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Azhar Shahzad

Measurement of horizontal angle with Theodolite including example

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Angle measurement

For angle measurement with theodolite vertical hair is used. Basically there are two methods horizontal angle measurement,

  • Repetition method (For single angle)
  • Reiteration method (For more than one angle)

1 - By Repetition method

Let suppose it is desire to measure the angle A from the following figure. We will use repetition method for this purpose.


  • Setup the theodolite at station A.
  • Bisect the point B with vertical hair of theodolite and move telescope in clockwise and direction to bisect at point C.
  • Note this circle reading in the book and fix this circle reading, then again bisect the point B by keeping the circle reading fixed.
  • Now, release the circle reading and rotate the telescope again in clockwise direction till it bisect again point C.
  • Similarly get 3rd and 4th repetition and note the circle reading after 4th repetition in the book.
  • Change the face of telescope and repeat the above steps, an example and method of booking observations have given below,


Inst. Station Angle Face Repetition Circle Reading (° ′ ″) Angle value(° ′ ″) Mean of faces (° ′ ″)
A BAC L 1 25 20 00 25 20 10 25 20 9.5
      4 101 20 40
    R 1 25 20 03 25 20 09
      4 101 20 36


2 - By Reiteration method

This method is used if there are more than one angles to be measure from a certain station point. Consider the following fiqure, we will measure angles AOB and BOC using this method.



  • Setup the theodolite at station O, bisect the point A with a certain circle reading with face left.
  • Rotate the instrument in clockwise direction and bisect B, note the circle reading.
  • Then rotate and the telescope till it bisect the point C, note this circle reading also. All these reading will book into face left position.
  • Transit the telescope and rotate the instrument through 180°, this time bisect the point C firstly and then rotate telescope in anti clockwise direction towards B and then ultimately towards A. Put these readings in face right position.
  • You can do more than one sets of measurements for the accurate results, i have done one set and booking method is as follows,


Inst. Station Stn. Sighted Face Circle reading(° ′ ″) Mean of faces(′ ″) Angle value(° ′ ″)
O A L 10 20 05 20 06 AOB 37 10 05
    R 190 20 07
  B L 47 30 10 30 11
    R 227 30 12 BOC 41 10 14
  C L 88 40 20 40 25
    R 268 40 30


One should start observation with some initial circle reading say 25°, if we start our observation with zero circle reading our calculations for computing mean will be little bit difficult.

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Guest jydoskee

Thanks, your article helped but I still don't get how you got your "mean" values... Thanks in advance

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Guest robert

In 1, by repition method i understand how you got the mean of faces from the angle value, where how did you get the angle value? thanks

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