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