The Gunning fog index uses a formula involving complex words, defined as words with three or more syllables, to estimate the number of years of education required for a reader to understand a text. Robert Gunning developed the index in 1952, using the below formula.

$$0.4\left[ \left(\frac{\text{words}}{\text{sentences}}\right) + 100\left(\frac{\text{complex words}}{\text{words}}\right) \right]$$

Gunning fog index scores correspond roughly to US grade levels, meaning that a higher index indicates a more difficult text. For example, an index of 6 corresponds to 6th grade and an index of 15 corresponds to a university junior.