The combined scale factor converts a distance measured on a map grid into the distance on the ground, and back. It combines the grid scale factor (how much the map projection stretches or shrinks distances at that place) with the elevation factor (the effect of the site's height above the reference ellipsoid). Close to 1, it matters little on a building and a great deal on a long corridor.
At a glance
| Combines | Grid scale factor × elevation factor |
| Ground from grid | Ground ≈ grid distance ÷ combined scale factor |
| Typical size | Within a few hundred parts per million of 1 on national grids |
| 150 ppm means | 150 mm per kilometre |
| Matters most | Long roads, railways, pipelines, large sites |
The parts
| Factor | Depends on | Effect |
|---|---|---|
| Grid scale factor | Position on the projection (distance from its central line) | Grid distances longer or shorter than on the ellipsoid |
| Elevation factor | Height above the ellipsoid | Ground distances at height are longer than on the ellipsoid |
| Combined scale factor | Both | Converts grid distances to ground distances at the site |
How it is used on projects
The project surveyor states the coordinate reference system and the combined scale factor, often by zone along a route. Teams then agree whether design coordinates are grid (in the projected system) or ground (at true size), and the factor is applied consistently: for setting out, for ordering lengths of pipe or rail, and when placing ground-scale models in a grid-based federation. Many long projects define a low-distortion project grid whose factor stays within a few ppm along the whole route, so grid and ground almost coincide.
Variations
- National grids (for example British National Grid, US State Plane systems) with varying factors across the area.
- Project grids (low-distortion projections) designed around one scheme.
- Local engineering grids with scale fixed at 1 near the site, tied to the national grid by a transformation.
Common mistakes
- One team working in grid, another in ground, without knowing it.
- Ordering materials from grid lengths on long routes.
- Applying the factor twice: in the survey software and again in the design tool.
- Ignoring the elevation factor on high sites.
Where to read more
Your national mapping agency's guidance on its grid (for example the Ordnance Survey's guide to coordinate systems in Great Britain, or NOAA's National Geodetic Survey documentation for State Plane coordinates); the project's survey specification; and the EPSG registry for the parameters of each CRS.