Most of pipelines are installed under the ground, so maintaining is one of the most critical issue. Furthermore, their own locations are difficult to be identified because of its environment. For those reason, identifying the location of pipelines is widely under the research with in-pipe robots. Most methods estimate the heading direction of pipe robots as the axial direction of pipelines. However, more detail research about the axial directions of pipelines is necessary because the defined directions are not always aligned with the heading direction of pipe robot. Therefore, this paper described the estimating method of pipeline radius and its axial direction relative the robot. The relative direction and radius of a pipe are estimated from location of contact points which is determined based on geometry. Geometric equation contains highly nonlinear term, so those are obtained by the numerical form instead of closed form. The suggested method is verified by an experiment approach. Since the real relative axial direction is hard to detect, the slope of pipes are computed from estimated value and inertial measurement unit attached to the robot. Estimated radius and slope have some error in discrete curved pipe, but estimated values are well matched under straight pipes condition.