Map Projections

Notice: The maps on this page have a 20 degree latitude and longitude grid.

This is a map of the whole globe in rectangular projection, more properly called Equidistant Cylindrical projection.
All the latitude and longitude sections have the same length, and the latitude sections have their true length.
Areas become distorted towards the poles, with more and more exaggerated west-to-east dimensions.
The map is a rectangle with 2:1 width-to-height ratio.
Rectangular

This is the same map in Mercator projection.
All the longitude sections have the same length, but the latitude sections become longer with increasing distance from the equator.
Areas become larger towards the poles, with more and more exaggerated west-to-east and north-to-south dimensions.
Notice that the poles can not be included, this map is cut off at approximately 85 deg latitude (both N and S).
This map is the same width but higher than the rectangular projection map.
Mercator

This is the same map in Sinusoidal projection, what is sometimes improperly called "conic" projection.
All the longitude sections have their true length, and also the latitude sections at latitude 0 (the center of the map), but the latitude sections become longer with increasing distance from latitude 0.
Areas have reasonably correct sizes, but angular distortion become larger towards the poles and away from latitude 0.
This map has the same proportions as the rectangular projection map.
Sinusoidal

This is the same map in "orange peel" projection, more properly called Interrupted Sinusoidal projection.
It is the same as the Sinusoidal projection, but divided into several sections of different widths.
Areas have reasonably correct sizes, and angular distortion is less than in the Sinusoidal projection.
This map has the same proportions as the rectangular projection map.
Orange peel

This is the north and south polar regions of the same map in Polar Stereographic projection.
The maps are centered on the pole. The latitudes are lines through the poles and have their true length.
Areas have reasonably correct sizes and the angular distortion is small within small areas, at least away from the equator.
North polar South polar

See http://www.fes.uwaterloo.ca/crs/geog165/cylproj.htm for more information on these map projections.

Here are "recipes" for manually converting map projections from rectangular to mercator, from mercator to rectangular, and from rectangular to sinusoidal.

Rectangular to Mercator
Increase height of latitude strip

5 deg strip 10 deg strip 20 deg strip

0-5 1,000915

5-10 1,007826 0-10 1,004371

10-15 1,022680

15-20 1,046070 10-20 1,034375 0-20 1,019373

20-25 1,078971

25-30 1,122846 20-30 1,100908

30-35 1,179819

35-40 1,252951 30-40 1,216385 20-40 1,158647

40-45 1,346709

45-50 1,467756 40-50 1,407232

50-55 1,626390

55-60 1,839300 50-60 1,732845 40-60 1,570039

60-65 2,135316

65-70 2,568799 60-70 2,352058

70-75 3,255937

75-80 4,498652 70-80 3,877294 60-80 3,114676

80-85 7,421760

(85-90) (26,173804) (80-90) (16,797782) (80-90) (16,797782)

Mercator to rectangular Decrease height of latitude strip
5 deg strip		10 deg strip		20 deg strip (a)		20 deg strip (b)
0-5	0,999086
5-10	0,992244	0-10	0,995665			-10..10	0,995665
10-15	0,977850
15-20	0,956013	10-20	0,966932	0-20	0,981298
20-25	0,926901
25-30	0,890735	20-30	0,908818			10-30	0,937875
30-35	0,847790
35-40	0,798392	30-40	0,823091	20-40	0,865955
40-45	0,742918
45-50	0,681791	40-50	0,712355			30-50	0,767723
50-55	0,615474
55-60	0,544473	50-60	0,579974	40-60	0,646164
60-65	0,469329
65-70	0,390612	60-70	0,429970			50-70	0,504972
70-75	0,308923
75-80	0,224883	70-80	0,266903	60-80	0,348437
80-85	0,139131
(85-90)	(0,052320)	(80-90)	(0,095725)	(80-90)	(0,095725)	(70-90)	(0,181314)

Rectangular to sinusoidal Decrease width of latitude strip Use perspective (decrease top/bottom edge by factor)
5 deg strip			10 deg strip			20 deg strip
	width	perspective		width	perspective		width	perspective
0-5	1,000000	0,003805
5-10	0,996195	0,011430	0-10	1,000000	0,015192	-10..10	1,000000	0,000000
10-15	0,984808	0,019173
15-20	0,965926	0,027159	10-20	0,984808	0,045811
20-25	0,939693	0,035527
25-30	0,906308	0,044447	20-30	0,939693	0,078395	10-30	1,000000	0,133975
30-35	0,866025	0,054125
35-40	0,819152	0,064832	30-40	0,866025	0,115448
40-45	0,766044	0,076938
45-50	0,707107	0,090961	40-50	0,766044	0,160900	30-50	0,866025	0,257773
50-55	0,642788	0,107673
55-60	0,573576	0,128277	50-60	0,642788	0,222138
60-65	0,500000	0,154763
65-70	0,422618	0,190711	60-70	0,500000	0,315960	50-70	0,642788	0,467911
70-75	0,342020	0,243264
75-80	0,258819	0,329075	70-80	0,342020	0,492287
80-85	0,173648	0,498090
85-90	0,087156	1,000000	80-90	0,173648	1,000000	70-90	0,342020	1,000000

Created 2001-09-06, last modified 2003-08-02
By Bo Johansson

Notice: The maps on this page have a 20 degree latitude and longitude grid.
This is a map of the whole globe in rectangular projection, more properly called Equidistant Cylindrical projection. All the latitude and longitude sections have the same length, and the latitude sections have their true length. Areas become distorted towards the poles, with more and more exaggerated west-to-east dimensions. The map is a rectangle with 2:1 width-to-height ratio.
This is the same map in Mercator projection. All the longitude sections have the same length, but the latitude sections become longer with increasing distance from the equator. Areas become larger towards the poles, with more and more exaggerated west-to-east and north-to-south dimensions. Notice that the poles can not be included, this map is cut off at approximately 85 deg latitude (both N and S). This map is the same width but higher than the rectangular projection map.
This is the same map in Sinusoidal projection, what is sometimes improperly called "conic" projection. All the longitude sections have their true length, and also the latitude sections at latitude 0 (the center of the map), but the latitude sections become longer with increasing distance from latitude 0. Areas have reasonably correct sizes, but angular distortion become larger towards the poles and away from latitude 0. This map has the same proportions as the rectangular projection map.
This is the same map in "orange peel" projection, more properly called Interrupted Sinusoidal projection. It is the same as the Sinusoidal projection, but divided into several sections of different widths. Areas have reasonably correct sizes, and angular distortion is less than in the Sinusoidal projection. This map has the same proportions as the rectangular projection map.
This is the north and south polar regions of the same map in Polar Stereographic projection. The maps are centered on the pole. The latitudes are lines through the poles and have their true length. Areas have reasonably correct sizes and the angular distortion is small within small areas, at least away from the equator.