Precise prediction for the W boson mass in U(1) extensions of the standard model

We present the one-loop correction to the $W$ boson mass in U(1)${}_z$ type extensions of the standard model. We compare it to an approximation, often used in high energy physics tools. We point out that if the $Z^{\mathrm{\prime }}$ boson – predicted in U(1)${}_z$ type extensions – is much heavier than the $Z$ boson, then the use of the complete set of one-loop corrections is necessary.