Determining geometric data of a conical measurement object comprises determining spatial coordinates at a plurality of measurement points of the measurement object. At least six spatial coordinates are determined on at least six different measurement points. Element parameters of a tangential conical substitute element are determined by means of a system of equations which describes difference values between the spatial coordinates and the tangential conical substitute element. The difference values are modeled by means of at least two difference parameters whose sum represents a perpendicular spacing between the tangential conical substitute element and a spatial coordinate. Geometric data of the conical measurement object is determined using the substitute element.