Stadia Tacheometry (Distance and Elevation)
The classic instrument method of reading a distance and rise off a rod interval, still used for topo checks.
Example
You enter
- Stadia interval (upper - lower, ft) 1.5
- Vertical angle from horizontal (deg, + up) 5
- Stadia interval factor K 100
- Height of instrument (ft, optional) 4.5
- Rod center reading (ft, optional) 5.2
- Station elevation (ft, optional) 500
You get
- Horizontal distance 148.86 ft
- Vertical distance 13.02 ft
- Target elevation 512.32
Checked against published worked examples from: US Navy (NAVEDTRA).
Details, formula, and sources
ScopeWith K = 100, the horizontal distance H = K s cos^2(theta) and vertical V = (K s/2) sin(2 theta) from the stadia interval s and vertical angle. A 1.50 ft interval at +5 degrees gives 148.9 ft and a 13.0 ft rise; on a level sight it reduces to the bare H = 100 s with no rise. Stadia constant C defaults to 0 (internal focusing); enter about 1 ft for an external-focusing instrument. No curvature/refraction correction. A computational aid; the instrument's stadia constants govern.
Formula or tableH = K s cos^2(theta) + C cos(theta); V = K s cos(theta) sin(theta) + C sin(theta); elevation = station_elev + HI + V - rod_center. (K = 100; stadia constant C = 0 for internal focusing)
Source and editionThe stadia-tacheometry distance and elevation reduction with the standard interval factor K = 100, as compiled in the standard surveying references, by name.
Free accessThe stadia-reduction formulas are public surveying results in any elementary-surveying reference.
What governsEstimate. AHJ and licensed professional govern.
API field namess_ft, theta_deg, k_f, hi_ft, rod_ft, sta_elev, h_ft, v_ft, elev_ft
- Horizontal distance H = K s cos^2(theta) with K = 100 for an internal-focusing instrumentstadia tacheometry
- Vertical distance V = (K s/2) sin(2 theta); elevation = HI + V - rod centerstadia tacheometry
- Stadia constant C = 0 by default (internal focusing); an external-focusing C adds C cos theta to H and C sin theta to VNAVEDTRA 14070 Engineering Aid Basic, p. 8-6