# 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 ($$l_w$$)