  We study different operator radii of homomorphisms from an operator algebra
into $B(H)$ and show that these can be computed explicitly in terms of the
usual norm. As an application, we show that if $\Omega$ is a $K$-spectral set
for a Hilbert space operator, then it is a $M$-numerical radius set, where
$M=\frac{1}{2}(K+K^{-1})$. This is a counterpart of a recent result of
Davidson, Paulsen and Woerdeman. More general results for operator radii
associated with the class of operators having $\rho$-dilations in the sense of
Sz.-Nagy and Foias are given. A version of a result of Drury concerning the
joint numerical radius of non-commuting $n$-tuples of operators is also
obtained.
