By using proton-proton collision data of the LHC Run 1, LHCb measured the forward-backward charge asymmetry for the process $\bar{q}q \to Z/\gamma^\ast \to \mu^+\mu^-$. We will present these results, which provide the most precise measurement of the effective electroweak mixing angle at the Large Hadron Collider. The measurement of the inclusive top, $W +b\bar{b}$, $W +c\bar{c}$ and $t\bar{t}$ production cross sections, also performed with LHCb Run 1 data, will be presented too.