To convert draw weight from pounds to the formula 1/2kx^2, use pounds-of-force directly with feet for x, resulting in energy measured in foot-pounds. For energy in Joules, convert pounds to Newtons using the conversion factor of 4.445 Newtons per pound and use meters for x. The discussion highlights the successful application of an alternative method involving arrow velocity to achieve the desired results. This approach demonstrates the flexibility in calculating energy based on different parameters. Understanding these conversions is essential for accurate energy calculations in archery.