For synthetic polymer, the weight average molecular weight will be

M_n​, the number average molecular weight, is calculated from the mole fraction distribution of different sized molecules in a sample, and M_w​, the weight average molecular weight, is calculated from the weight fraction distribution of different sized molecules.

$$\begin{gathered} {\mathrm{M}}_{\mathrm{w}}=\sum _{ }{\mathrm{W}}_{\mathrm{i}}{\mathrm{M}}_{\mathrm{i}}=\frac{\sum _{ }{\mathrm{N}}_{\mathrm{i}}{\mathrm{M}}_{\mathrm{i}}^2}{\sum _{ }{\mathrm{N}}_{\mathrm{i}}{\mathrm{M}}_{\mathrm{i}}} \left(\mathrm{Wi}=\frac{{\mathrm{N}}_{\mathrm{i}}{\mathrm{M}}_{\mathrm{i}}}{\sum _{ }{\mathrm{N}}_{\mathrm{i}}{\mathrm{M}}_{\mathrm{i}}}\right) \\ {\mathrm{M}}_{\mathrm{n}}=\frac{\sum _{ }{\mathrm{N}}_{\mathrm{i}}{{\displaystyle \stackrel{-}{\mathrm{M}}}}_{\mathrm{i}}}{\sum _{ }{\mathrm{N}}_{\mathrm{i}}} \end{gathered}$$

Here, N_i is the number of molecules, M_i is the weight of the sample polymer, and W_i is the weight average of each molecule.

M_w is always greater than M_n.