An estimation device calculates a first perpendicular vector and a second perpendicular vector. The first perpendicular vector is a component of a vector in a movement of a first position, which is a provisional pivot position of a surgical tool, the component being perpendicular to a direction of an axis of the surgical tool. The second perpendicular vector is a component of a vector in a movement of a second position of the surgical tool, the component being perpendicular to the direction of the axis. Then, a first distance, which is a length from a reference point on a rear end side or a reference point on a front end side of the surgical tool to the first position, is updated based on an inner product of the first and second perpendicular vectors.