MAP Projection Converter
Our free earth measurements converter handles map projection conversions. See tables, ratios, and examples for quick reference.
MAP Projection Converter
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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 are projected coordinates used for?
Projected coordinates express locations as X and Y distances on a flat surface rather than angular latitude and longitude. They are essential for GIS analysis, engineering, urban planning, and any task requiring accurate distance or area measurements on a map. Common projected coordinate systems include UTM zones and state plane coordinates, each optimized for a particular region of the globe.
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.
What is the difference between a conformal and an equal-area projection?
A conformal projection preserves local angles and therefore the shapes of small features, but it inflates areas away from its lines of true scale; Mercator and Lambert Conformal Conic are examples. An equal-area projection preserves the relative size of regions while shearing their shapes; Albers and Mollweide are examples. No projection can do both at once, so the choice depends on whether the map serves navigation and surveying or comparison of quantities between regions.
Why do web maps use Web Mercator instead of the true Mercator projection?
Web Mercator, registered as EPSG:3857, applies spherical Mercator formulas to coordinates that are actually referenced to the WGS84 ellipsoid. That shortcut makes tile arithmetic fast and simple, at the cost of a scale error of a few tenths of a percent and the loss of strict conformality. It is also clipped near 85.05 degrees of latitude so the world forms a square. It should not be used for area or distance measurement.
What is a datum and how does it differ from a projection?
A datum defines the reference ellipsoid and its position and orientation relative to Earth, fixing what a given latitude and longitude actually mean on the ground. A projection is the separate mathematical step that flattens those coordinates onto a plane. Two maps can share a projection yet disagree by hundreds of metres if their datums differ, which is why a complete coordinate reference system statement names both.
How does a standard parallel reduce distortion in a conic projection?
A conic projection is conceptually a cone touching or slicing the globe. Where the cone meets the surface, along the standard parallel or parallels, scale is true and distortion is zero. Using two standard parallels spreads the error, making scale slightly small between them and slightly large outside. Choosing parallels roughly one sixth in from the northern and southern edges of the mapped area keeps distortion small across a mid-latitude region.
What does an EPSG code identify?
An EPSG code is a numeric identifier from a public registry of coordinate reference systems, originally compiled by the European Petroleum Survey Group. It names a full definition, including the datum, the projection, its parameters and the units, so that software can interpret a dataset unambiguously. EPSG:4326 is WGS84 geographic coordinates, and EPSG:32633 is UTM zone 33 north on WGS84. Quoting the code avoids restating every parameter.
Which projection should I choose for a map of a single country?
Match the projection to the shape of the area and the purpose of the map. A country that is wide east to west in the mid-latitudes suits a conic projection, Lambert Conformal Conic for shape or Albers for area. A tall narrow country suits a Transverse Mercator. Equatorial regions suit a cylindrical form. Tissot's indicatrix, which draws distortion ellipses across the map, is a quick way to check the result.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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