I have been known to do a lot of thinking. And it just so happens that today, I was *thinking* about going on a fat loss journey to get into a more healthy shape. So naturally, instead of heading to the gym, I decided to engage in some mathematical calculations, and some coding, to figure out how long it would take me to get that coveted six-pack of abdominal muscles. I have realized (mostly by glancing through several fitness articles online) that in order to get to a menacingly ripped physique, I cannot just focus on the goal weight. Because weight loss occurs from both muscle and fat, and I need to figure out how realistically I can cut my fat, while preserving some or most of my muscles. So, a goal *body fat percentage* is what I am trying to achieve. Let’s get into the math.

First, we identify some variables -

Assuming I lose \(a\%\) from fat and the rest from muscle

(and setting \(k=\)\(a \over 100\) for convenience)

So,

Therefore, we can say that

\(w_f-kl \over w_t-l\)\(=\)\(f_g \over 100\)

Solving for \(l\), and substituting values, we get

\(l=\)
\((\)
\(f_c-f_g \over a-f_g\)
\()\)
\(\times w_t\)

if my weight loss per week is \(l_w\), and \(n\) is the number of weeks needed, we have \(l=l_w \times n\), and finally get

\(n=\)
\((\)
\(f_c-f_g \over a-f_g\)
\()\)
\(\times\)
\(w_t \over l_w\)

Now let’s put this formula into action. (This will work for any unit of mass)

Current body weight (\(w_t\))

Current body fat percent
(\(f_c\))

Goal body fat percent (\(f_g\))

Fat loss percent (\(a\))

Weight lost per week (\(l_w\))