TI-60 and HP 65: Distance by Stadia Tacheometry
Introduction
The stadia calculation measures the distance from the level or theodolite (measuring device) to a graduated staff. Two readings are taken from the graduated staff, an upper reading (UR) and a lower reading (LR). The word tacheometry means "swift calculation". The distance between the theodolite and the staff is calculated as:
dist = k * s
k = is a factor taken of a radius of focal distance over image distance. Typically, k is set to 100, and will be assumed that k = 100 for these programs.
s = the difference between the upper reading and lower reading on the graduated staff. (UL - RL). The readings are assumed to be in meters.
If the theodolite is tilted at angle α, known as the vertical angle, then the distance becomes:
dist = k * s * cos² α
α is usually given in degrees-minutes-seconds and must be converted to decimal degrees.
TI-60 Program: Stadia Tracheotomy
Store before running: R1: UR (m), R2: LR (m), R3: α (D.MMSS)
Code:
00: 1 ; 01
01: 0 ; 00
02: 0 ; 00
03: × ; 65
04: ( ; 53
05: RCL; 71
06: 1 ; 01
07: - ; 75
08: RCL; 71
09: 2 ; 02
10: ) ; 54
11: × ; 65
12: RCL; 71
13: 3 ; 03
14: DMS-DD; 39
15: cos; 33
16: x²; 96
17: = ; 95
18: R/S; 13
19: RST; 22
HP 65 Program: Stadia Tracheotomy
Input Stack:
Z: vertical angle in degrees-minutes-second (V.MS)
Y: upper reading (UR)
X: lower reading (LR)
Code:
23: LBL
14: D
51: -
02: 2
32: f^-1
08: LOG (10^x)
71: ×
35 07: x<>y
32: f^-1
03: →D.MS (→DD)
31: f
05: COS
32: f^-1
09: √ (x²)
71: ×
24: RTN
Examples
Example 1:
V: 1°05' (Z stack, R3)
UR: 2.014 m (Y stack, R1)
LR: 1.668 m (X stack, R2)
Result: distance ≈ 34.5876 m
Example 2 (from HP 35):
V: 4°17' (Z stack, R3)
UR: 3.144 m (Y stack, R1)
LR: 1.761 m (X stack, R2)
Result: distance ≈ 137.5285 m
Example 3 (from HP 35):
V: -7°21' (Z stack, R3)
UR: 2.817 m (Y stack, R1)
LR: 0.731 m (X stack, R2)
Result: distance ≈ 205.1860 m
Sources
CivilFerba "Measure the distance by stadia method" Video posted on YouTube on December 8, 2018. https://www.youtube.com/watch?v=oon5ayl9DYs Retrieved March 22, 2026
HP-35 Surveying. Hewlett Packard. Buchs, Switzerland. February 1973. pp. 19-20
fx-FD10 Pro. User's Guide. Casio. Tokyo, Japan. 2014. pg. α-16 (alpha-16)
Eddie
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