  We provide very effective methods to convert both asymptotic and explicit
numeric bounds on the prime counting function $\psi(x)$ to bounds of the same
type on both $\theta(x)$ and $\pi(x)$. This follows up our previous work on
$\psi(x)$ in \cite{FKS}, and prove that $ | \pi(x) - \mathrm{Li}(x) | \leq
9.2211\, x\sqrt{\log(x)} \exp \big( -0.8476 \sqrt{\log(x)} \big) $ for all
$x\ge 2$. Additionally, we are able to obtain the best numeric bounds for $x$
on a very large interval (all $x$ up to $\exp(1.8\cdot10^9)$).
