THE CONVERSION TABLE
Every score from 55 to 160
IQPERCENTILERARITYBAND
16099.997th1 in 31,560Highly gifted+
15599.99th1 in 8,137Highly gifted+
15099.96th1 in 2,330Highly gifted+
14599.87th1 in 741Highly gifted+
14099.62nd1 in 261Gifted
13599.02nd1 in 102Gifted
13097.7th1 in 44Gifted
12595.2nd1 in 21Superior
12090.9th1 in 11Superior
11584.1st1 in 6High average
11074.8th1 in 4High average
10563.1st1 in 3Average
10050th1 in 2 (median)Average
9536.9th1 in 3Average
9025.2nd1 in 4Average
8515.9th1 in 6Low average
809.1st1 in 11Low average
754.8th1 in 21Borderline
702.3rd1 in 44Borderline
650.98th1 in 102Extremely low
600.38th1 in 261Extremely low
550.13rd1 in 741Extremely low
Percentile = Φ((IQ − 100) / 15) × 100, where Φ is the standard normal CDF. Rarity is the share at or above the score (at or below, under 100). The row matching the left converter is highlighted.
PERCENTILES PEOPLE ASK ABOUT
Reference points, with the score each one needs
WHY PERCENTILES BEAT RAW SCORES
Small gaps at the tails are huge in rarity
The same 15 points mean very different things depending on where they start. Pick a gap.
16.9×From 130 to 145 the share at or above shrinks 16.9 times, for the same 15 points. 1 in 44 becomes 1 in 741.
HOW ACCURATE IS A PERCENTILE?
It depends on where you sit
IQ 80–120Well calibratedAbout 80% of people. A measured 110 reliably corresponds to roughly the 75th percentile.
ABOVE 130ShakierStandardisation samples of 1,500–2,200 hold only about 30–50 people above 130: not enough to pin down 145 vs 150 vs 155.
ABOVE 160Largely theoreticalExtended norms reach further, but scores above 160 are extrapolated, not measured. Treat 180+ with extreme scepticism.
The curve is assumed normal by construction for roughly 70–130. Past about 145 or below 55, calibration samples are thin and real distributions may have slightly fatter tails.
WHERE PERCENTILE INTERPRETATION CAME FROM
1916Stanford-BinetTerman's normative sample: the historical foundation for IQ percentile tables.1918Army AlphaAbout 1.7 million WWI recruits showed test scores are roughly normal at population scale.1935Iowa TestsAnnual school administration built one of the largest cognitive norm datasets.1942AGCTGiven to about 12 million WWII service members.
QUICK ANSWERS
What does an IQ percentile mean?The share of the population scoring at or below you. The 98th percentile means 98 in 100 score lower.
How do I convert IQ to percentile?Use the normal CDF: Φ((IQ − 100)/15). Quick anchors: 70 ≈ 2nd, 85 ≈ 16th, 100 = 50th, 115 ≈ 84th, 130 ≈ 98th, 145 ≈ 99.9th.
Is the 99th percentile rare?Yes: 1 in 100, about IQ 135. The 99.9th (1 in 1,000) is about 146; the 99.99th about 156.
Why do other charts show different numbers?Rounding, a different SD (16 or 24), or simple errors. This chart computes every figure from the formula.