Hello my friend I want to know the procedure and calculation involved in finding the excluded angle by repetition method

my observations are here  for OAB

TOTAL STATION AT 'O'  SITE AT A  I SET MY ANGLE TO 0d0'0" then I turned to B my angle is 207d55'14"

then I hold the angle 207d55'14", again I site to A then I free the angle then I turned to B again, my angle is


like this I repeat 5 set of values they are

0d0'0"             first site at A







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I'm not sure exactly what you are asking. I don't see enough information to determine an excluded angle. In fact, unless I am mistaken, between point O, A, & B we can determine only one angle from this data.

From your description it sounds like you are operating the total station (a theodolite) like a transit with a Vernier, often called "winding up the angle". The total of the added angles is divided by the number of turns to arrive at the recorded angle.

I calculate the observation this way.
  000° 00' 00"
  207° 55' 14"
  415° 28' 58"
  623° 22' 09"
  831° 06' 18"
 1039° 01' 11"
  207° 48' 14" observed  ((1039° 01' 11")/5)
  000° 09' 17" Std. Dev.

(Note: the deviations between reading seems unusually varied with a standard deviation of over 9 arc minutes.)

A preferred method is to use the instrument as a directional theodolite. One doesn't "set" the backsight precisely but rather simply near zero, turn and record, then backsight near 90°, turn and record - repeat with backsights at 180° & 270°. Determine the magnitude of each turn by subtracting the backsight from the foresight and calculate a simple average of those.

Without a Vernier using the repeating method gains no precision. Using the recommended theodolite method compensates for eccentricities of the circle.

Had there also been distances measured one could calculate the triangle with one angle and two sides and from that result deduce the other two angles.


yes sir you are correct

please tell me how you calculated the observation and standard deviation

 000° 00' 00"
  207° 55' 14"
  415° 28' 58"
  623° 22' 09"
  831° 06' 18"
 1039° 01' 11"
  207° 48' 14" observed  ((1039° 01' 11")/5)
  000° 09' 17" Std. Dev. what calculation involved here sir.........

my raw data is

like this I repeat 5 set of values they are

0d0'0"             first site at A






What you are doing with the method of "winding up" the angle, is mechanically adding the second measurement to the first by holding the first reading and pointing at the backsight and measuring the angle again, &c.

I will make my example simpler by only using the degrees.

1) You started with 0° backsight and turned (almost) 208° to the foresight.

2) Then you backsighted with 208° and turned past 360° to 55° so adding 360°+55°=415°.

3) Then you backsighted with 415° and turned to 263° adding 360°+263°=623°.

4) Then you backsighted with 623° and turned past 360° a second time to 111° so adding 360°+360°+111°=831°.

5) Then you backsighted with 831° and turned to 319° adding 360°+360°+319°=1039°

So with 5 observations you measured a total of 1039° so 1039°/5=a little less than 208°.


thank you sir.....I got it

how to find standard deviation here sir

To get the standard deviation, I didn't do it manually, I used Excel.

I determined the magnitude of each observation by subtracting the first from the second, then the second from the third, &c.

Then, for ease of use in Excel, I converted them to decimal degrees. If I was doing it manually I would likely skip that step. Next, using Excel I applied the function for Average and, separately, the function StdDev. I converted the result back to  ° ' " and reported them to you.


P.S. There are many tutorials on the use of Excel. Very early-on one is introduced to the use of functions.

can u send me the excel file sir so I can refer it for my future use

thanks sir I checked it in excel I got the same answer you gived me



hello sir i am surveyor fikadu.T i have 2 years road & topographic surveying and also if can help me plc share me the file that helps to those surveying work like excel & software....? my email [email protected]

can u send me that excel file sir....?

[email protected] my email

just measuring angle between two points sir which are inaccessible and keep moving ,signal buoy in sea I need the location of about 5 to 7 meter accuracy so I decide to take average of the angles.......


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