A position measuring apparatus includes a holder having storage spaces in which a three-point support member for supporting a backside of a substrate being a mask at three points, and a vacuum chuck member for holding a backside of a substrate being a mask are prepared, a stage on which one of the three-point support member and the vacuum chuck member prepared in the storage spaces of the holder is mounted, a vacuum pump to hold and chuck the substrate through the vacuum chuck member in a state of being mounted on the stage, and a recognition unit to recognize a position of a pattern written on the substrate supported by the three-point support member mounted on the stage and a position of a pattern written on the substrate held by the vacuum chuck member on the stage.