Convert IQ ↔ Stanine
How the conversion works
IQ and Stanine 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.
- Stanine: 1-9 scale with mean 5 and standard deviation 2. Each stanine band covers a fixed percentile range of the normal distribution. Stanines were developed by the US Air Force during WWII as a single-digit format for cognitive testing.
IQ-equivalent = (target − meantarget) / SDtarget × 15 + 100
target-equivalent = (IQ − 100) / 15 × SDtarget + meantarget
Common IQ ↔ Stanine reference table
| IQ | Stanine | Percentile |
|---|---|---|
| 70 | 1 | bottom 4% |
| 80 | 2 | 4-11% |
| 90 | 4 | 23-40% |
| 100 | 5 | 40-60% |
| 110 | 6 | 60-77% |
| 120 | 7 | 77-89% |
| 130 | 8 | 89-96% |
| 140 | 9 | top 4% |
Important caveats
- Stanines are a coarser format than IQ; they round to one of 9 bands, so the conversion is approximate by design. The exact percentile-to-stanine cutoffs are defined by convention (4%, 7%, 12%, 17%, 20%, 17%, 12%, 7%, 4%).
- 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 stanine score, and how does it relate to IQ?
A stanine is a standard score on a simple 1-to-9 scale with a mean of 5 and a standard deviation of about 2, where stanine 5 marks the exact middle of the population (roughly the 40th to 60th percentile). Because both stanines and IQ scores are derived from the same normal distribution, every stanine band maps to a fixed percentile range, and that percentile maps directly to an IQ on the standard 100/15 scale. A stanine 5 lines up with an IQ near 100, while each step up or down shifts the IQ equivalent by roughly half a standard deviation.
The word stanine is a contraction of "standard nine," and the scale was created by the US Army Air Forces during World War II as a compact, single-digit way to report cognitive and aptitude results on punch cards. The nine bands are not evenly sized in population terms; they follow a bell-curve pattern that places about 4 percent of people in stanine 1, 7 percent in stanine 2, 12 percent in stanine 3, 17 percent in stanine 4, 20 percent in the middle stanine 5, then mirrors back down to 4 percent in stanine 9. Stanines are widely used in K-12 achievement and ability testing, school placement reports, and some military and occupational screening, because a 1-to-9 number is easy for parents, teachers, and counselors to read at a glance. Since IQ and stanines are both normal-curve standard scores, converting between them is a matter of matching one score's position on the curve to the other's, which is exactly what this free converter does instantly in both directions.
How the IQ to stanine conversion math works
Both scales describe the same thing, where a score sits on the normal distribution, just with different anchors. IQ uses a mean of 100 and a standard deviation of 15. The stanine uses a mean of 5 and a standard deviation of about 2. To convert, you translate the IQ into a z-score (how many standard deviations it is from the mean), then re-express that same z-score in stanine units.
The two core formulas are:
- Stanine = ((IQ - 100) / 15) x 2 + 5
- IQ = ((Stanine - 5) / 2) x 15 + 100
Because the stanine is rounded to whole numbers from 1 to 9, the result is intentionally coarse. A single stanine band covers a span of IQ points rather than a single value, so the converter reports the closest band and the percentile it represents.
IQ to stanine quick reference
This table shows where each stanine falls on the IQ scale and what slice of the population it captures. Stanine 5 is dead center, and the bands widen as you move toward the average and narrow at the extremes.
Values are rounded to whole IQ points. The exact cutoffs follow the standard 4, 7, 12, 17, 20, 17, 12, 7, 4 percentage convention used in education.
What stanines are good for, and where they fall short
Stanines are popular in schools because they smooth out the false precision of raw scores. A child who scores in stanine 6 one year and stanine 6 the next is performing consistently, even if the underlying raw numbers wobbled. That stability and the easy 1-to-9 format make stanines excellent for communicating results to non-specialists.
The tradeoff is resolution. Because each band lumps together a range of ability, two students in the same stanine can differ by several IQ points. The middle bands (4, 5, and 6) are also the widest, so most people land there and small differences get blurred. At the extreme tails (stanine 1 and 9) the conversion is less precise because both IQ and stanine tests have fewer calibration cases far from the mean. Use a stanine to understand a general standing, and a full-scale IQ or percentile when you need finer detail.
Frequently asked questions
What IQ does a stanine 5 equal?
A stanine 5 is the exact center of the scale and corresponds to an IQ of about 100, the population average. It covers roughly the 40th to 60th percentile, which on the standard 100/15 IQ scale spans about IQ 97 to 103. If your result is stanine 5, your measured ability is squarely in the average range.
What IQ is a stanine 9?
Stanine 9 is the top band, representing the highest-scoring 4 percent of the population, which is roughly the 96th percentile and above. On the standard IQ scale that translates to an IQ of about 126 or higher. Because the band is open-ended at the top, very high IQ scores all collapse into stanine 9, so the stanine cannot distinguish, for example, an IQ of 130 from an IQ of 150.
Is a stanine a good predictor of IQ?
A stanine derived from a well-normed cognitive or ability test is a direct, mathematically exact translation of an IQ percentile, so it reflects the same underlying standing on the bell curve. The limitation is resolution rather than accuracy: a stanine tells you which ninth of the population you fall in, not a precise IQ point. For a general read it is reliable, and for an exact figure you would use the full IQ score or percentile.
How accurate is converting an IQ to a stanine?
The conversion itself is exact because both scales sit on the same normal distribution, but the stanine output is deliberately coarse, rounding to one of nine bands. That means a single stanine covers a span of several IQ points. The middle bands are the widest, so most people share a stanine with others who differ slightly in IQ, and the tail bands are the least precise because there are fewer calibration cases there.
Why does the stanine scale only go from 1 to 9?
The scale was designed during World War II as a single-digit code that fit neatly on punch cards, which is why it stops at 9. Nine bands give enough spread to separate low, average, and high performers while keeping the format simple to read and report. The mean is fixed at 5 with a standard deviation of about 2, so the whole 1-to-9 range maps cleanly onto the bell curve.
Is stanine the same as percentile or IQ?
No, but all three describe the same standing in different units. A percentile tells you the exact share of people you scored above, an IQ expresses that standing on a 100/15 scale, and a stanine compresses it into a 1-to-9 band. This converter moves between IQ and stanine and also reports the matching percentile so you can see all three at once.
Related tools
IQ percentile calculator · IQ to Z-score converter · IQ to T-score 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.