There are countless models, from different perspectives (theory/econometric/etc.) on price impact of trade volume. The seminal model in market microstructure---the Kyle model (85 Econometrica) addresses this very issue. There are many descendents of this model.
To demand a "formula" is a little simplistic. The usual framework for these models, if micro-founded, is strategic. The price impact is a property of the resulting game-theoretic equilibrium. In the Kyle model, one has
\Delta p = \lambda\cdot Q
where $\Delta p$ is the price adjustment of market maker when the incoming total order flow is (only market orders are considered) $Q$. The coefficient $\lambda$ (Kyle's lambda) is a measure of price impact, and is determined by the severity of the adverse selection problem faced by the market maker.