broad descriptive bands such as Average, High Average, Superior, and Very Superior. On the SD 15 scale, scores between 90 and 109 are commonly described as Average, 110–119 High Average, 120–129 Superior, and 130 or above Very Superior. On lower-score bands, 80–89 is often Low Average, 70–79 Borderline, and below 70 Extremely Low.
These classifications are guidelines rather than rigid labels. Performance on a single test can be influenced by test anxiety, fatigue, language, cultural familiarity, disability accommodations, practice effects, and whether the test was professionally administered. A psychologist interprets scores in the context of a full assessment, not as a standalone online number.
Worked example: 130 IQ on two scales
On the SD 15 scale, z = (130 − 100) / 15 = 2.00. Looking up Φ(2.00) gives about 97.72%, so the score is usually rounded to the 98th percentile. The upper-tail share is about 2.28%, or roughly 1 in 44 people scoring higher under the model.
On the SD 24 scale, z = (130 − 100) / 24 = 1.25. That maps to about the 89th percentile, not the 98th. The raw IQ number is the same, but the scale is wider, so the percentile changes materially.
Why IQ percentiles are still only approximations
The calculator uses a normal-distribution model because that is the familiar way IQ standard scores are explained. But intelligence tests are not all perfectly interchangeable, and some use different scaling choices, age-specific norms, subtest composites, confidence intervals, or test-specific reporting rules.
A percentile calculator is best viewed as an interpretation aid, not as a substitute for a psychologist’s report. It helps you understand the distribution, but it does not tell you whether a test was validly administered, whether the score is current, or what the result means for a school, clinical, employment, or legal decision.
Common mistakes when using an IQ rarity calculator
The first mistake is reading percentile as percent correct. A 98th percentile result does not mean the person answered 98% of items correctly; it means the score is at or above about 98% of the reference population under the selected scale.
The second mistake is comparing online practice-test scores with professionally normed tests. Practice tools can be interesting, but they are not equivalent to a supervised, standardized assessment. The third mistake is ignoring the confidence interval: real test reports usually include uncertainty around the reported score.
Frequently asked questions
What percentile is an IQ of 130?
On the common IQ scale with mean 100 and standard deviation 15, an IQ of 130 is about the 98th percentile. That means roughly 98% of the reference population scored at or below that level, and about 2% scored higher.
What IQ is the 88th percentile?
On the common SD 15 scale, the 88th percentile is about IQ 118. Depending on rounding, you may see nearby values such as 117 or 118, but the practical takeaway is that the 88th percentile sits a little above one standard deviation above average.
Is IQ score the same as percentile?
No. IQ is a scaled score with a mean of 100 and a chosen standard deviation. Percentile is the proportion of people who score at or below that IQ. They are related through the normal distribution but express different things.
Why does the calculator offer SD 15, SD 16, and SD 24?
Different IQ references and test traditions have used different standard deviations. SD 15 is the common Wechsler-style public reference, SD 16 appears in some Stanford-Binet-style references, and SD 24 is often associated with Cattell-style comparisons. The same raw IQ can map to different percentiles on different scales.
Is 130 IQ always the same percentile on every test?
Not exactly. It is about the 98th percentile on the common SD 15 scale, but the exact percentile can shift if the test uses a different scale, norm group, age band, or reporting method.
What percentile is Mensa level?
Mensa describes eligibility in terms of the upper two percent of the general population on an approved, properly administered intelligence test. On an SD 15 model, that is close to IQ 130, but official eligibility depends on the specific approved test and score report.
How should I interpret an IQ percentile in plain language?
The percentile tells you how a score compares with the reference group. For example, the 90th percentile means the score is at or above about 90% of the reference population. It does not mean a person is 90% smart or that intelligence can be reduced to a single number.
What is the difference between percentile and rarity?
Percentile describes the share at or below the score. Rarity usually describes the smaller tail, such as how many people score higher than a high IQ score. For IQ 130 on SD 15, the percentile is about 97.7%, while the upper-tail rarity is roughly 1 in 44 scoring higher.
Can I convert percentile back to IQ?
Yes, if you know the scale. Convert the percentile to a z-score using the inverse normal distribution, then use IQ = 100 + z × SD. The calculator’s reverse mode does that automatically.
What IQ is the 95th percentile?
On the SD 15 scale, the 95th percentile is about IQ 125. On a wider scale such as SD 24, the same percentile corresponds to a higher raw score because each standard deviation spans more IQ points.
Why do different IQ percentile charts disagree slightly?
They may use different standard deviations, rounding rules, rarity wording, or classification bands. Some charts also mix SD 15, SD 16, and high-IQ society score traditions. Always check which scale the chart assumes.
Can this calculator diagnose giftedness, disability, or clinical status?
No. It only converts a score under a normal-distribution model. Diagnosis, placement, eligibility, and accommodations require the original test report, administration details, confidence intervals, and qualified professional interpretation.
