Convert IQ ↔ T-score
How the conversion works
IQ and T-score scores are normalised on bell-curve distributions. The conversion maps a person's standing in one distribution to the equivalent standing in the other.
- IQ: mean 100, standard deviation 15.
- T-score: mean 50, standard deviation 10. T-scores avoid negative numbers by shifting the mean from 0 to 50. They are common in clinical assessment, the MMPI, the NEO-PI, and similar instruments.
IQ-equivalent = (target − meantarget) / SDtarget × 15 + 100
target-equivalent = (IQ − 100) / 15 × SDtarget + meantarget
Common IQ ↔ T-score reference table
| IQ | T-score | Percentile |
|---|---|---|
| 70 | 30 | ~2nd |
| 85 | 40 | ~16th |
| 100 | 50 | ~50th |
| 115 | 60 | ~84th |
| 130 | 70 | ~98th |
| 145 | 80 | ~99.9th |
Important caveats
- IQ and T-scores are mathematically equivalent representations of the same standing on a normal distribution. The conversion is exact (T = (IQ − 100) / 15 × 10 + 50), not an estimate.
- Extreme-tail conversions are less reliable because both tests have fewer calibration cases there.
- No score entered here is stored, submitted, or connected to an account.
What is a T-score, and how does it relate to IQ?
A T-score is a standardized score with a mean of 50 and a standard deviation of 10, used widely across psychology and clinical assessment to place an individual result on a common, easy to read scale. A T-score of 50 marks the exact average of the reference population, while every 10 points represents one standard deviation away from that average. Because both T-scores and IQ scores (mean 100, SD 15) are standard scores built on the normal distribution, you can convert between them exactly through the percentile rank they share.
The T-score scale was designed to keep results positive and whole, avoiding the negative and decimal values of a raw z-score. It is the backbone of many of the most established instruments in the field, including the MMPI family of personality inventories, the BASC and Conners behavior rating scales, and a wide range of neuropsychological subtests. On this scale, a T of 50 is average, a T of 60 sits one standard deviation above the mean, and a T of 40 sits one standard deviation below. Clinicians often treat T-scores at or above 65 to 70 as the range warranting clinical attention, depending on the test. Converting a T-score to IQ is a pure linear standard score transformation, so the relationship is fixed and reliable rather than an approximation, as long as both scales describe the same underlying normal distribution.
How the IQ to T-score conversion actually works
Both IQ and T-scores are standard scores, which means each one expresses how far a result falls from its own average in standard deviation units. The conversion runs through a shared intermediate value called the z-score, the number of standard deviations from the mean.
The two formulas are simple and exact:
- z = (IQ minus 100) divided by 15
- T = 50 plus (z times 10)
Combined into a single step, T equals 50 plus (IQ minus 100) times 10 divided by 15, which simplifies to T = 50 plus (IQ minus 100) times two thirds. To go the other direction, IQ = 100 plus (T minus 50) times 15 divided by 10, or IQ = 100 plus (T minus 50) times 1.5.
Because the math is linear, there is no estimation or fudge factor. An IQ of 100 always equals a T of 50, and both always sit at the 50th percentile.
Reference points across the two scales
The table below shows matching values so you can sanity check any single conversion at a glance. Each row shares the same z-score and the same percentile rank, which is what makes the scales interchangeable.
Notice that a 15 point move on the IQ scale equals a 10 point move on the T scale, because 15 IQ points and 10 T points each represent exactly one standard deviation. That fixed ratio of 1.5 to 1 is the entire relationship between the two systems.
Where T-scores are used and why
T-scores dominate clinical and personality assessment because they keep scores positive, whole, and comparable across very different tests. A score of 65 on a depression scale and a 65 on an anxiety scale both mean the same distance above average, which makes profiles easy to read side by side.
Common instruments that report T-scores include:
- The MMPI and MMPI-2-RF personality inventories
- The BASC behavior assessment system for children
- The Conners rating scales for attention and behavior
- Many neuropsychological and memory subtests
IQ tests such as the Wechsler and Stanford-Binet scales instead use the mean 100, SD 15 metric, while their internal subtests often use scaled scores (mean 10, SD 3). Converting between T-scores and IQ lets you compare a clinical result against an intellectual benchmark on one common footing.
Frequently asked questions
What IQ does a T-score of 50 equal?
A T-score of 50 equals an IQ of exactly 100. Both are the average of their scales and both fall at the 50th percentile, so a T of 50 is the textbook definition of average performance.
What IQ does a T-score of 60 or 70 equal?
A T-score of 60 equals an IQ of 115, one standard deviation above average at roughly the 84th percentile. A T-score of 70 equals an IQ of 130, two standard deviations above average at about the 98th percentile. Each 10 point rise in T equals a 15 point rise in IQ.
How do I convert a T-score to IQ by hand?
Use IQ = 100 plus (T minus 50) times 1.5. For example, a T of 65 gives 100 plus 15 times 1.5, which is 100 plus 22.5, for an IQ of about 122. The reverse formula is T = 50 plus (IQ minus 100) times two thirds.
Is a T-score the same as an IQ score?
No. They measure on different scales. A T-score uses a mean of 50 and standard deviation of 10, while IQ uses a mean of 100 and standard deviation of 15. They are interchangeable through conversion because both are standard scores on the same normal distribution, but a raw T value is not an IQ number.
How accurate is the IQ to T-score conversion?
The conversion is mathematically exact, not an estimate, because both are linear standard scores tied to the same percentile. The only real limit is that any single test score carries measurement error, so the converted value is as precise as the original score it came from.
What is a high or clinically significant T-score?
On most clinical instruments, T-scores of 65 to 70 and above flag results that warrant attention, since they sit one and a half to two standard deviations above the mean. The exact cutoff depends on the specific test and what it measures.
Related tools
IQ percentile calculator · IQ to Z-score converter · IQ to Stanine converter · IQ score chart
Cite this converter
Editorial content and curation are released under CC BY-SA 4.0. This converter is part of the What's Your IQ educational resources.