How to Calculate Your IQ Percentile: Using the Normal Distribution and z-Scores

"What percentile is an IQ of 125?" You can work this out yourself using the properties of the normal distribution. It takes three steps.

Step 1: Compute the z-score

IQ is standardized to a normal distribution with a mean of 100 and a standard deviation of 15. So first calculate the z-score, which expresses how many standard deviations you are from the mean.

• z = (IQ − 100) ÷ 15

For an IQ of 125, z = (125 − 100) ÷ 15 = 1.67. For an IQ of 130, z = 2.00 — exactly two standard deviations.

Step 2: Read the percentile from the normal distribution

With z in hand, look up the cumulative probability Φ(z) — the proportion of people at or below that z — in a table or a spreadsheet. The top percentage is 1 − Φ(z). In a spreadsheet, use `=1-NORM.S.DIST(z, TRUE)`. For z = 1.67, that gives about the top 4.8%.

Step 3: Convert to '1 in how many people'

Turn the top percentage into a decimal and take the reciprocal. The top 4.8% (0.048) gives 1 ÷ 0.048 ≈ 21, or about 1 in 21 people. The main values are:

• IQ 110: top ~25% (about 1 in 4)
• IQ 115: top ~16% (about 1 in 6)
• IQ 120: top ~9% (about 1 in 11)
• IQ 125: top ~4.8% (about 1 in 21)
• IQ 130: top ~2.3% (about 1 in 44)
• IQ 135: top ~1.0% (about 1 in 102)
• IQ 140: top ~0.4% (about 1 in 261)
• IQ 145: top ~0.13% (about 1 in 741)
• IQ 150: top ~0.04% (about 1 in 2,330)

The full list for IQ 70–160 is on the IQ reference table, and population shares by band are in the IQ distribution data.

Converting to a deviation score

To convert to the Japanese deviation score (mean 50, SD 10), multiply z by 10 and add 50.

• Deviation score = 50 + (IQ − 100) ÷ 15 × 10

IQ 130 becomes 70; IQ 115 becomes 60. Note that a school deviation score reflects position within whoever sat that exam, so the same number can mean different things across populations. See converting between IQ and deviation scores.

Caution: not every test uses SD 15

Every calculation above assumes a standard deviation of 15. Some Stanford–Binet versions use 16 and Cattell-style tests use 24, so the same percentile prints a different IQ number. Before comparing figures from different sources, read the difference between IQ standard deviations of 15 and 16.

Prefer to skip the math?

NekoIQ's free IQ test runs this calculation for you: 20 questions in about 10 minutes give your estimated IQ, deviation score, percentile, and national ranking.