There are two ways to calculate the coupling constant of the weak interaction $g$.

1. From the electromagnetic coupling constant and the weak mixing angle, using the relation $${\sf e} = g\sin(\theta_W)$$ where ${\sf e}=\sqrt{4\pi\alpha}$ is the elementary electric charge in natural units ($\alpha$ being the fine structure constant). Using the CODATA values of $\sin^2(\theta_W)=0.2223$ and $\alpha=7.297\cdot 10^{-3}$ this gives $$g=0.641.$$
2. From the definition of the Fermi coupling constant $$G_F = \frac{\sqrt{2}}{8}\frac{g^2}{m_W^2}$$ where $m_W$ is the mass of the W boson. Using the CODATA value of $G_F=1.166\cdot 10^{-5}\;{\rm GeV}^{-2}$ and the PDG value of $m_W=80.385\;{\rm GeV}$ this gives $$g=0.653.$$ The difference is not big but nonetheless is significant. How can this be explained, since all the parameters used in the calculation are known with high precision?