A system and method for determining an elevator car position uses position markers situated in the elevator shaft and each assigned a discrete car position, first and second detection devices on the elevator car detecting first and second position markers respectively, and an evaluation unit that determines first and second discrete car positions based on the detected first and second position markers respectively. A single interpolation device of the position determining system determines first and second interpolated car positions. The evaluation unit determines first and second car positions based on the first and second discrete car positions and the first and second interpolated car positions respectively. The interpolation device generates an interpolation parameter that characterizes a position of the first detection device relative to the first position marker and determines the first and second interpolated car positions on the basis of the interpolation parameter.