Let $(M^n,g(t))$, $t\in I$, be a smooth Ricci flow on a smooth manifold, where the statement is understood locally in space and time. Use the curvature convention $R^\ell{}_{ijk}=\partial_{x_j}\Gamma_{ik}^\ell-\partial_{x_k}\Gamma_{ij}^\ell+\Gamma_{jm}^\ell\Gamma_{ik}^m-\Gamma_{km}^\ell\Gamma_{ij}^m$ and $\operatorname{Ric}_{ij}=R^k{}_{ikj}$. Then the scalar curvature $S(t)$ satisfies

\begin{align*} \partial_t S=\Delta S+2|\operatorname{Ric}|^2. \end{align*}