IQ Percentile Calculator
An IQ score of 115 is about the 84th percentile on a mean-100, SD-15 scale. This IQ percentile calculator turns an IQ score into an approximate percentile by using a bell-curve model. Enter the score and choose the standard deviation used by your test, usually 15 or 16, to estimate what share of the reference group scored lower.
Quick answer
This tool assumes an IQ mean of 100.
What this tells you
- •This tool assumes an IQ mean of 100.
- •The percentile comes from a normal distribution, often called a bell curve.
- •Most modern IQ scales use SD 15, while some older or alternate norms use SD 16.
- •The result is an approximation, not an official score report.
How to Use
- 1Enter the IQ score you want to convert.
- 2Choose the standard deviation used by the test norm table if you know it.
- 3Calculate to see the approximate percentile, z-score, and the share of the group scoring lower.
- 4Use the result as a rough norm-reference estimate, not as a diagnostic or admissions decision.
How It Works
Formula
z = (IQ score - 100) ÷ standard deviation
Approximate percentile = standard normal CDF of z × 100The calculator first converts the IQ score into a z-score by comparing it with the fixed mean of 100. It then uses the standard normal curve to estimate how much of the reference group falls below that z-score. Because real test publishers may use their own age bands, norm samples, and rounding rules, the output is an approximation rather than an official percentile rank.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Common SD-15 example
The z-score is (115 - 100) ÷ 15 = 1.00. A z-score of 1.00 maps to about 84.1%, so roughly 84 out of 100 people in the reference group score lower.
Higher score on an SD-16 scale
The z-score is (130 - 100) ÷ 16 = 1.875. On a normal curve that is about the 96.96th percentile, which rounds to about the 97th percentile.
Common IQ Scores and Approximate Percentiles
These lookups assume a mean of 100 and an SD of 15.
| IQ score | Approximate percentile | Plain reading |
|---|---|---|
| 70 | 2.3% | About 2 out of 100 score lower |
| 85 | 15.9% | About 16 out of 100 score lower |
| 100 | 50.0% | About half score lower |
| 115 | 84.1% | About 84 out of 100 score lower |
| 130 | 97.7% | About 98 out of 100 score lower |
Percentiles shift slightly if the test uses SD 16 or publisher-specific norm tables.
Common mistakes
- Treating percentile as the percent of questions answered correctly
- Choosing SD 15 when the score report or manual is based on SD 16, or the other way around
- Reading a model-based percentile as an exact clinical, school, or employment decision threshold
Limitations
This calculator uses a simplified bell-curve model with a fixed mean of 100 and the standard deviation you choose. Real IQ tests may use age-specific norm tables, publisher-specific rounding, different composite scores, confidence intervals, and updated standardization samples. A percentile from this tool may not match an official report exactly.