In tacheometry, horizontal and vertical distances are determined by angular observations with a tacheometer. Tacheometry is more accurate than the chaining/taping, and more rapid in rough and difficult terrain where levelling is tedious and measuring distance by chaining/taping is not only inaccurate but slow and laborious. It is a best suited method when taking observations for steep and undulating/broken ground, river, water or swampy areas. Tacheometry is preferably used for traversing, but it is also used for contouring.

The main instruments used in tacheometry are a tacheometer and a levelling rod. A tacheometer is a transit theodolite where the telescope is fitted with a special diaphragm, called stadia hairs, i.e., a diaphragm fitted with three horizontal hairs; one at the top, another in the middle and the third at the bottom of the diaphragm. These horizontal hairs are equidistant from the central one. The types of stadia diaphragm commonly used in tacheometers are shown in Figure 1.46. The term tacheometer is restricted to a transit theodolite which is provided with an anallactic lens in the telescope. The essential characteristics of a tacheometer are that the value of the multiplying constant (K= f / I) should be 100 and additive constant (C= f + d) should be zero. Levelling rod used is similar to those used in levelling work. To make the value of the additive constant zero, an additional convex lens, known as anallatic lens, is provided in the telescope. By having K=100 and C=0, the calculation work is considerably reduced.

The principle used in tacheometry is that the horizontal distance between an instrument station and a point where the levelling rod is kept can be determined with the staff intercept (difference of top reading and bottom reading). For determining the horizontal distance between two points, a tacheometer is kept at one point and levelling staff is kept at another, and stadia readings on the levelling staff are read.

In a simplified form, the above equation for horizontal distance (D) can be written as D = K S + C, where K is the multiplying constant (usually 100), S is the staff intercept and C is the additive constant (usually zero). There could be situations when the ground is undulating and the levelling staff is either above or below the line of sight. In such cases, a vertical angle subtended by the point at instrument station is also measured, in addition to stadia readings, to determine the horizontal distance using trigonometrical relationships.

In case the ground is undulating and horizontal sights are not possible, inclined sights are taken. In this case, the staff may be held either vertical or normal to the line of sight. In general, most commonly adopted method is when the staff is held vertical as it is simpler in calculation. When the staff is held vertically.