Map projection distortion calculator
Compare one shortest spherical route on three maps, then inspect the local length and area distortion at your chosen latitude.
At 60° latitude, Mercator enlarges local lengths 2 times and areas 4 times. Cylindrical equal-area keeps the product of its two length multipliers at one. North-polar equidistant keeps radial distance true while tangential scale is 1.047 times. The same surface route is drawn below on all three maps.
Angles preserved locally; route bends. Latitudes beyond 85.05° are clipped.
Areas preserved; longitude and latitude stretching differ.
Distances from the North Pole preserved; other routes distort.
Read this calculation
Mercator k = sec φ; polar transverse k = c / sin c
Mercator preserves local angles but enlarges both length directions by sec(latitude), giving an area multiplier sec²(latitude). Cylindrical equal-area keeps area by enlarging east–west scale and shrinking north–south scale reciprocally.
On the north-polar azimuthal equidistant map, radial distances from the pole remain true. Tangential scale changes with angular distance from that centre. Equal distance from one map centre does not preserve every pairwise distance.
Each map receives identical latitude–longitude samples along the great circle. A bend in the displayed route reflects the projection; it does not add kilometres to that surface path. Rectangle maps split the line at the date line instead of drawing a false segment across the world.