Fixed-budget theory is concerned with computing or bounding the fitness value achievable by randomized search heuristics within a given budget of fitness function evaluations. Despite recent progress in fixed-budget theory, there is a lack of general tools to derive such results. We transfer drift theory, the key tool to derive expected optimization times, to the fixed-budged perspective. A first and easy-to-use statement concerned with iterating drift in so-called greed-admitting scenarios immediately translates into bounds on the expected function value. Afterwards, we consider a more general tool based on the well-known variable drift theorem. Applications of this technique to the LeadingOnes benchmark function yield statements that are more precise than the previous state of the art.