The number-average functionality calculated by Carothers equation 𝑓 𝑏𝑟 ̅̅̅̅ ：The number-average functionality calculated by Eq. ( ) According to the comparison of Table , Eq.( ) can perfectly calculate the number-average functionalities of pre-polymers and intermediates especially for grafting or branched polymerization. The number-average functionality of thepolymer mixture (𝑓 ̅ ) can be calculated easily once the number and the functionality of component A and B are fixed. Similarly, the number of component A (𝑁 𝑎 ) can be calculated, when the number of component B (𝑁 𝑏 ) , the average functionality of the polymer mixture (𝑓 ̅ ), component A (𝑓 𝑎 ̅ ) and component B (𝑓 𝑏 ̅ ) are fixed. This equation can be used to predict the structure of Polyurethane prepolymers.