The formula to calculate your Max Weighted Pull-Up (MWP) is:
\[ MWP = BW - \left( BW \times \frac{100}{100 - R \times 2.75} \right) \]
Where:
The Max Weighted Pull-Up (MWP) is a measure of the maximum additional weight you can pull during a one-rep max pull-up. This calculation helps you estimate how much extra weight you could handle for a single pull-up, based on your body weight and the number of unweighted reps you can perform. This formula provides a fairly accurate estimate up to around 25-30 reps.
Let's consider an example:
Using the formula to calculate the Max Weighted Pull-Up (MWP):
\[ MWP = 180 - \left( 180 \times \frac{100}{100 - 10 \times 2.75} \right) \approx 180 - \left( 180 \times \frac{100}{72.5} \right) \approx 180 - 248.28 = -68.28 \, \text{lbs} \]
In this case, the formula gives a negative result, which indicates that the person should be able to do the pull-up without additional weight with room to spare. However, in practical terms, this means you can handle more weight than body weight alone (so the formula would need to be adjusted or interpreted carefully).