Turning a percentile into an IQ score, and where the conversion breaks

0 The short answer

On the standard IQ scale, with a mean of 100 and a standard deviation of 15, the 90th percentile is an IQ of 119.2, the 95th is 124.7, the 98th is 130.8 and the 99th is 134.9, and "top 1 percent" names the same cutoff as the 99th percentile. The conversion is the inverse of the normal curve, so it is exact only for a population percentile on a scale whose standard deviation you know. A scale with a standard deviation of 16 puts the 99th percentile at 137.2, a scale with a standard deviation of 24 puts it at 155.8, and a percentile earned among people who chose to take a test is not a percentile among all adults. Convert only after you know the scale and the reference group.

1 What Does a Percentile Mean, and Is the Top 1 Percent the 99th Percentile?

A percentile is a position inside a stated group, and "top 1 percent" and "99th percentile" describe the same cut from opposite ends. The glossary of the Standards for Educational and Psychological Testing defines a percentile as the score below which a given percentage of the scores for a specified population occurs, and a percentile rank as the rank of a score based on the percentage of scores in a specified distribution that are below it. If 99 percent of a group scores below a cutoff, 1 percent scores at or above it. That is the whole relationship: the top share equals 100 minus the percentile. The 95th percentile is the top 5 percent, the 90th is the top 10 percent, and the 97.7th is the top 2.3 percent. The page on how rare a given IQ is states the same cut as one person in a number.

Printed percentile ranks do not all count the same way. Pearson's clinical assessment primer defines a percentile rank as the percentage of people who obtained a score or a lower one, says that ranks run from 1 to 99 with 50 as the median, and adds that, unlike standard scores, percentile ranks do not have equal intervals. The GRE program counts the other way: the ETS guide to the use of GRE scores reports the percent of test takers who scored lower than a given score. The MCAT program counts at or below: the AAMC table of MCAT percentile ranks gives the percentage of scores equal to or less than each score point, and it prints 74 beside a total of 508 and 71 beside 507. Because MCAT totals are whole numbers, the percent scoring strictly below 508 is the 71 printed beside 507. The same 508 is therefore a 74 under one convention and a 71 under the other, a gap of three points that comes from counting alone. Crawford, Garthwaite and Slick counted three coexisting definitions of a percentile in neuropsychological norms and reported that they can produce substantially different results (Clinical Neuropsychologist, 2009).

None of this disturbs the conversions below, which treat IQ as a continuous normal variable in which ties do not exist and "below" and "at or below" give the same answer. It matters when a report prints a whole number rank for tied scores, because the printed number then hides a rounding choice. If a printed rank of 99 was rounded to the nearest whole number, it can stand for anything from the 98.5th to the 99.5th percentile, which on the scale with a standard deviation of 15 spans about 132.6 to 138.6 (our arithmetic).

The phrase "top 5th percentile" is a trap. Read literally, the 5th percentile is a low position, because 5 percent of the group scores below it (an IQ of 75.3 on the scale with a standard deviation of 15, our arithmetic). Writers who use the phrase mean the top 5 percent, which is the 95th percentile. When a result says "top", read the number as a share counted down from the highest score. When it says "percentile" without "top", read it as the share scoring below. The page on why scores and percentiles cannot be averaged explains the shape problem behind that rule: equal steps in percentile are not equal steps in IQ.

2 How Does a Percentile Become an IQ Score?

A percentile becomes an IQ score in three steps: find the standard normal z score that leaves that share of the curve below it, multiply it by the standard deviation (SD) of the scale, and add the mean of the scale. As a formula, IQ equals the mean plus the standard deviation times z, which on the common scale is 100 plus 15 times z. The 95th percentile has a z score of 1.645, so the IQ is 100 plus 24.7, which is 124.7. The 99th percentile has a z score of 2.326, which gives 134.9. A z score counts how many standard deviations a score sits above or below the mean, and the page on the standard deviation of 15 explains why that unit is the natural ruler for IQ.

The first step has no pencil and paper formula. The NIST/SEMATECH e-Handbook of Statistical Methods states in its section on the normal distribution that the percent point function, the function that turns a percentile into a z score, does not exist in a simple closed formula and is computed numerically. Every conversion on this page is our arithmetic using the inverse of the standard normal distribution, rounded to one decimal place, and none of it comes from a test publisher.

Why is the normal curve the right model? The honest answer has two parts. Pearson's primer says that standard scores are called standard because the original distribution of raw scores is transformed to produce a normal curve. A study of 440 large sample achievement and psychometric measures found every one of them significantly nonnormal, with tails ranging from lighter than normal to heavier, as Micceri reported in Psychological Bulletin in 1989. Put together, those two statements describe the situation. Raw score distributions are rarely normal, the publisher reshapes them during norming, and the reported score then follows the normal curve by construction. The conversion is exact for the reported scale and only as good as the norming for the ability underneath. The primer adds the corollary: where a distribution is skewed, percentiles and standard deviation units do not line up the way they do on the normal curve. The page on how IQ scores are normed explains the norming step, and the page on the IQ distribution covers the curve itself.

A published report lets us check the claim. Pearson's sample WAIS-5 score report, dated September 16, 2024 and built for a demonstration examinee, prints each composite score beside a percentile rank. We computed the normal curve percentile for every composite in the report and rounded it to a whole number. All 21 agree with the printed rank. Table 1 shows nine of them.

The agreement covers scores from 97 to 126, the range of that one report. It shows that, for a current Wechsler battery, the printed percentile in the middle and upper middle of the scale is the normal curve percentile rounded to a whole number. It says nothing about the far tail, where section 10 explains that no norm sample reaches. The page on the WAIS-5 describes the battery that produced the sample report.

3 What IQ Score Matches Each Percentile?

On a scale with a standard deviation of 15, the 90th, 95th, 98th and 99th percentiles sit at 119.2, 124.7, 130.8 and 134.9, and every one of them sits higher on a scale with a wider standard deviation. Table 2 is the master conversion. Read the percentile in the first column, then read across to the scale your score uses. The z score column is the scale free quantity: it is the same for every instrument, and the three IQ columns are the z score multiplied by 15, 16 or 24 and added to 100.

Three features of Table 2 are worth reading slowly. The first is the spacing. Going from the 50th to the 60th percentile adds 3.8 IQ points on the scale with a standard deviation of 15, while going from the 89th to the 99th percentile adds 16.5, so equal percentile steps are very unequal IQ steps. The second is the landmark that most pages quote. A score one standard deviation above the mean, which is exactly 115, sits at the 84.13th percentile, so the 84th percentile row reads 114.9 and not 115. The third is the bottom of the table. The last four rows are what the formula returns for very small tail shares, and section 10 explains why they describe the model more than any person.

The table also shows that "130" is not the 98th percentile on the scale with a standard deviation of 15. The 98th percentile is 130.8. A score of 130 is two standard deviations above the mean and sits at the 97.7th percentile, which rounds to 98. Section 6 explains that difference because it drives most of the arguments about thresholds. The page on IQ 130 takes that single score in detail, and the page on IQ score classification labels covers the wording attached to ranges of scores, which this page deliberately leaves alone.

The reverse question, which percentile a known IQ score has, is the job of two other tools: the IQ to percentile chart reads single scores off a table, and the calculator that returns the percentile of any score you type does the same for any score. Table 2 read from the IQ column back to the percentile column answers the same question for the landmarks, which is a useful consistency check on any conversion you are given.

4 What IQ Score Puts You in the Top 1, 2, 5, 10 and 25 Percent?

To be inside the top 1 percent you need a score of at least 134.9 on a scale with a standard deviation of 15, which a whole number report reaches at 135, and the other common top shares follow the same rule. People often ask the question as a share rather than as a percentile, so Table 3 rearranges the same arithmetic by top share. The exact column is the cutoff on the continuous curve. The next column is the smallest whole number IQ that sits at or above that cutoff, which is the number a reader holding an integer score actually needs.

The whole number column has an edge case worth stating. A whole number score of 124 sits at the 94.5th percentile, just short of the top 5 percent, and 125 sits at the 95.2nd, just inside it. The top 1 percent line works the same way: 134 sits at about the 98.8th percentile and 135 at about the 99.0th. The smallest whole number is therefore the honest answer to the question "what do I need to be in the top 5 percent", provided the score is exact. A reported score is an estimate with an error band, and section 9 explains why a one point difference at the boundary carries no information.

Table 3 also shows how the spacing grows. The top 25 percent and top 15 percent lines are 5.4 points apart, while the top 1 percent and top 0.1 percent lines are 11.5 points apart. The page on gifted IQ ranges places the 130 and above region against percentiles and rarity.

5 Why Do Standard Deviations of 16 and 24 Change the Number?

The same percentile produces a larger number on a scale with a wider standard deviation, because the scale stretches the distance from 100 without changing anyone's rank. The mean is 100 on each scale discussed here, and the standard deviation is not. A Mensa resource page by American Mensa's supervisory psychologist states that the Stanford-Binet scale used a standard deviation of 16, and that the Cattell IIIB and the old form of the Raven's Advanced Progressive Matrices have a mean of 100 and a standard deviation of 24. The Wechsler composites use 15, which is the scale behind the sample report in Table 1.

To move a score from one scale to another, keep the z score and change the ruler: the new score is 100 plus the old distance from 100 multiplied by the new standard deviation and divided by the old one. From a standard deviation of 15 to 24, the distance from 100 is multiplied by 1.6, and to 16 it is multiplied by 1.067. Table 4 applies the rule to the landmark scores.

The rule reproduces the worked example on the Mensa page, where a score of 178 on the old Cattell IIIB is described as equivalent to 152 on the Stanford-Binet. A score of 178 is 3.25 standard deviations above 100 on a scale with a standard deviation of 24, and 3.25 standard deviations on a scale with a standard deviation of 16 is exactly 152. On the common scale the same position is 148.8, our arithmetic. The cost of misreading the scale is large. A printed 132 is the 98.4th percentile on a scale with a standard deviation of 15, the 97.7th on a scale with 16 and the 90.9th on a scale with 24. That is the point behind the remark in the Mensa International FAQ that a result of 132 on one test can be the same as 148 on another.

The practical rule follows. A score printed without its standard deviation cannot be converted to a percentile, and a percentile printed without its reference group cannot be converted to a score. That is why Mensa states its rule as a percentile and leaves the required score to each test.

6 Why Are the 95th, 98th and 99th Percentiles Not Exactly 125, 130 and 135?

The familiar benchmarks 125, 130 and 135 are rounded landmarks, and each sits a little away from the exact percentile it is quoted for. Table 5 shows where the whole number benchmarks fall on the scale with a standard deviation of 15, using the same normal curve arithmetic as the tables above.

The last column depends on a publisher choice. Pearson's primer says that percentile ranks range from 1 to 99, while the AAMC table prints 100 beside its highest total scores. Three separate mechanisms open the gap between a landmark and an exact value. The first is rounding of the percentile itself. A report prints a whole number rank, so 97.72 prints as 98. Abbie Salny, supervisory psychologist for American Mensa, writes on a Mensa resource page reprinted from the American Mensa website that the 98th percentile is two standard deviations above the mean, rounded off. Two standard deviations above the mean is exactly percentile 97.72 on the normal curve, and the exact 98th percentile is 130.8.

The published qualifying scores fit that reading. American Mensa's qualifying test scores page, read on October 6, 2026, lists a Wechsler full scale IQ of 130, 132 on the row named Stanford Binet and 130 on the row named Stanford Binet 5, and 148 for the Cattell. The same Salny page identifies the Stanford-Binet scale as having a standard deviation of 16 and the Cattell IIIB scale as having a standard deviation of 24. Two standard deviations above 100 are therefore 130 on the Wechsler scale, 132 on the Stanford-Binet scale with a standard deviation of 16 that Salny describes and 148 on the Cattell scale, and each of those three thresholds is exactly the plus two standard deviation score of its own scale. Against the exact 98th percentile, which is 130.8, 132.9 and 149.3 on the three scales, each listed threshold sits 0.8 to 1.3 points lower. That pattern is what a threshold defined at the rounded 98th percentile would produce. The Salny page states the rule as two standard deviations, rounded off, and the 0.8 to 1.3 point gap against the exact 98th percentile is our arithmetic. The Mensa International FAQ states the rule in percentile terms, membership for persons in the upper two percent of the general population on an approved test.

The second mechanism is whole number reporting. If a reported IQ of 135 stands for a true value from 134.5 to 135.5, it covers percentiles 98.93 to 99.10 on the normal curve, and a reported 134 covers percentiles 98.72 to 98.93. A boundary at the 99th percentile therefore falls inside the 135 reading, not between 134 and 135. The third mechanism is wording. A program that writes "at or above the 99th percentile" and one that writes "at or above 135" ask for thresholds one tenth of a point apart, a difference no instrument can resolve, yet they can disagree on a printed report because the first follows whatever whole number rank the publisher prints.

The same issue appears at the 99.9th percentile. The exact value is 146.4, the three standard deviation landmark (the 99.87th percentile) is exactly 145.0, and the smallest whole number inside the top 0.1 percent is 147, so tables that quote 145, 146 or 147 for "the 99.9th percentile" are rounding three different things. The page on high IQ society requirements shows how societies state their thresholds, the page on the Mensa IQ test covers the score that society requires, and the pages on IQ 135 and IQ 145 take two landmark scores one at a time.

7 How Do You Read a Band Such as "Top 1st to 5th Percentile"?

A five point band such as "top 1st to 5th percentile" is a range of IQ scores whose edges depend on how the report counts, so the safe reading is a range several points wide and never a single number. Some score reports and result pages describe a result with a sentence of the form "your score falls between the top 1st and 5th percentiles among IQ test takers". We could not verify how a report that uses this sentence defines its edges, so two readings are possible, and Table 6 gives the range on the scale with a standard deviation of 15 under each for the five bands of that form.

The first reading counts slices from the top. The first percentile slice is the top 1 percent, the second slice is the next 1 percent, and so on. The band "1st to 5th" is then slices 1 to 5, which is the top 5 percent, and the band "6th to 10th" is slices 6 to 10, from the top 5 percent cutoff to the top 10 percent cutoff. These bands tile the scale with no gaps, and their edges are the cutoffs for the top 5, 10, 15, 20 and 25 percent in Table 3. The top band then has no upper edge, unless the report also prints a separate top 1 percent band, in which case the top band runs from 124.7 to 134.9. The second reading treats the labels as cut points. The band "1st to 5th" runs from the top 1 percent cutoff to the top 5 percent cutoff, and the band "6th to 10th" runs from the top 6 percent cutoff to the top 10 percent cutoff. These bands leave small gaps, because the stretch between the top 5 percent and top 6 percent cutoffs belongs to no band.

Which reading is right is the report's decision, and a report that places every taker in some band can do so only if its bands tile. That is our inference, not something we verified, and it favors the first reading. The two readings disagree by at most 1.4 IQ points at any upper edge below the top band, and they agree exactly on every lower edge. The lower edge is therefore the safe statement: "top 1st to 5th" means at least about 125 on a population scale with a standard deviation of 15, "top 6th to 10th" means about 119 and above, and so on down to about 110 for "top 21st to 25th".

The bands also narrow sharply, which is the practical lesson of the table. Under the first reading the second to fifth bands are 5.5, 3.7, 2.9 and 2.5 IQ points wide. Under the second reading the top band is 10.2 points wide and the fifth is 2.0. The lower bands are narrower than the uncertainty around almost any individual score. Pearson's sample WAIS-5 report prints a 95 percent interval of 106 to 116 around a Full Scale IQ of 111, a span of 10 points, so a true position often straddles three or four adjacent bands. A five percentile band is a coarse label, not a measurement.

The phrase "among IQ test takers" carries the most important qualifier in the sentence. It names the denominator, which is the people who took that particular test. Table 6 assumes the denominator is the adult population, and the next section shows how far that assumption can fail.

8 Is a Percentile Among Test Takers the Same as a Percentile in the Population?

No: a percentile among test takers ranks you inside the people who chose to take that test, and reading it as a population percentile can misstate the IQ by many points in either direction. The Standards for Educational and Psychological Testing name the problem. Their glossary entry for user norms describes descriptive statistics, including percentile ranks, for a group of test takers that does not represent a well defined reference population, for example all persons tested during a certain period or a set of self selected test takers (Standards glossary).

Real testing programs show how large the effect can be. The ETS guide says that GRE percentile ranks are always based on the population of test takers within a given three year period. In its table for July 1, 2022 to June 30, 2025, a Verbal Reasoning score of 170 is at the 99th percentile, meaning 99 percent of Verbal Reasoning test takers scored lower. A Quantitative Reasoning score of 170, the highest in the same table, is at the 89th, meaning 89 percent of Quantitative Reasoning test takers scored lower. The same scaled score sits at two very different places in two pools of people.

The AAMC publishes percentile ranks for MCAT total scores in effect from May 1, 2026 to April 30, 2027, based on all MCAT results from 2023, 2024 and 2025 combined, a group of 305,494 scores with a mean of 500.6 and a standard deviation of 11.2. A total of 515 is the 91st percentile of that group. If a reader took that 91 for a population percentile and ran it through the formula in this page, the output would be 120.1 on the scale with a standard deviation of 15. That number would not estimate the person's IQ, because MCAT takers are a group formed by who decides to sit that exam. The page on IQ and the MCAT covers what the research says about the relationship.

American Mensa gives the clearest worked example. Its general rule is the 98th percentile on a standardized, supervised test. For the LSAT, however, its qualifying scores table lists a total percentile rank of 95, and its page on past test scores explains the lower rank in a frequently asked question. The answer says that the people taking the LSAT are not a normally distributed sample, that they have probably completed three to four years of college, and that the scores are adjusted to reflect this. A percentile among LSAT takers is not a percentile among adults, and Mensa corrects for it by accepting a lower rank. The page on IQ and the LSAT and the page on IQ and the GRE cover the score relationships directly.

The direction of the error depends on the pool. Table 7 is a hypothetical illustration, not a measurement of any real pool. It assumes a pool whose members score on average above the population mean, with the same standard deviation of 15, and asks what the pool's 90th, 95th and 99th percentiles are in population IQ.

If the pool averages 105, a person at the pool's 95th percentile has a population IQ near 129.7, not 124.7. Reading a pool percentile as a population percentile understates the score when the pool is above average and overstates it when the pool is below average. Real pools also differ in spread, which changes the numbers but not the direction of the lesson.

Online tests raise the same problem in its sharpest form. Bethlehem's review concluded that undercoverage and self selection can bias estimates from web surveys, and that self selection leads to unreliable survey outcomes (International Statistical Review, 2010). An online test whose percentiles are computed from its own visitors inherits that problem. The page on free and paid IQ tests compares what they report, and a review of a free online battery asks who the 100 on its scale refers to. The rule is short. Ask who the denominator is. If the answer is "people who took this test", "users of this site" or "test takers this year", the percentile ranks you among them, and nothing in this page's tables applies directly.

9 How Much Uncertainty Surrounds a Percentile Converted to IQ?

A converted IQ carries four separate uncertainties, which are measurement error, norm sampling, norm age and counting conventions, and a single percentile hides all four. The first uncertainty is plain measurement error. Pearson's sample WAIS-5 score report prints a 95 percent confidence interval for every composite. The Full Scale IQ of 111 has an interval of 106 to 116 and a standard error of measurement of 3.00. The Verbal Comprehension Index of 124 has an interval of 115 to 130 and a standard error of measurement of 4.50. The report states that its intervals are calculated using the standard error of estimation, and the interval around 124 is not centered on 124. Table 8 turns the printed intervals into percentiles, which is our arithmetic on the report's numbers.

A single printed percentile is therefore one point inside a band of 14 to 39 percentile points. The same logic applies to any score near a boundary. Take a score of 130 with an interval of plus or minus 6 points, a width chosen to be in line with the intervals above and not drawn from any one test. It spans 124 to 136, which is the 94.5th to the 99.2nd percentile. Such a score cannot be separated from the top 5 percent line at its low end or from the top 1 percent line at its high end. The page on reliability and validity explains where the error band comes from.

The second uncertainty is norm sampling. Crawford, Garthwaite and Slick note that using a normative sample to estimate the standing of a score in the normative population creates an uncertainty that is unavoidable but whose extent can be quantified. Pearson's one page WAIS-5 summary lists a normative sample of 2020 examinees, which we read as 2,020. In a group that size, the arithmetic expects about 20 people at or above the 99th percentile and about 2 at or above the 99.9th. A percentile table at the top of the scale therefore rests on very few people.

The third uncertainty is the age of the norms. Flynn showed in 1984 that every Stanford-Binet and Wechsler standardization sample from 1932 to 1978 set a higher standard than its predecessor, a total gain of 13.8 points in mean IQ over 46 years, and that obsolete norms had acted as an unrecognized confounding variable in hundreds of studies (Psychological Bulletin). Trahan and colleagues pooled 285 studies and found a meta-analytic mean of 2.31 standard score points per decade, and 2.93 points per decade for 53 comparisons involving modern Stanford-Binet and Wechsler tests (Psychological Bulletin, 2014). Pearson's primer states that norms tend to shift approximately 3 to 4 points every 10 years. Our arithmetic on the 2.31 to 2.93 points per decade of Trahan and colleagues: a score of 130 earned against norms 20 years old would be about 124 to 125 against current norms, roughly the 95th percentile and not the 98th. At the 3 to 4 points per decade in the Pearson primer, the same 130 would be about 122 to 124, roughly the 93rd to 95th percentile. Pearson's WAIS-5 overview brochure says the normative samples were collected in 2023 and 2024, so those norms are recent. The page on the Flynn effect covers the research.

The fourth uncertainty is the one from the opening section: tied scores, whole number ranks and the three counting conventions. It is small next to the first three, and it matters at the boundary of a rule. A person near a threshold who has a measurement band of 10 points, a norm that is 15 years old and a rank that was rounded cannot be said to be in or out of the top 5 percent on the strength of a conversion.

10 What Lies Beyond the 99th Percentile, and What Does the Top 1 Percent Hide?

Above the 99th percentile the formula keeps producing numbers long after any norm sample has run out of people, so those numbers describe the model more than the person. Table 9 sets the conversion beside the number of people a norm sample of 2,020 would be expected to hold at or above each point. The counts are our arithmetic, using the sample size Pearson lists for the WAIS-5.

An expected count below one means a norm sample of that size will usually hold nobody at that point, so the percentile comes from extending the curve fitted to everyone else. That extension deserves caution for two documented reasons. Micceri's finding that all 440 psychometric and achievement distributions he examined were nonnormal means the real tails need not follow the fitted curve. The APA's Guidelines for Psychological Assessment and Evaluation list ceiling and floor effects among the reasons that normative data or decision rules may not be accurate. A battery without items hard enough for the top of the range cannot separate a person at the 99.9th percentile from one at the 99.99th, because both can answer everything the battery asks. The practical reading is that a converted score above about 146, the 99.9th percentile, means "in the top tenth of one percent by the publisher's model". It does not mean a measured 146, 156 or 160. The page on high range IQ tests covers tests built for scores above the usual range, and the page on the highest recorded IQs covers why numbers at this level are so hard to verify.

The 99th percentile also hides a spread. Park, Lubinski and Benbow followed 1,586 intellectually talented adolescents, the top 1 percent, who took the mathematics part of the SAT by age 13, for more than 25 years, and reported that within each degree group the proportion with at least one patent or scientific publication rose with the early score (Psychological Science, 2008). That study used a mathematics test taken by adolescents, not an adult IQ test, and it describes a group, so it says nothing about any one person. What it does show is that "top 1 percent" is not one level. A reader told that a result is at the 99th percentile has learned only where a wide band begins.

11 Five Worked Conversions, Step by Step

Five conversions cover most of what readers bring to this page: a plain percentile, a top share, a high percentile on a wider scale, a band, and a percentile from a pool of test takers. Each one uses the formula from the second section and the landmark rows of Table 2 as a check.

Example 1: a report says the 92nd percentile. Assume the reference group is the adult population and the scale has a standard deviation of 15. The z score for the 92nd percentile is 1.405, and the IQ is 100 plus 15 times 1.405, which is 121.1. The check against Table 2 holds, because 121.1 sits between the 90th percentile at 119.2 and the 95th at 124.7, closer to the 90th. With a 10 point interval like the one in Pearson's sample report, the honest statement is about 121, within roughly 116 to 126, which is the 86th to the 96th percentile.

Example 2: a result says "top 3 percent". The top 3 percent is the 97th percentile, with a z score of 1.881 and an IQ of 128.2. A whole number score has to be 129 to be inside it, because 128 sits at the 96.9th percentile.

Example 3: a number quoted from an older, wider scale. A result described as the 99.5th percentile on a scale with a standard deviation of 24 is 100 plus 24 times 2.576, which is 161.8. The same rank on the common scale is 138.6. A score of 162 on that older scale and a score of 139 on the common scale describe the same position, and reading 162 as if it were on the common scale would claim a rank about 280 times rarer than the one reported, our arithmetic.

Example 4: a band. A result says "top 6th to 10th percentile among IQ test takers". If the group is the adult population and the scale has a standard deviation of 15, the range is 119.2 to 124.7 under the first reading and 119.2 to 123.3 under the second, so about 119 to 124. If the group is a pool that averages 105 instead, Table 7 shows the same band would correspond to roughly 124.2 to 129.7 in population terms. The band alone cannot tell which case applies.

Example 5: a percentile from a pool. An MCAT total of 515 is the 91st percentile of MCAT takers. The formula would return 120.1, but that output is not an IQ because the pool is not the population. Leave it as a percentile among MCAT takers.

Two checks catch most errors: the number should grow with the standard deviation for the same percentile, and it should agree with the landmark rows of Table 2.

12 What Do the Testing Standards Say, and What Should You Do With a Converted Number?

The Standards for Educational and Psychological Testing and the American Psychological Association's assessment guidelines treat a percentile as an interpretation that needs a described norm group, current norms and a stated error, so a converted IQ should be written down with all three. The Standards for Educational and Psychological Testing, published jointly by the American Educational Research Association, the American Psychological Association and the National Council on Measurement in Education in 2014, contain the rules that bear on a conversion. Standard 5.8 requires norms to refer to clearly described populations. Standard 5.9 asks reports of norming studies to specify the population, the sampling procedures, the participation rates, any weighting and the dates of testing, and to indicate the precision of the norms. Standard 5.11 makes renorming the publisher's responsibility. Standard 5.17 asks for direct evidence of score comparability when scores of tests that cannot be equated are linked, with the population specified, and moving a percentile from one test onto the scale of another is such a link.

The APA's guidelines add practice rules for psychologists. Guideline 8 of the APA Guidelines for Psychological Assessment and Evaluation, approved in March 2020, asks for an appropriate normative comparison and calls the agedness of the norms an important consideration. It adds that normative data or decision rules may not be accurate when important features of the person are missing from the norm group, or when the test has ceiling and floor effects. Guideline 11 says that people who are not appropriately represented in a normative sample have a greater chance of having their performance misinterpreted. The page on what IQ scores mean applies the same caution to a full report.

In practice, five questions turn a percentile into something usable:

1. Who is the reference group: the adult population, an age band, or the people who took this test?
2. What is the standard deviation of the scale, and is it the one the conversion assumes?
3. When were the norms collected, and has the test been renormed since?
4. Was the percentile rounded to a whole number, and does the threshold in question follow the score or the rank?
5. How wide is the interval around the score, and does the decision depend on a single point?

A converted result is then written as a range with its context, for example "about 125, within roughly 119 to 131, against adult norms with a mean of 100 and a standard deviation of 15", and not as "125".

We sell a paid assessment, so treat this paragraph as a disclosure and check it against the rest of the page. A reader who wants a measured score instead of a conversion can take ACIS, which reports a Full Scale IQ and six primary indices on the standard scale with a mean of 100 and a standard deviation of 15, each with a percentile and a 95 percent confidence interval, against adult norms for ages 16 to 90. The prices below were read on the home page on October 6, 2026 and can change. All are one time payments with no subscription: Quick is 15 dollars for 6 subtests in 3 domains and takes about 45 minutes, Optimized is 30 dollars for 13 subtests in 5 domains and takes about 110 minutes, and Full Scale is 50 dollars for all 20 subtests in six domains and takes about 175 minutes. Breaks are allowed, there is a 5 day quality guarantee, a purchased form can be completed within 30 days, and the free trial needs no card. The test is online and unsupervised, it is not a clinical or diagnostic instrument, it is not for hiring, school accommodations or admission to high IQ societies, and it is offered in English only. The technical manual documents the instrument. A report that prints the percentile and its interval removes the need for these conversions for that score, though not for a percentile from another test.

13 Sources Behind This Page

Every figure on this page traces to one of the sources below, or is labeled as our own arithmetic on the normal curve. All conversions between percentiles and IQ scores, the smallest whole number scores, the band edges, the percentiles at the ends of intervals, the expected counts in a norm sample, the pool illustration and the worked examples are our arithmetic, computed with the inverse of the standard normal distribution on the stated scale, and none of them is a figure published by a test publisher. Pages from Pearson, American Mensa, Mensa International, ETS and the AAMC were read on October 6, 2026 and can change.

• American Educational Research Association, American Psychological Association and National Council on Measurement in Education. Standards for Educational and Psychological Testing. AERA, 2014, glossary entries for percentile, percentile rank and user norms, and Standards 5.8, 5.9, 5.11 and 5.17.
• American Psychological Association, APA Task Force on Psychological Assessment and Evaluation Guidelines. APA Guidelines for Psychological Assessment and Evaluation, approved by the APA Council of Representatives in March 2020, Guidelines 8 and 11.
• Pearson Clinical Assessment Scientific Council. Standardized Clinical Assessment for Practitioners: A Primer, Pearson, 2023.
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14 Frequently Asked Questions