When the measurements from the FCC-ee become available, an improved determination of the standard-model “input” parameters will be needed to fully exploit the new precision data towards either constraining or fitting the parameters of beyond-the-standard-model theories. Among these input parameters is the electromagnetic coupling constant estimated at the Z mass scale, $(m^2_{\rm Z})$. The measurement of the muon forward-backward asymmetry at the FCC-ee, just below and just above the Z pole, can be used to make a direct determination of $(m^2_{\rm Z})$ with an accuracy deemed adequate for an optimal use of the FCC-ee precision data.