A theodolite (or "transit") is an instrument for measuring both horizontal and vertical angles. It consists of a telescope mounted movably within two perpendicular axes, the horizontal or trunnion axis, and the vertical axis. These must be mutually perpendicular. The condition where they deviate from perpendicularity (and the amount by which) is referred to as horizontal axis error.

The optical axis of the telescope, called sight axis and defined by the optical center of the objective and the center of the cross-hairs in its focal plane, must similarly be perpendicular to the horizontal axis. If not, we call the deviation from perpendicularity collimation error.

Both axes of a theodolite are equipped with graduated circles that can be read out through microscopes. The vertical circle (the one associated with the horizontal axis!) should read 90° or 100 gon when the sight axis is horizontal (or 270°, 300 gon, when the instrument is in its second position, "turned over"). If not, we call half of the difference with 300 gon index error.

Horizontal axis error, collimation error and index error are regularly determined by calibration, and removed by mechanical adjustment at the factory in case they grow overly large. Their existence is taken into account in the choice of measurement procedure in order to eliminate their effect on the measurement results.