From AMS Glossary
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(Also called isogonal map, orthomorphic map.) A map that preserves angles; that is, a map such that if two curves intersect at a given angle, the images of the two curves on the map also intersect at the same angle.
On such a map, at each point, the scale is the same in every direction. Shapes of small regions are preserved, but areas are only approximately preserved (the property of area conservation is peculiar to the equal-area map). The most commonly used conformal map is probably the Lambert conic projection, with standard latitudes at 30°and 60°N. On the standard latitudes, the scale is exact; between them, it is decreased by not more than about 1%; outside them, distortion increases rapidly. The Mercator and stereographic projections are also conformal maps.
Saucier, W. J. 1955. Principles of Meteorological Analysis. 24–38.