The Ketogenic Index Formula and the Top 1000 Ketogenic Foods

Imagine a three-dimensional space where the three axes are the three macronutrients: protein, carbohydrates, and fat.

Every food can be represented by a point in this space with coordinates $(p, c, f)$, where $p$ is the protein, $c$ is the carbohydrate, and $f$ is fat content of the food.

The Macronutrient Index $MI$ is defined as the Euclidean distance between a food's coordinates and those of a point representing the "optimal" macronutrients $(P, C, F)$.

\[ MI_{(P, C, F)}(p, c, f) = \sqrt{ (p - P) ^ 2 + (c - C) ^ 2 + (f - F) ^ 2 } \]

If $(P, C, F)$ is expressed as gram ratios (like $(0.20,0.30,0.50)$ for example), and $(p, c, f)$ is expressed as grams in a 100 gram portion of a food, then the formula for $MI$ becomes \[ MI_{(P, C, F)}(p, c, f) = \sqrt{ \left(\frac{p}{100} - P\right) ^ 2 + \left(\frac{c}{100} - C\right) ^ 2 + \left(\frac{f}{100} - F\right) ^ 2 } \]

Because we are only considering ratios of macronutrients, we can exclude water $w$ from the 100 gram food portion and arrive at the final fomula:

\[ MI_{(P, C, F)}(p, c, f, w) = \sqrt{ \left(\frac{p}{100 - w} - P\right) ^ 2 + \left(\frac{c}{100 - w} - C\right) ^ 2 + \left(\frac{f}{100 - w} - F\right) ^ 2 } \] \[ \begin{align} MI_{(P, C, F)} &: \text{Macronutrient Index} \\ P &: \text{optimal protein ratio, } & 0.0 \le P \le 1.0 \\ C &: \text{optimal carbohydrate ratio, } & 0.0 \le C \le 1.0 \\ F &: \text{optimal fat ratio, } & 0.0 \le F \le 1.0 \\ & & P + C + F = 1.0 \\ p &: \text{grams of protein per 100 gram portion, } & 0 \le p \le 100 \\ c &: \text{grams of carbohydrate per 100 gram portion, } & 0 \le c \le 100 \\ f &: \text{grams of fat per 100 gram portion, } & 0 \le f \le 100 \\ w &: \text{grams of water per 100 gram portion, } & 0 \le w \le 100 \\ & & p + c + f + w \le 100 \\ \end{align} \]

Note: Because $MI$ is a measure of distance to the optimal point, the closer to zero the better.