State-Plane Grid-to-Ground Distance
The grid-to-ground scale factor: elevation factor EF = R/(R+h) with R = 20,906,000 ft.
Example
You enter
- Grid (map) distance (ft) 10000
- Grid scale factor (near 1.0) 0.9999
- Ellipsoid height h = H + N (ft) 5280
You get
- Ground distance 10003.5 ft
- Combined factor 0.999648
Details, formula, and sources
Combined factor CF = grid-scale-factor x EF, and ground = grid / CF. A 10,000 ft grid distance at a 0.9999 scale factor and 5,280 ft ellipsoid height is 10,003.53 ft on the ground. Enter the ellipsoid height h = orthometric elevation H + geoid height N (N ~ -30 m in the US), not the elevation alone. Per the NGS State Plane Coordinate System; the published control governs.
elevation factor EF = R/(R+h), R = 20,906,000 ft (NGS mean earth radius); combined factor CF = grid_scale_factor x EF; ground = grid / CF (grid = ground x CF).
NGS / NOAA State Plane Coordinate System grid-to-ground reduction, by name; first-principles.
The elevation-factor and combined-factor relations are public NGS results; the grid scale factor is available from the free NGS SPC/UTM tools.
Estimate. AHJ and licensed professional govern.
Field names used by the API: grid_distance_ft, grid_scale_factor, ellipsoid_height_ft, ground_distance_ft, combined_factor
- Mean radius R = 20,906,000 ft (NGS mean earth radius)NGS
- Grid scale factor the projection value at the point, near 1.0, user-supplied from NGS tools/softwareState Plane Coordinate System
- Ellipsoid height h = orthometric elevation H + geoid height N (N negative in the conterminous US)geodetic convention