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.