A Calculator for Duration of Fat Loss

DISCLAIMER: THE INFORMATION ON THIS PAGE DOES NOT CONSTITUTE MEDICAL ADVICE AND AS SUCH, IS PRESENTED AS-IS, WITHOUT GUARANTEE OF ACCURACY.

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 -

  • My current (total) body weight: \(w_t\)
  • My current body fat percent: \(f_c\)
  • My current fat weight: \(w_f=\)\(f_c \over 100\)\(\times w_t\)
  • My current muscle weight: \(w_m = w_t - w_f\)
  • My goal body fat percent: \(f_g\)
  • The amount of weight I need to lose: \(l\) (This is what we need to find out)
  • Assuming I lose \(a\%\) from fat and the rest from muscle
    (and setting \(k=\)\(a \over 100\) for convenience)

  • Fat lost: \(kl\)
  • Muscle lost: \((1-k)l\)

    So,

  • My goal weight is \((w_t-l)\)
  • My goal fat weight is \((w_f-kl)\)

    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 (\(l_w\))