Modern IQ standard score
Mean 100 and standard deviation 15. This is the most common convention for contemporary Wechsler, Stanford–Binet and many other cognitive composites.
+2 SD = 130What is an IQ test scale?
An IQ score is usually a norm-referenced standard score. It describes how performance on a standardized set of cognitive tasks compares with an age-based reference group. On the most common modern scale, the mean is 100 and the standard deviation is 15.
The number is not a percent correct, a fixed quantity of intelligence or a direct measure of a person’s worth. A professional report should identify the exact test and edition, the normative group, percentile rank, confidence interval, validity considerations and the pattern of broad and narrow scores.
This guide explains score systems and responsible interpretation without reproducing secure test items, answer keys or protected administration rules.
Last updated: July 2026
100
Common IQ mean
The center of the normative scale
15
Common IQ standard deviation
One typical composite-score SD
50th
Percentile at IQ 100
The median in the idealized model
≈98th
Percentile at IQ 130
Two SD above the mean
IQ score, percentile and scale converter
Enter a score and choose the scale printed on the report. The calculator estimates its z score, percentile, rarity and equivalent values on several common standard-score systems.
Estimated standing
84th
High average range
z score+1.00
RarityAbout 1 in 6 at or above
IQ, SD 15115
IQ, SD 16116
Cattell, SD 24124
T score60
Complete IQ score range chart
Descriptive labels are conventions, not diagnoses. Publishers and professionals may use different names, cut points or confidence-interval rules. The actual report is the authority for the score it contains.
| IQ range | Approximate z score | Approximate percentile | Common wording | Interpretive note |
|---|---|---|---|---|
| 130 and above | +2.00 or higher | About 98th and above | Very high / extremely high | Roughly the highest 2% on a mean-100, SD-15 scale. |
| 120–129 | +1.33 to +1.93 | About 91st–97th | High / very high | Well above the normative mean. |
| 110–119 | +0.67 to +1.27 | About 75th–90th | High average | Above the middle half of the reference group. |
| 90–109 | −0.67 to +0.60 | About 25th–73rd | Average | The broad central band used by many reports. |
| 80–89 | −1.33 to −0.73 | About 9th–23rd | Low average | Below the central band, but not a diagnosis. |
| 70–79 | −2.00 to −1.40 | About 2nd–8th | Very low | Interpret with confidence intervals, adaptive functioning and context. |
| 69 and below | Below −2.00 | About 2nd and below | Extremely low | An IQ score alone cannot establish intellectual disability. |
The 68–95–99.7 rule
About 68% of a normal distribution falls within one standard deviation of the mean: roughly IQ 85–115.
About 95% falls within two standard deviations: roughly IQ 70–130.
About 99.7% falls within three standard deviations: roughly IQ 55–145.
The tails need extra caution. Extreme scores are based on fewer normative cases and may be affected by test floors, ceilings and larger practical uncertainty.
IQ percentiles and rarity
A percentile rank tells you the percentage of the normative group that scored at or below a result. It is not an equal-interval scale: the difference between the 50th and 60th percentiles is not psychometrically equivalent to the difference between the 90th and 100th percentiles.
85≈16th percentile
10050th percentile
115≈84th percentile
120≈91st percentile
130≈98th percentile
145≈99.87th percentile
| IQ (SD 15) | z score | Approximate percentile | Approximate tail rarity |
|---|---|---|---|
| 55 | −3.00 | 0.13th | About 1 in 741 at or below |
| 60 | −2.67 | 0.38th | About 1 in 261 at or below |
| 65 | −2.33 | 0.98th | About 1 in 102 at or below |
| 70 | −2.00 | 2.28th | About 1 in 44 at or below |
| 75 | −1.67 | 4.78th | About 1 in 21 at or below |
| 80 | −1.33 | 9.12th | About 1 in 11 at or below |
| 85 | −1.00 | 15.87th | About 1 in 6 at or below |
| 90 | −0.67 | 25.25th | About 1 in 4 at or below |
| 95 | −0.33 | 36.94th | About 1 in 3 at or below |
| 100 | 0.00 | 50th | The median |
| 105 | +0.33 | 63.06th | About 1 in 3 at or above |
| 110 | +0.67 | 74.75th | About 1 in 4 at or above |
| 115 | +1.00 | 84.13th | About 1 in 6 at or above |
| 120 | +1.33 | 90.88th | About 1 in 11 at or above |
| 125 | +1.67 | 95.22nd | About 1 in 21 at or above |
| 130 | +2.00 | 97.72nd | About 1 in 44 at or above |
| 135 | +2.33 | 99.02nd | About 1 in 102 at or above |
| 140 | +2.67 | 99.62nd | About 1 in 261 at or above |
| 145 | +3.00 | 99.87th | About 1 in 741 at or above |
Rarity estimates assume an ideal normal distribution and are rounded. Do not use them as exact population counts or clinical thresholds.
Converting between IQ scales and standard scores
The safest bridge between score systems is the z score. First express the original score as standard deviations from its mean; then rebuild it on the target mean and standard deviation.
z = (score − mean) ÷ SD
target score = target mean + (z × target SD)
Worked example: the 98th percentile
A score at approximately +2 SD has a z score of about 2.00. That becomes 130 on an SD-15 IQ scale, 132 on an SD-16 IQ scale, 148 on an SD-24 Cattell-style scale and 70 on a T-score scale.
This is why a larger number does not necessarily indicate a higher percentile. The scale’s spread determines the printed value.
Legacy SD-16 IQ scale
Some historical tests and older tables use a standard deviation of 16. A score must be interpreted with the test name and edition.
+2 SD = 132Cattell-style IQ scale
A wider scale sometimes seen in older high-IQ contexts. The same percentile produces a much larger-looking number.
+2 SD = 148T score
A standard-score system used widely in psychology. The mean is 50 and each 10 points equals one standard deviation.
+2 SD = 70Subtest scaled score
Many individually administered cognitive subtests use a mean of 10 and standard deviation of 3 before they are combined into composites.
+2 SD = 16z score
The universal statistical scale. A z score says how many standard deviations a score is above or below the mean.
+2 SD = z 2.00
A mathematical conversion is not a test conversion.
Two batteries can place a person at different percentiles because they sample different abilities, use different norms, have different ceilings and were administered under different conditions.
How to interpret an IQ score correctly
Read an IQ result as one part of an assessment argument. The score should answer a real question—such as educational planning, diagnostic clarification or documentation—and should be integrated with history, observations, other tests and everyday functioning.
Name the test
Record the exact battery, edition, language, age norms and date of administration.
Check validity
Review engagement, standardization, accommodations, health, attention, language and sensory access.
Use the interval
Interpret the confidence interval, not only the single obtained score.
Read the profile
Compare overall, index and subtest patterns without overinterpreting small differences.
Compare real life
Ask whether the findings fit school, work, communication and daily functioning.
Act on it
Prioritize practical recommendations, supports and follow-up questions.
Confidence intervals and measurement error
No obtained score is perfectly precise. A clinician uses the test’s standard error of measurement to create a confidence interval. For illustration, if an IQ of 100 had a standard error of 3 points, an approximate 95% interval would be about 94–106. The actual standard error varies by test, score and age.
Best practice: Say “the obtained score was 100, with the report’s stated confidence interval” rather than treating 100 as an exact, permanent quantity.
The same overall IQ can hide different profiles
Illustrative profile A
Relatively even performance around the mean.
Illustrative profile B
Large strengths and weaknesses can make a single overall number less representative.
The profiles above are invented examples for explanation only and are not based on real test records.
Major kinds of IQ and cognitive ability tests
“IQ test” is an umbrella term. Different batteries vary in age range, length, theory, language demands, administration method, score structure and intended use. A score should never be detached from the instrument that produced it.
Wechsler scales
Individually administered age-based batteries that typically report an overall composite plus domain and subtest scores.
Stanford–Binet
A broad individual intelligence battery descended from the Binet–Simon tradition, with verbal and nonverbal routes to major factor and full-scale scores.
Woodcock–Johnson cognitive batteries
Flexible batteries organized around broad and narrow cognitive abilities, often integrated with academic achievement evaluation.
Kaufman batteries
Child-focused or brief measures that can emphasize processing, acquired knowledge, nonverbal performance or efficient screening.
Nonverbal reasoning measures
Reduce spoken-language demands and focus more heavily on visual reasoning, patterns or nonverbal problem solving; “nonverbal” does not mean culture-free.
Group ability tests
Administered to many students at once for screening or program decisions. They are not automatically interchangeable with an individual clinical IQ assessment.
Individual clinical testing vs. group screening
Individual assessment
- One examiner and one examinee
- Standardized prompts, timing and behavioral observation
- Often produces domain and subtest profiles
- Can be integrated with interviews and other clinical data
Group or online screening
- Efficient for many people at once
- Usually offers less individualized observation
- May estimate a narrower set of abilities
- May not satisfy documentation or diagnostic requirements
What IQ scores are used for—and what they cannot decide alone
Educational planning
Understanding cognitive strengths and needs alongside achievement, classroom evidence and intervention history.
Gifted identification
Contributing evidence to local program criteria, often with achievement, creativity or teacher data.
Clinical evaluation
Describing a cognitive profile within broader neurodevelopmental, psychiatric, neurological or medical assessment.
Disability documentation
Supporting decisions when combined with functional evidence and the receiving organization’s requirements.
Research
Studying cognitive development, group patterns, intervention effects and relationships with other outcomes.
Personal clarification
Helping a person understand a profile when the assessment has a clear purpose and qualified interpretation.
A score can contribute evidence about
- Performance on sampled cognitive tasks under standardized conditions
- Relative standing compared with an age-based normative group
- Broad and domain-specific strengths or weaknesses
- Questions that merit further assessment or support
A score cannot independently establish
- ADHD, autism, dyslexia or another diagnosis
- Intellectual disability without adaptive-behavior evidence
- Creativity, wisdom, morality, motivation or future success
- A fixed limit on learning or a person’s value
History of the IQ scale
The history is both scientifically influential and ethically complicated. Intelligence testing grew from efforts to identify educational needs, then became entangled with mass classification, eugenics, immigration policy and racial hierarchy. Modern practice must acknowledge that history while applying stronger standards for validity, fairness and responsible use.
Galton’s anthropometric laboratory
Francis Galton measured sensory acuity, reaction time and physical characteristics in an early effort to quantify individual differences.
“Mental tests” enter psychology
James McKeen Cattell used the phrase “mental tests” for a battery emphasizing sensory and motor performance.
Binet–Simon preliminary scale
Alfred Binet and Théodore Simon published a practical set of tasks for identifying children who might need educational support. It did not yet produce the modern deviation IQ.
Age levels and mental age
Revisions organized tasks by the ages at which children typically succeeded, supporting the idea of a mental-age estimate.
Stern proposes the intelligence quotient
William Stern described a quotient relating mental age to chronological age; later users multiplied the ratio by 100.
Stanford revision
Lewis Terman adapted and standardized the Binet–Simon approach for the United States, helping popularize the term IQ.
Army Alpha and Beta
Group tests were used at unprecedented scale during World War I, demonstrating administrative reach while also exposing major language, education and fairness problems.
Wechsler–Bellevue and deviation scores
David Wechsler introduced an adult battery that compared performance with age peers and combined several task types rather than relying on ratio IQ.
The Flynn effect is documented
James Flynn’s work drew attention to generational changes in test performance and the problem of aging norms.
Profiles, uncertainty and context
Modern interpretation emphasizes current norms, multiple cognitive domains, confidence intervals, fairness, adaptive functioning and the intended use of the score.
Ratio IQ vs. deviation IQ
- Historical ratio IQ
- Mental age ÷ chronological age × 100. This approach worked poorly as a universal adult scale because mental-age growth does not continue linearly through life.
- Modern deviation IQ
- A standard score showing how far performance lies from the age-group mean. The mean is commonly 100 and the standard deviation is often 15.
- Why norms are revised
- Language, education, demographics, test familiarity and population performance change. Updated norms reduce the risk of comparing current examinees with an obsolete reference group.
Fairness, culture, language and testing conditions
Fair testing is not achieved by pretending context does not exist. It requires evidence that score interpretations are valid for the intended use and the examinee, plus careful attention to access, language, opportunity, disability, administration and consequences.
Sleep and fatigue
Severe tiredness can reduce attention, working memory, speed and persistence.
Health and pain
Illness, pain, neurological conditions and medication effects can change performance.
Language proficiency
Testing in a weaker language can affect instructions, verbal tasks, rapport and even nonverbal task performance.
Vision, hearing and motor access
Sensory or motor demands can lower scores unless access needs are anticipated and documented.
Anxiety and motivation
Test anxiety, low engagement, perfectionism or fear of failure may influence speed and accuracy.
Education and opportunity
Schooling, literacy, enrichment and familiarity with formal problem solving affect many test performances.
Culture and experience
Knowledge, communication style and assumptions embedded in testing may not be equally familiar to every examinee.
Prior exposure
Retesting or practice with similar material can create practice effects, especially over short intervals.
Testing conditions
Interruptions, poor technology, time pressure, examiner behavior and nonstandard administration can matter.
Individual interpretation is essential.
Group averages cannot diagnose an individual or justify stereotypes about race, ethnicity, nationality, gender, disability, income, neighborhood or language background.
Accommodations and modifications
Some accommodations improve access while preserving the intended construct; others change the task enough that standard norms may no longer apply cleanly. A report should document what changed, why it changed and how the modification affects interpretation.
High scores, giftedness and low-score interpretation
High scores and gifted identification
There is no universal “gifted IQ.” Many programs use thresholds near the upper few percentiles, but local definitions, accepted tests, age limits, score recency, confidence intervals and required supporting evidence vary. Mensa uses the upper 2% on an approved, properly administered and supervised test rather than one universal IQ number.
Use percentile first. “At or above the 98th percentile on an accepted test” is clearer than assuming that every scale uses the same cutoff number.
Low scores and intellectual disability
AAIDD defines intellectual disability through significant limitations in both intellectual functioning and adaptive behavior, originating during the developmental period. An obtained IQ near or below 70 may prompt careful evaluation, but diagnosis cannot be made from that number alone.
- Review the confidence interval and test validity.
- Assess conceptual, social and practical adaptive skills.
- Confirm developmental-period onset with history and records.
- Consider language, culture, disability, education and access.
- Focus on support needs rather than reducing the person to a score.
Online IQ tests: what makes one credible?
Online delivery is not automatically invalid, and in-person delivery is not automatically excellent. The key questions are standardization, norms, security, identity, environment, accessibility, reliability, validity and appropriate interpretation.
Better signs
- Clear test purpose and target age range
- Transparent norming sample and publication date
- Reliability and validity evidence
- Percentile and confidence information
- Secure, supervised administration when documentation matters
- Limits and privacy practices stated plainly
Warning signs
- Guaranteed genius scores or instant diagnosis
- No named test, norms or technical documentation
- Scores designed mainly to trigger payment or sharing
- Unrealistically precise results from a few items
- Leaked or copied professional test content
- Claims that the score is permanent and complete
Do not train on protected test items.
Exposure to authentic questions, answer keys or close replicas can invalidate future results and undermine fairness and test security.
Common IQ scale myths
“A percentile is the percent correct.”
A percentile is a rank within a normative group. The 75th percentile does not mean 75% of items were answered correctly.
“An IQ of 130 means exactly the same on every test.”
The scale, norms, edition, confidence interval and construct coverage differ. Percentile and test name are essential.
“One number reveals every kind of intelligence.”
IQ tests sample selected cognitive performances. They do not fully measure creativity, wisdom, practical judgment, motivation, character or expertise.
“A high score guarantees success.”
Life outcomes depend on many personal, social, educational, health and opportunity factors beyond test performance.
“A low score proves intellectual disability.”
Diagnosis requires limitations in both intellectual functioning and adaptive behavior with developmental-period onset.
“Nonverbal tests are culture-free.”
They reduce language demands, but familiarity, education, visual experience, motivation and testing context can still affect performance.
“Online quizzes are equivalent to a clinical IQ test.”
Most online quizzes lack controlled administration, secure content, robust norms and professional interpretation.
“You can raise a valid score by studying leaked items.”
Training on protected content threatens standardization, validity, fairness and future clinical usefulness.
“The obtained score is perfectly exact.”
Every test score includes measurement error. Reports should include a confidence interval and discuss validity.
Frequently asked questions about the IQ test scale
What is the average IQ score?
On the most common modern scale, the normative mean is 100. A score near 100 represents performance near the center of the age-based reference group, not a percentage correct.
What is the standard deviation of IQ?
Many current intelligence composites use a standard deviation of 15. Some tests or historical systems use 16, 24 or another value, which is why the test name and edition matter.
What percentile is an IQ of 115?
On a mean-100, SD-15 normal scale, 115 is one standard deviation above the mean and is approximately the 84th percentile.
What percentile is an IQ of 130?
On a mean-100, SD-15 scale, 130 is two standard deviations above the mean and is approximately the 98th percentile. Exact test tables may round differently.
Is 100 exactly the 50th percentile?
In the idealized normal model, yes. Official normative tables can use discrete score conversions and rounding, so a report may show a nearby percentile.
Why can the same percentile have different IQ numbers?
Different score systems use different standard deviations. The 98th percentile is about 130 on an SD-15 scale, 132 on an SD-16 scale and 148 on an SD-24 scale.
What is a z score?
A z score is the number of standard deviations a result is above or below the mean. On an SD-15 IQ scale, z = (IQ − 100) ÷ 15.
What is a confidence interval?
It is a range around the obtained score that communicates measurement uncertainty. A 95% interval is wider than a 90% interval and should be interpreted with the test manual and referral context.
Can two people with the same IQ have different abilities?
Yes. One person may have a flat profile across domains, while another has strong verbal reasoning and lower processing speed or working memory. The same overall score can summarize different patterns.
What IQ is considered gifted?
There is no universal definition. Some programs use approximately the 95th, 97th or 98th percentile; others combine ability, achievement, creativity, teacher evidence and local criteria.
What IQ qualifies for Mensa?
Mensa describes eligibility as performance in the upper 2% on an approved, properly administered and supervised intelligence test. The qualifying number depends on the test and scale.
Does an IQ below 70 diagnose intellectual disability?
No. Intellectual disability requires significant limitations in intellectual functioning and adaptive behavior with onset during the developmental period. A clinician considers the score, confidence interval, validity and multiple sources of evidence.
Can IQ change over time?
Scores can change because of development, health, education, intervention, testing conditions, measurement error, practice effects and updated norms. The amount and meaning of change require professional interpretation.
How accurate are online IQ tests?
Quality varies greatly. A well-designed online research or screening measure may estimate a narrow ability, but unsupervised quizzes generally cannot substitute for a standardized professional assessment or official documentation.
Can I convert an old score to a modern IQ?
You can estimate an equivalent percentile when the original mean and standard deviation are known, but this does not correct for old norms, different constructs, score ceilings, test editions or administration conditions.
What is the difference between IQ and an index score?
An overall IQ composite summarizes broad performance across selected tasks. Index scores summarize narrower domains such as verbal comprehension, fluid reasoning, visual-spatial ability, working memory or processing speed, depending on the test.
Why are extreme IQ scores less precise?
Normative samples contain fewer people at the far tails, score ceilings may compress performance, and a small raw-score change can produce a large standard-score difference. High and low extremes need cautious interpretation.
Should I compare scores from different tests directly?
Only cautiously. First compare percentiles and confidence intervals, then consider the constructs measured, norms, age range, edition, administration method and purpose of each test.
IQ scale glossary
Adaptive behavior
Conceptual, social and practical skills used in everyday life. It is essential to intellectual-disability evaluation.
Age norm
A comparison group made up of people in the same or a closely similar age range.
Composite score
A standard score formed by combining performance across several subtests.
Confidence interval
A score range that expresses uncertainty around an obtained result.
Deviation IQ
A standard score showing distance from the age-group mean, usually on a mean-100 scale.
Floor
The lowest level a test can measure with useful differentiation.
Ceiling
The highest level a test can measure with useful differentiation.
FSIQ
Full Scale IQ, an overall composite estimate of broad cognitive functioning on certain test families.
Index score
A composite representing a cognitive domain rather than the entire battery.
Norms
Reference data used to convert raw performance into interpretable scores.
Percentile rank
The percentage of the normative group scoring at or below a result, subject to test-specific rounding.
Practice effect
Improvement caused by familiarity or prior exposure rather than a true change in the target ability.
Raw score
The initial points or credit earned before conversion through normative tables.
Reliability
The consistency or precision of scores under defined conditions.
Standard error of measurement
An estimate of expected score variation caused by measurement imprecision.
Validity
Evidence supporting the interpretation and use of scores for a particular purpose.
z score
A standardized value with mean 0 and standard deviation 1.
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Professional and primary sources
- APA Dictionary of Psychology — deviation IQ Definition of deviation IQ and the common mean-100 scoring convention.
- APA Dictionary of Psychology — IQ Background on ratio IQ and modern deviation scores.
- Pearson — Standardized Clinical Assessment for Practitioners: A Primer Professional overview of standard scores, percentile ranks and assessment interpretation.
- Standards for Educational and Psychological Testing Joint AERA, APA and NCME standards addressing validity, fairness and responsible use.
- AAIDD — Defining Criteria for Intellectual Disability Current definition requiring limitations in intellectual functioning and adaptive behavior.
- Mensa International — Getting Your IQ Tested FAQs Explains top-2% eligibility and why qualifying score numbers differ across scales.
- Flynn, J. R. (1984) — IQ Gains and the Binet Decrements Early systematic documentation of generational changes in intelligence-test performance.
- Pearson — Wechsler Adult Intelligence Scale, Fifth Edition Official publisher information for a current individually administered adult cognitive measure.
- Riverside Insights — Woodcock–Johnson assessment systems Official publisher overview of cognitive, achievement and language assessment.
- Pearson — Kaufman Assessment Battery for Children, Second Edition Normative Update Official publisher information for a child cognitive battery.
Image credits: Alfred Binet portrait and the 1917 Army testing photograph are public domain. The David Wechsler photograph is credited to New York University School of Medicine and licensed CC BY 4.0. Source and license pages are available through Wikimedia Commons.