# Estimating Fitness Levels: FFMI Method

I recently discovered the Fat Free Mass Index a couple of days ago. I actually have to thank the YouTube Algorithm for suggesting another video series by Vitruvian Physique on distinguishing whether or not someone is "natty" or not. I did a good bit of research investigating it and found that these 4 articles summarize the pro-cons of the method the best IMO:

If you want to see the academic article that spurned this whole operation here's the link. Anyways, here's the formula:

\begin{align*} \rm
FFMI & = \dfrac{ FFM_{kg} }{ (Height_m)^2 } \\& \\& =
\left[ \dfrac{ 0.45359237 }{ (0.0254)^2 } \right]
\dfrac{ FFM_{lb} }{ (Height_{in})^2 } \\& \\& \approx
703.07\left[ \dfrac{ FFM_{lb} }{ (Height_{in})^2 } \right]
\end{align*}

\begin{align*}
\rm{ Normalization \: Correction} & =
6.3(1.8- \rm{H_m}) \\& \\& \approx
0.16(70.87 - \rm{H_{in}})
\end{align*}

\begin{aligned}
\rm{ Height \: Normalized \: FFMI = FFMI - Normalization \:Correction}
\end{aligned}

If you want to get some perspective on what the values mean I suggest watching these videos. Specifically the third one as he graphically depicts his views (occurs right after 5:00).

## Maximum FFM

The study clearly indicates 25 as being the maximal index. I went ahead and did some math to figure that equation out. As you can see from:

https://www.wolframalpha.com/input/?i=25%3D(0.45359237%2F(0.0254%5E2))*W*(H%5E(-2))-(6.3)(0.0254)(1.8%2F0.0254+-H),+solve+for+W

the equation stands at:

\begin{align*}
W_{lb} & = (H_{in})^2 (0.0516876 - 0.000227602 (H_{in})) \\& \\& \approx (H_{in})^2 (0.0517 - 0.00023(H_{in}))
\end{align*}

Therefore the maximum weight as predicted by the FFMI at a specific BF% is found via:

\begin{align*}
W_t & =\dfrac{W_{lb}}{1-0.01(\rm{Body \: Fat \: Percentage})} \\& \\& \approx
\dfrac{(H_{in})^2 (0.0517 - 0.00023(H_{in}))}{1-0.01(\rm{Body \: Fat \: Percentage})}
\end{align*}

You can compare this to another estimate I modeled off of
Martin Berkhan found below. In general, from quick comparison the FFMI method gives a higher maximum result.

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