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TRIGONOMETRIC LEVELING
Trigonometric leveling or indirect leveling is defined as the determination of differences in
elevation from observed vertical angles and either horizontal or inclined distances.
The figure below illustrates a typical setup for trigonometric leveling where the observed
vertical angle is  and the known horizontal and inclined distances, measured in meters, are
d and s, respectively.
The height of the instrument above point A is denoted as h.i., and the reading on the rod
held at the distant point B is RR. The vertical distance, V, could be determined in two ways
as follows:
V = d tan 
or V = s sin 
Eq. (1)
Eq. (2)
The difference in elevation between A and B may be determined by any of the following
equations
DEab = V  h.i. – RR
Eq. (3)
If the elevation of A is known, the elevation of B can then be determined as follows:
Elev B = Elev A + DEab
Eq. (4)
When trigonometric leveling is employed in much longer sights, the slope distance is
measured using EDM instruments and precise optical theodolites are utilized for measuring
vertical angles. Also, the correction for the combined effects of curvature and refraction is
added when the vertical angle is an upward sight; it is subtracted when downward sight is
observed. That is
Upward sight
DEab = V + h.i. – RR + hcr
Eq. (5)
Downward sight
DEab = V – h.i. – RR – hcr
Elementary Surveying Notes of AM Fillone
Eq. (6)
Upward line of sight
RR
B
s
V
D.E.ab

h.i.
A
d
Elev. B
Elev. A
Datum
Downward line of sight
d

h.i.
A
s
V
DEab
RR
B
Elev. A
Elev. B
Datum
Elementary Surveying Notes of AM Fillone