MAP Projection Converter
Our free earth measurements converter handles map projection conversions. See tables, ratios, and examples for quick reference.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
MAP Projection Converter
Calculator
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Formula: Mercator: x = R * lon_rad, y = R * ln(tan(pi/4 + lat_rad/2))
Worked example โ x = 1111.95 km, y = 8362.75 km, scale distortion = 2.0x
Formula
Mercator: x = R * lon_rad, y = R * ln(tan(pi/4 + lat_rad/2))
Each projection applies a different mathematical transformation to convert spherical latitude/longitude coordinates into flat X/Y coordinates. The Earth radius R is 6371 km. Distortion factor indicates how much the projection stretches distances at the given latitude compared to the equator.
Worked Examples
Example 1: Mercator Projection at 60N
Problem:Convert latitude 60N, longitude 10E to Mercator projected coordinates.
Solution:x = R * lon_rad = 6371 * (10 * pi/180) = 1111.95 km y = R * ln(tan(pi/4 + lat_rad/2)) = 6371 * ln(tan(75deg)) = 8362.75 km Distortion factor = 1/cos(60) = 2.0
Result:x = 1111.95 km, y = 8362.75 km, scale distortion = 2.0x
Example 2: Sinusoidal Projection at the Equator
Problem:Convert latitude 0, longitude 90E using sinusoidal projection.
Solution:x = R * lon_rad * cos(lat) = 6371 * (pi/2) * cos(0) = 10007.54 km y = R * lat_rad = 6371 * 0 = 0 km Distortion factor = 1.0
Result:x = 10007.54 km, y = 0 km, no distortion at equator
Frequently Asked Questions
What is a map projection and why are there so many types?
A map projection is a mathematical method for representing the curved surface of the Earth on a flat plane. Because it is impossible to flatten a sphere without some distortion, different projections preserve different properties. The Mercator projection preserves angles and shapes at the cost of area distortion near the poles. Equal-area projections preserve area but distort shapes. No single projection is ideal for all uses, so cartographers choose based on the purpose of the map.
How does the Mercator projection distort landmasses?
The Mercator projection stretches areas increasingly as you move away from the equator. At 60 degrees latitude the scale distortion is 2x, meaning objects appear twice as wide as they really are compared to the equator. Greenland appears roughly the same size as Africa on a Mercator map even though Africa is actually 14 times larger. This distortion occurs because the projection preserves compass bearings, which was essential for maritime navigation.
What is a scale factor in map projection?
A scale factor describes how much a map projection stretches or compresses distances at a given point compared to the true distances on the Earth surface. A scale factor of 1.0 means no distortion. Values greater than 1 mean the map stretches distances, and values less than 1 mean it compresses them. The scale factor typically varies across the map and depends on both the projection type and the latitude.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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