IQ Scale Converter: Wechsler, Stanford-Binet and Cattell

The same IQ number means different things on different tests. Enter one score and see what it equals on every other scale.

Why the Same Number Means Different Things

Every modern IQ test sets the population average at 100. That part is shared. What is not shared is how widely the test spreads scores around that average, which is the standard deviation.

On a Wechsler test, one standard deviation is 15 points. On the Cattell III B it is 24 points. So being one standard deviation above average is a 115 on one test and a 124 on the other, from the same person on the same day.

This is the single most common source of confusion in any conversation about IQ scores. Someone reports a 148 from a Cattell and it sounds extraordinary next to a 130 from a WAIS. They are the same result.

How the Conversion Works

Converting between scales takes two steps and no judgment calls.

First, the score becomes a z-score, which is simply how many standard deviations it sits from the average. Subtract 100, then divide by that test's standard deviation. A 148 on the Cattell becomes 48 divided by 24, which is a z-score of 2.0.

Second, that z-score is rebuilt on the target scale. Multiply by the new standard deviation and add 100 back. A z-score of 2.0 on a Wechsler scale is 2.0 times 15 plus 100, which is 130.

The z-score is the part that actually travels between tests. Everything else is presentation. The percentile is derived from the same z-score, which is why the percentile is identical across every scale while the numbers are not.

Quick Conversion Table

Common reference points across the three scales in general use.

Look at the 98th percentile row. Three different numbers, one identical standing in the population. That row alone explains most online arguments about what counts as a qualifying score.

Three Worked Conversions

Following the arithmetic once on real numbers makes the rest of this page obvious, and it is exactly what the IQ scale converter above does in one step.

A Cattell 148 into Wechsler terms

The Cattell III B uses a standard deviation of 24. Subtract 100 from 148 to get 48, then divide by 24, which gives a z-score of exactly 2.0. Rebuilding that on a Wechsler scale means multiplying 2.0 by 15 and adding 100, which gives 130. Both figures are the 98th percentile, and both clear the Mensa threshold.

An older Stanford-Binet 116 into Wechsler terms

Older Stanford-Binet forms use a standard deviation of 16. Subtract 100 from 116 to get 16, divide by 16, and the z-score is 1.0. On a Wechsler scale that is 115. The one-point gap between 116 and 115 looks trivial and is, but the same logic at the top of the range produces gaps of twenty points or more.

A Wechsler 145 into Cattell terms

Subtract 100 from 145 to get 45, divide by 15, and the z-score is 3.0. On the Cattell scale that becomes 3.0 times 24 plus 100, which is 172. Somebody reporting 172 from a Cattell and somebody reporting 145 from a WAIS are describing identical standing, roughly the 99.9th percentile, even though the numbers look wildly different.

Which Scale Did Your Score Come From?

Most score reports state the test by name. Match it against this list.

• SD 15: the Wechsler family, meaning WAIS for adults and WISC for children, plus the modern Stanford-Binet Fifth Edition.
• SD 16: older editions of the Stanford-Binet, which you will mostly see on school records from earlier decades.
• SD 24: the Cattell III B, used by British Mensa among others.

If the report names no test at all, assume SD 15, because it is by far the most common, and treat the result as approximate. If a free online test gave you the number and never said which scale it used, that is worth knowing about the test itself.

The Flynn Effect and Why Norms Drift

There is a second reason two scores can disagree even after the scale is accounted for, and it catches people comparing results across generations.

Through most of the twentieth century, raw performance on intelligence tests rose steadily across many countries, at roughly three points per decade. The researcher James Flynn documented the pattern and it now carries his name. Better nutrition, more years of schooling and greater familiarity with abstract reasoning are the usual explanations.

Because publishers renorm periodically to keep the average at 100, those gains never appear in reported scores. They only become visible when an old test is scored using its original norms, at which point average performance today would have ranked well above average in the 1950s.

The practical consequence is that a score measured against a 1985 reference group and a score measured against a 2020 reference group are not directly comparable, even on the same scale. Converting between them cleanly hides a real difference in the comparison population. If you are comparing your result to a parent's from decades earlier, that is the effect at work. Our guide on whether IQ changes with age covers the research in more depth.

When You Should Not Convert at All

An IQ scale converter is the right tool less often than people assume. Three situations call for something else.

For a Mensa or society application. These organisations evaluate the original documented score from an approved supervised test. A figure you converted yourself is not evidence and will not be accepted. Use the Mensa eligibility checker to understand where you stand, then submit the original report.

When the source score has no stated scale. If a test never told you its standard deviation, any conversion is a guess dressed up as arithmetic. A test unwilling to state its scale has not given you enough information to interpret the number at all, which says something about the test.

When comparing a verbal-heavy result to a nonverbal one. Both report an IQ, but a vocabulary-weighted battery and a matrix reasoning test sample different abilities. Converting the number puts them on the same axis without making the underlying measurements interchangeable.

Where Conversion Breaks Down

The arithmetic is exact. The assumptions behind it are not always.

Norms drift over time. Raw performance on IQ tests rose across the twentieth century, a pattern called the Flynn effect, so publishers periodically renorm. A score from a test standardised in 1985 and a score from one standardised in 2020 are not measuring against the same reference group, and converting between them cleanly hides that.

Precision collapses in the tails. Standardisation samples contain very few people above about 145, so the norms out there rest on a handful of cases. Converting a 160 to another scale produces a confident-looking number built on thin evidence.

Different tests measure slightly different things. A verbal-heavy battery and a nonverbal matrix test both report an IQ, but they sample different abilities. Converting the number does not make the underlying measurements interchangeable.

None of this makes conversion useless. It means a converted score is a reasonable estimate of standing, not a result you can quote as if you sat that test.

What the Standard Deviation Actually Is

One term does all the work in any IQ scale conversion, so it is worth defining properly.

The standard deviation is a measure of spread. It describes how far a typical result sits from the average. On a scale where the standard deviation is 15, about 68 percent of people fall between 85 and 115, and about 95 percent fall between 70 and 130. Widen the standard deviation to 24 and those same proportions now stretch from 76 to 124 and from 52 to 148.

Nothing about the population changed. Only the ruler did. This is why the percentile is stable while the raw score is not: the percentile describes the share of people, and the raw score describes a position on one particular ruler.

A Full Cross-Scale Reference

If you would rather read a table than use the IQ scale converter, these are the equivalents at every common landmark. Each row describes one identical standing expressed four ways.

Two things stand out. Below the average the SD 24 column runs lower than the others, not higher, because a wider spread pushes scores further from 100 in both directions. And the gap between columns widens as you move away from the centre, which is why scale confusion causes far more trouble at the top of the range than in the middle.

Why This Matters More Than It Sounds

IQ scale confusion is not a technicality. It produces real errors that people act on.

Someone reads that Mensa requires 132, checks their WAIS report showing 130, and concludes they missed by two points. In fact 130 on a Wechsler is exactly the threshold, and 132 is the equivalent figure on a different instrument entirely. That person talks themselves out of an application they would have passed.

The reverse happens too. Someone scores 140 on a test using a standard deviation of 24, reads that 140 is near-genius territory on the Wechsler scale, and forms a picture that the underlying result does not support. On an SD 24 scale, 140 is roughly the 95th percentile rather than the 99.6th.

Both mistakes come from treating the number as though it were absolute. It never is. The scale is part of the measurement, and a score quoted without one is incomplete in the same way a distance quoted without a unit is incomplete.

Common Questions