IIF Certified Assessment
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IIF Certified Assessment
Drag anywhere on the curve. Switch to compare mode to see what sits between two scores — and whether the gap between them is real.
Drag on the chart to move the marker. Hover to read any point.
| Range | Share of people | Note |
|---|---|---|
| 85 – 115 | 68.3% | One SD either side of the mean |
| 70 – 130 | 95.4% | Two SD |
| 55 – 145 | 99.7% | Three SD — the reportable range |
| 100 – 110 | 24.8% | A 10-point gap at the middle |
| 120 – 130 | 6.8% | The same 10 points, at the shoulder |
| 135 – 145 | 0.8% | The same 10 points, in the tail |
Set two scores to compare them.
You can read the curve. Can you place yourself on it? The distribution above is fixed — it is the same shape for everyone. The only variable is where your marker sits, and that depends entirely on the quality of the test that put it there.
The curve is steepest in the middle, which is why most people cluster there and why the same number of IQ points means less and less as you move outward.
68.3% of people. One standard deviation either side of the mean. Two thirds of the population sits inside this 30-point stretch.
95.4% of people. Two standard deviations. Almost everyone you will ever meet scores somewhere in this range.
2.3% of people, about 1 in 44. This is where high-IQ societies set their thresholds — Mensa uses the 98th percentile.
2.3% of people. A single online result at this level says very little on its own and should never be treated as a diagnosis.
About 1 in 741. Past this point the curve is extrapolation — real tests have too few people at the extremes to measure it reliably.
IQ 100 is the 50th percentile by construction. Tests are standardised so the population mean is fixed at 100, at every age.
Because the curve is not flat, an identical gap covers a completely different share of people depending on where it sits.
Ten points near the middle separates a quarter of everyone. The same ten points out at the edge separates fewer than one person in a hundred. It is the same distance on the number line and a completely different distance in the population.
Knowing that 68% of people fall between 85 and 115 is genuinely useful — right up to the moment you want to know where you fall. That single question is the one a distribution cannot answer on its own. It needs a measurement, and the measurement needs to have been taken properly.
Scored on the standard scale — mean 100, standard deviation 15 — the scale this curve is drawn on.
Because IQ tests are deliberately built that way. Raw scores are converted so the population mean sits at 100 and the spread follows a normal distribution with a standard deviation of 15. The bell shape is a property of how the scale is constructed, not a discovery about the brain. How IQ tests work explains how raw answers become a normed score.
About 68.3% of people score between 85 and 115, which is one standard deviation either side of the mean. Roughly 95.4% score between 70 and 130, and about 99.7% between 55 and 145. The IQ percentile calculator converts any score into its exact share of the population.
Because the curve is tallest in the middle. Moving from 100 to 110 passes 24.8% of the population, while moving from 135 to 145 passes only 0.8%. The same distance on the scale covers a very different share of people depending on where it sits. The IQ comparison tool puts a number on how much a given gap is worth.
Usually not. Because every score carries measurement error, two results only differ reliably when the gap is larger than about 1.96 times the standard error of the difference. On a test with a reliability of .90 that threshold is roughly 13 points, so a 10-point gap is within the range you would expect from noise alone. The IQ comparison tool runs that test for any two scores.
Because beyond roughly three standard deviations the normal curve is being extrapolated rather than measured. Standardisation samples contain very few people at the extremes, so rarity figures past that point describe the mathematical model and not an observed count. The IQ score converter shows how the same tail looks on SD 15, SD 16 and Cattell III B.
Not exactly. The scale is constructed to be normal, and it fits well through the middle, but the lower tail carries more very low scores than the model predicts because some causes of severe impairment sit outside normal variation. Treat the curve as a good working model rather than a literal description. Our page on how accurate IQ tests are covers where the model stops being reliable.
The percentile is simply the area of the curve to the left of your score. IQ 100 is the 50th, 115 the 84th, 130 the 97.7th. It is the one figure that stays identical no matter which scale the test used, which makes it the safest number to quote. The IQ percentile calculator gives it exactly for any score.
Usually they do not — the point is the same and only the label changed. A score of 130 on an SD 15 test and 148 on Cattell III B are the identical position on this curve, because the two tests chose different sizes for one standard deviation. The IQ score converter moves a number between scales so you can see the marker stay put.
Your position is always measured against people your own age, so the curve itself never moves — the norm group underneath it does. Fluid abilities drift down with age while crystallised ones hold or climb, which can leave a composite score remarkably stable. IQ and age shows how the underlying abilities separate.
Take the assessment to get a measured score, its percentile, and where it actually falls on this distribution.
