We express the entropy of a scalar field $\phi$ directly in terms of its spacetime correlation function $W(x,y)=\bra\phi(x)\phi(y)\ket$, assuming that the higher correlators are those of a"Gaussian state". The resulting formula associates an entropy $S(R)$ to any spacetime region $R$; and when $R$ is globally hyperbolic with Cauchy surface $\Sigma$, $S(R)$ can be interpreted as the entropy of the reduced density-matrix belonging to $\Sigma$. One acquires in particular a new expression for the entropy of entanglement across an event-horizon. Thanks to its global character, this expression makes sense in a causal set as well as in a continuum spacetime.