# Natural Earth projection

Natural Earth projection of the world.
The natural Earth projection with Tissot's indicatrix of deformation

The natural Earth projection is a pseudocylindrical map projection designed by Tom Patterson and introduced in 2012. It is neither conformal nor equal-area.

It was designed in Flex Projector, a specialized software application that offers a graphical approach for the creation of new projections.[1][2]

## Definition

The natural Earth is defined by the following formulas:

\displaystyle{ \begin{align} x &= 0.8707 \times l(\varphi) \times \lambda, \\ y &= 0.8707 \times 0.52 \times d(\varphi) \times \pi, \end{align} },

where

• x, y are the Cartesian coordinates;
• λ is the longitude from the central meridian;
• φ is the latitude;
• l(φ) is the length of the parallel at latitude φ;
• d(φ) is the distance of the parallel from the equator at latitude φ.

l(φ) and d(φ) are given as polynomials, initially from interpolation of the following values in Flex Projector:[3]

φ (degrees) l(φ) d(φ)
0 1.0000 0.0000
5 0.9988 0.0620
10 0.9953 0.1240
15 0.9894 0.1860
20 0.9811 0.2480
25 0.9703 0.3100
30 0.9570 0.3720
35 0.9409 0.4340
40 0.9222 0.4958
45 0.9006 0.5571
50 0.8763 0.6176
55 0.8492 0.6769
60 0.8196 0.7346
65 0.7874 0.7903
70 0.7525 0.8435
75 0.7160 0.8936
80 0.6754 0.9394
85 0.6270 0.9761
90 0.5630 1.0000

The values for the southern hemisphere are calculated by changing the sign of the corresponding values for the northern hemisphere.