Convert an IQ score to a percentile
Calculate a percentile under a normal distribution with mean 100 and a standard deviation of 15, 16, or 24.
Free, with no sign-up.
For Readers comparing IQ scoring scales.
About 2 minutes.
How does it work?
Enter a score from 40 to 160 and select the standard deviation used by the test. The mean stays at 100.
What will you get?
See the modeled percentile, the share scoring higher, and a rounded frequency.
What does this score mean in the model?
IQ score: 100; standard deviation: 15.
- Percentile
- 50%
- Share scoring higher
- 50%
- Frequency at or above this score
- About 1 in 2
These percentiles assume a normal distribution. They describe that mathematical model, not observed results from Lelfy visitors.
The calculation subtracts 100 from the score and divides by the selected standard deviation to obtain z. The normal cumulative distribution gives the share at or below that score.
The frequency uses the share at or above the score, with N rounded to the nearest whole number. For a continuous normal distribution, the share at an exact score is zero.
An online test is not a clinical assessment. Changing the standard deviation changes the scoring scale; use the scale stated by the test.
How do common scores compare?
This table uses the selected standard deviation of 15.
| IQ score | Percentile |
|---|---|
| 70 | 2.28% |
| 85 | 15.87% |
| 100 | 50% |
| 115 | 84.13% |
| 130 | 97.72% |
| 145 | 99.87% |