Total-Station Slope-to-Horizontal Reduction
The right-triangle reduction of an EDM/total-station slope distance to horizontal distance and elevation.
Example
You enter
- Angle type zenith
- Slope distance S (ft) 250
- Angle (deg) 86
You get
- Horizontal distance 249.391 ft
- Vertical distance 17.439 ft
Checked against published worked examples from: Ghilani, Elementary Surveying (plane-survey reduction).
Details, formula, and sources
ScopeWith a zenith angle Z, H = S sin Z and V = S cos Z; with a vertical angle a, H = S cos a and V = S sin a; ground-to-ground elevation difference = V + instrument height - reflector height. A 250 ft slope shot at an 86 deg zenith is 249.39 ft horizontal and 17.44 ft up. The step that feeds the horizontal distance into a COGO forward computation. No curvature/refraction or grid scale factor; the instrument and control govern.
Formula or tablezenith angle Z: H = S sin(Z), V = S cos(Z). vertical angle a: H = S cos(a), V = S sin(a). ground-to-ground elevation difference = V + instrument_height - reflector_height.
Source and editionStandard plane-survey EDM/total-station slope reduction by right-triangle trigonometry, as compiled in the standard surveying references (Ghilani, Elementary Surveying), by name.
Free accessThe slope-reduction relations are public surveying results in any elementary-surveying reference.
What governsEstimate. AHJ and licensed professional govern.
API field namesangle_mode, slope_distance_ft, angle_deg, horizontal_ft, vertical_ft
- Angle basis zenith from vertical (90 = level) or vertical from horizontal (0 = level)surveying convention
- Elevation ground-to-ground = V + instrument height - reflector heighttotal-station reduction
- Plane reduction no earth curvature/refraction or grid scale factor appliedplane-survey assumption