  Due to the high anticipated experimental precision at the Future Circular
Collider FCC-ee (or other proposed $e^+e^-$ colliders, such as ILC, CLIC, or
CEPC) for electroweak and Higgs-boson precision measurements, theoretical
uncertainties may have, if unattended, an important impact on the
interpretation of these measurements within the Standard Model (SM), and thus
on constraints on new physics. Current theory uncertainties, which would
dominate the total uncertainty, need to be strongly reduced through future
advances in the calculation of multi-loop radiative corrections together with
improved experimental and theoretical control of the precision of SM input
parameters. This document aims to provide an estimate of the required
improvement in calculational accuracy in view of the anticipated high precision
at the FCC-ee. For the most relevant electroweak and Higgs-boson precision
observables we evaluate the corresponding quantitative impact.
