Height of instrument = benchmark level + backsight; each point's level = HI − its staff reading. With BM 100.000 and a 1.250 backsight, HI is 101.250; readings of 1.800, 0.950 and 2.400 give levels of 99.450, 100.300 and 98.850, so B is 0.850 m higher than A.
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Formula
HI = RL(BM) + backsightRL(point) = HI − foresightDifference = RL(B) − RL(A) = FS(A) − FS(B)
Worked example
Point
Backsight
Foresight
HI
Reduced level
BM
1.250
101.250
100.000
A
1.800
99.450
B
0.950
100.300
C
2.400
98.850
B is 1.800 − 0.950 = 0.850 m higher than A.
Good levelling practice
Keep backsight and foresight distances roughly equal to cancel collimation error.
Read the staff vertically and to the nearest millimetre.
Close the run back on a benchmark and check the misclosure against your tolerance.
Frequently Asked Questions
How do you calculate level difference with a dumpy level?
Take staff readings at both points from the same instrument position. The difference in level is the difference between the readings: a smaller reading means a higher point.
What is the height of instrument method?
Add the backsight on a benchmark to the benchmark level to get the height of the instrument's line of sight, then subtract each foresight to get that point's reduced level.
What are backsight and foresight?
The backsight is the first reading taken on a point of known level (benchmark) from a set-up; foresights are readings on points whose levels you want.
