Quadcopters are increasingly popular for robotics applications. Being able to efficiently calculate the set of positions reachable by a quadcopter within a time budget enables collision avoidance and pursuit-evasion strategies.This paper examines the set of positions reachable by a quadcopter within a specified time limit using a simplified 2D model for quadcopter dynamics. This popular model is used to determine the set of candidate optimal control sequences to build the full 3D reachable set. We calculate the analytic equations that exactly bound the set of positions reachable in a given time horizon for all initial conditions. To further increase calculation speed, we use these equations to derive tight upper and lower spherical bounds on the reachable set.