How Much Time is Required to Reach a Specific BF%?

I've long wondered this question so I thought I'd do some research based on past experiences and information given from various fitness outlets. I stumbled upon a good video by Vitruvian Physique that you can see here. I'm slightly adjusting his model to a more generalized format ... you'll see shortly. Note this method assumes you are at a higher BF% than the BF% you wish to achieve.


Generalized Declining Vitruvian Method


\begin{align*} &
(1) \Longrightarrow {\rm{Current \: Lean \: Body \: Mass }}: M_c \\&
(2) \Longrightarrow {\rm{Goal \: Lean \: Body \: Mass }}: M_g \\&
(3) \Longrightarrow {\rm{Goal \: Weight }}: W_g \\&
(4) \Longrightarrow {\rm{Time \: Required }}: T \\& \\&M_c = {\rm{\left( Current \: Weight \right)}} \left[ 1-0.01\left( {\rm{Current \: Body \: Fat \: Percent}} \right) \right] \\& \\& \\&M_g = M_c {\rm{\left( Retention \: Constant \right)}} \: ; \:
0.8 \leq {\rm{ Retention \: Constant }} \leq 0.97 \\& \\&\therefore M_g = {\rm{\left( Current \: Weight \right)}} \left[ 1-0.01\left( {\rm{Current\: Body \: Fat \: Percent}} \right) \right] {\rm{\left( Retention \: Constant \right)}} \\& \\& \\&W_g = \dfrac{M_g}{\left[ 1-0.01\left( {\rm{Goal \: Body \: Fat \: Percent}} \right) \right]} \\& \\&\therefore W_g = \dfrac{{\rm{\left( Current \: Weight \right)}} \left[ 1-0.01\left( {\rm{Current \: Body \: Fat \: Percent}} \right) \right] {\rm{\left( Retention \: Constant \right)}}}{\left[ 1-0.01\left( {\rm{Goal \: Body \: Fat \: Percent}} \right) \right]} \\& \\& \\&T = \dfrac{{\rm{\left( Current \: Weight \right)}} - W_g}{{\rm{\left( Declination \: Constant \right)}}{\rm{\left( Current \: Weight \right)}}} \: ; \: 0.005 \leq {\rm{\left( Declination \: Constant \right)}} \leq 0.01 \\& \\&\therefore \: T = \dfrac{1}{{\rm{Declination \: Constant}}}
\left[ 1 - \dfrac{W_g}{{\rm{Current \:Weight}}} \right] \\& \\& \\&\therefore \: T = \dfrac{
\left[ 1 - \dfrac{ \left[ 100-\left( {\rm{Current \: Body \: Fat \: Percent}} \right) \right] {\rm{\left( Retention \: Constant \right)}}}{\left[ 100-\left( {\rm{Goal \: Body \: Fat \: Percent}} \right) \right]} \right] }{{\rm{Declination \: Constant}}} \\&
\end{align*}


Retention and Declination Constants Explained


When in a caloric deficit the main concern for athletes is how much muscle they maintain AKA Retention Constant. It is statistically impossible to maintain much more than 97% of deficit prior LBM. Caloric deficits compounded with cardio heavy workouts can bring this retention all the way down to 80%, however if you know what you're doing you can usually maintain 90 - 95% of deficit prior LBM. So a good rule of thumb is to use 90 - 95% as the Retention Constant.

The Declination Constant refers to how quickly you want to lose Fat Mass in relation to your Starting Weight. A healthy boundary is 0.5 to 1% of Starting Weight per week for most people. This boundary usually takes the form of 0.5 - 2lb.'s per week lost and is within the CDC's guidelines for healthy weight loss.

To create shortest time required: high retention and declination.
To create longest time required: low retention and declination.

Note that the actual time frame itself is independent of any weights, rather it's based on the BF% and constants relative to your situation. Also, the result is in weeks, so if you want to have the answer in days multiply it by 7!

Example

The fastest someone at 18% can get to 10% realistically is in 81 days. If the goal was 12% it'd be 67 days. Comparatively, the slowest for those 2 situations: 380 and 320 days respectively.

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