We present efficient algorithms for approximately answering distance queries in disk graphs. Let G be a disk graph with n vertices and m edges. For any fixed ε > 0, we show that G can be preprocessed in O(m√nε-1 + mε-2 log S) time, constructing a data structure of size O(n3/2ε-1 + nε-2 log S), such that any subsequent distance query can be answered approximately in O(√nε-1+ε-2log S) time. Here S is the ratio between the largest and smallest radius. The estimate produced is within an additive error which is only e times the longest edge on some shortest path. The algorithm uses an efficient subdivision of the plane to construct a sparse graph having many of the same distance properties as the input disk graph. Additionally, the sparse graph has a small separator decomposition, which is then used to answer distance queries. The algorithm extends naturally to the higher dimensional ball graphs.