Mercator Projection Formula

The Mercator Projection formula is an important equation in cartography which is used to produce a world map or other map projection onto a two-dimensional surface. The formula was created in 1569 by the Flemish geographer and cartographer Gerardus Mercator, and it became the standard map projection for navigation because it preserved angles at sea.

The Formula

x = λ * cos φ
y = λ * sin φ

What Does the Formula Do?

The formula transforms coordinates on the globe into a 2D rectangular projection which preserves shapes and directions without distorting them. It allows for accurate navigation on maps, because any angles or distances will be preserved on the map projection. This formula is used when creating maps of the whole world.

Components of the Formula

The formula has two components: λ and φ. λ is the longitude of a geographic point, and φ is the latitude. These two components are used to calculate the two coordinates of a point in a two-dimensional rectangular projection.

Table of Formula Components

Uses of the Formula

The Mercator Projection formula is used in many fields such as navigation, cartography, and geography. It is used to construct world maps and to preserve directions for accurate navigation.

History

The formula was created in 1569 by the Flemish geographer Gerardus Mercator. He created the formula so that it would be easier for sailors to accurately navigate their ships by preserving angles and directions on a map. This made it very useful to navigators and cartographers, and it soon became the standard projection for navigation.

Since then, the formula has become widely used in many fields. Many modern map projections use some kind of variation of the Mercator Projection formula to accurately represent the Earth's surface.