How to Calculate the RL by HI Method in Surveying.
In this article i will explain how to Calculate the RL by HI method in surveying, Let us consider an example as given below.
The leveling instrument was used to observe the subsequent readings.
0.450, 1.860, 2.755, 3.250, 3.675, 3.930, 0.885, 1.150, 1.945, 2.850, 3.635, 0.975, 1.950, & 2.585. The instrument was shifted after the Sixth and Eleventh readings. The elevation of the first reading was 480.65m. Calculate the RL of all the points by using the Height of instrument method.
Calculation.
As u can observe in the above drawing, the instrument is shifted after the Sixth and Eleventh reading.
So, first, seventh, and twelfth readings 👉 BS
Sixth, Eleventh, and 14th readings 👉 FS &
All of other remaining readings 👉 IS
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Please remember:
👉 While Surveying, the first reading becomes BS and the last reading becomes FS.
Note:

BS 👉 backsight.

FS 👉 foresight.

IS 👉 intermediate sight.

CP 👉 change point.

HI 👉 height of instrument.

RL 👉 reduced level.
Now, let us prepare the Height of the instrument table from the abovementioned data.
Following are the rules or formulas u should remember while calculating the RL in the height of the instrument method.
1 – HI = [RL + BS]
Whenever u get the BS reading, u have to calculate the height of the instrument in that particular change point. By adding the RL to the BS u will get the HI when u establish the instrument in the new change point.
2 – RL = [HI – IS or FS]
Once the height of the instrument is calculated, u have to deduct the IS & FS from the HI to calculate the RL of that particular station. This procedure should be continued until u get the new HI at the change point.
Keeping in mind, the above given formulas, let us start the calculation procedure.

First HI = [1st given RL + 1st BS] = [480.65 + 0.45] = 481.10

Second RL = [1st HI – First IS] = [481.10 – 1.860] = 479.240

Third RL = [1st HI – Second IS] = [481.10 – 2.755] = 478.345

Forth RL = [1st HI – Third IS] = [481.10 – 3.250] = 477.850

Fifth RL = [1st HI – Forth IS] = [481.10 – 3.675] = 477.425

Sixth RL = [1st HI – First FS] = [481.10 – 3.930] = 477.170
As u can observe in the belowgiven table, the IS And FS is deducted from the same HI until u shift the instrument & note down the new BS reading.
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Once u note down the BS reading for the change point, again u have to calculate the HI And by adding RL to the BS.

Second HI = [ 6th RL + 2nd BS] = [477.170 + 0.885] = 478.055

7th RL = [2nd HI – Fifth IS] = [478.055 – 1.150] = 476.905

8th RL = [2nd HI – Sixth IS] = [478.055 – 1.945] = 476.110

9th RL = [2nd HI – Seventh IS] = [478.055 – 2.850] = 475.205

10th RL = [2nd HI – Second FS] = [478.055 – 3.635] = 474.420
Again calculate HI for the 3rd BS

Third HI = [ 10th RL + Third BS] = [474.420 + 0.975] = 475.395

Eleventh RL = [3rd HI – Eighth IS] = [475.395 – 1.950] = 473.445

Twelfth RL = [3rd HI – Third FS] = [475.395 – 2.585] = 472.810
All the calculated values should be entered as shown in the belowgiven table.
Station 
BS 
IS 
FS 
HI 
RL 
Remark 
1  0.450  481.10  480.650  BM  
2  1.860  479.240  
3  2.755  478.345  
4  3.250  477.850  
5  3.675  477.425  
6  0.885  3.930  478.055  477.170  CP1  
7  1.150  476.905  
8  1.945  476.110  
9  2.850  475.205  
10  0.975  3.635  475.395  474.420  CP2  
11  1.950  473.445  
12  2.585  472.810  
Total Ʃ  2.310  10.150 
Arithmetic check
[∑FS – ∑BS] = [First RL – last RL] [∑FS – ∑BS] = [ 10.150 – 2.310] = 7.840 ✔ [First RL – last RL] = [ 480.650 – 472.810] = 7.840 ✔Hence, the calculation is the correct.