How to calculate height of instrument in surveying | BS, FS, IS

In this method, at first Height of the instrument is calculated for each set of the instrument by adding backsight (BS) to the elevation of the benchmark.

The height of the instrument is nothing but the reduced level of the top of the levelling machine. The top level of the levelling machine has been marked with scratch as shown in the figure below. Before calculating the height of the instrument in surveying, we should know some important terms used for levelling.

1) BS (Back Sight)

The first reading of staff in surveying taken by the first placing of levelling machine is known as back sight-reading. The staff is placed on the point whose benchmark is given. Like 100 m, 150 m from sea level.

2) IS (Intermediate Sight)

All the staff reading after BS and before FS in the surveying is known as Intermediate reading.

3) Fore Sight (FS)

The last reading of staff in surveying taken before replacing or changing the position of the tripod or levelling is known as fore sight-reading.

How to read Staff rod?

How to calculate height of instrument in surveying | BS, FS, IS

How to calculate height of instrument in surveying?

First of all, we should do temporary and permanent adjustments to the levelling. Let me tell you in short, temporary adjustment of the levelling is to level the tripod, horizontal and vertical centring etc. and Permanent adjustment of the level is to focus on the staff with telescope head.

How to calculate height of instrument in surveying | BS, FS, IS

Now, let us go through step by step procedures to calculate the height of the instrument.

1) fix levelling machine with accurate temporary and permanent adjustments.

2) Put the staff on the ground whose R.L.

3) Take a reading of staff with the help of levelling machine.

4) now apply the formula below to calculate the height of the instrument.

5) Now, take further reading as I.S and FS. to complete the survey.

So, Height of instrument = R.L + Staff Reading

or, RL = HI – FS

or, RL = HI – IS

Where HI is the height of the instrument.

Let us take an example,

The Known R.L of the ground on which we put staff to be 100. m. and the staff reading is 1.5 meters. Then we have a height of the instrument will be R.L + Staff reading. i.e = 100 + 1.5 m = 101.5 meter.


Different readings were taken with the help of a 4-meter levelling staff rod and levelling machine continuously sloping the ground at 30-meter intervals. The value of the benchmark is 520.450 meters. The first reading of staff at point A is 0.585 meters. 0.936, 1.953, 2.846, 3.644, 3.938, 0.962, 1.035, 1.689, 2.534, 3.844, 0.956, 1.579, 3.016 on B. Apply usual Check.



1) HI  = RL + BS

=  520.450 + 0.585

HI  =  521.035 meter @A

2) RL = HI – IS

RL = 521.035 – 0.936

RL = 520.099 meter @30 m

3) RL = HI – IS

RL = 521.035 – 1.953

RL = 519.082 meter @60 m

Follow the similar steps.

Now, Arithmetic  Check

∑ BS – FS = Last RL – First RL

2.503 – 10.798 =  512.155 – 520.450

– 8.295 = – 8.295 (OK)

I hope this article remains helpful for you.

A00.585  521.035520.450Bench-Mark
 30 0.936 521.035520.099 
 60 1.953 521.035519.082 
 90 2.846 521.035518.189 
 120 3.644 521.035517.391 
 1500.962 3.938518.059517.097CP1
 180 1.035 518.059517.024 
 210 1.689 518.059516.370 
 240 2.534 518.059515.525 
 2700.956 3.844515.171514.215CP2
 300 1.589 515.171513.592 
B330  3.016 512.155 

Happy learning – Civil concept

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