Conformal Projection

Overview Conformal projections, also called orthomorphic projections, preserve angular relationships at every point on the map, meaning that the shapes of small features are accurately represented. At any given point, the scale is identical in all directions (isotropic), although the scale value changes across the map. This property is achieved mathematically by ensuring that the projection equations satisfy the Cauchy-Riemann conditions, which guarantee that angles between any two lines on the Earth's surface are preserved on the map.

The Mercator projectionMercator ProjectionThe Mercator projection is a cylindrical conformal map projection that preserves angles and shapes locally, making it... is the most well-known conformal projection, preserving bearings as straight lines (rhumb lines), making it indispensable for navigation. The Transverse Mercator is the basis for the UTM coordinate system and national mapping grids worldwide. The Lambert Conformal Conic is widely used for aeronautical charts and regional mapping of mid-latitude areas. The Stereographic projection provides conformal mapping of polar regions and is used for ice navigation and polar scientific research.

Navigation relies on conformal projections because preserved angles mean that compass bearings measured on the map correspond to bearings in the real world. Topographic mapping uses conformal projections (particularly Transverse Mercator) because local shapes and feature orientations are accurately depicted. Engineering surveys use conformal projections to ensure that angular measurements in the field correspond to angles on plans and drawings. Weather mapping uses conformal projections because wind directions and frontal orientations are correctly represented.

While local shapes are preserved, conformal projections distort area, sometimes dramatically. The Mercator projectionMercator ProjectionThe Mercator projection is a cylindrical conformal map projection that preserves angles and shapes locally, making it..., for example, greatly exaggerates the apparent size of regions near the poles, making Greenland appear comparable in size to Africa despite being 14 times smaller. This area distortion means conformal projections should not be used for thematic maps comparing region sizes or for area calculations.