How to Convert Between IQ and Deviation Score: Formula and Chart

Many people wonder how IQ differs from the deviation score used in schools, or what their IQ becomes when expressed as a deviation score. In fact, both are indicators of your relative position within a group, and you can convert between them with a simple calculation. This article lays out the relationship between IQ and the deviation score, the conversion formula, and quick reference values, without exaggeration.

Both IQ and the deviation score are relative indicators

Neither IQ nor the deviation score measures an absolute amount of ability; both express where you sit relative to others in the same group. The only difference is how the scale is anchored. IQ is conventionally expressed on a normal distribution with a mean of 100 and a standard deviation of 15, while the deviation score uses a mean of 50 and a standard deviation of 10. For the underlying idea of the distribution, see our explanation of average IQ and the distribution.

The formula: deviation score = 50 + (IQ - 100) / 15 * 10

Since both simply express the same normal distribution on different rulers, you can convert with this formula: deviation score = 50 + (IQ - 100) / 15 * 10. To go the other way, from deviation score back to IQ: IQ = 100 + (deviation score - 50) / 10 * 15. In short, you first work out how many standard deviations you are from the mean, then re-apply that to each scale.

Worked example: IQ 130 equals a deviation score of 70

Let us plug the numbers in. For IQ 130: 50 + (130 - 100) / 15 * 10 = 50 + 2 * 10 = 70, so it corresponds to a deviation score of 70. That is +2 standard deviations from the mean, roughly the top 2% (about 1 in 50). Check the position on the IQ 130 reference page and the shape of the distribution in the IQ distribution data. Likewise, IQ 120 is about a deviation score of 63, and IQ 115 is a deviation score of 60.

Quick reference values

To list some representative pairings: IQ 85 is a deviation score of 40, IQ 100 is 50, IQ 115 is 60, IQ 130 is 70, and IQ 140 is about 77, not 67 (50 + 40 / 15 * 10). Because the standard deviations differ, IQ tends to look like it moves more for the same relative gap. You can review the relative position of each IQ score together in the IQ reference chart.

Things to watch when converting

Keep in mind that the conversion is only a mathematical substitution that assumes the same normal distribution. School deviation scores shift their baseline depending on the group that took the exam, and IQ tests themselves use subtly different rulers depending on the test type and the year of standardization. You cannot simply convert and compare scores from different tests or different populations. We publish how scores are estimated on the methodology page. These are also relative guides, not a medical diagnosis.

If you would like to know where you currently stand on both IQ and the deviation score, try the free IQ test to see your estimated IQ, deviation score, and percentile together.