Forward

${\displaystyle {\begin{aligned}x&=R(\lambda -\lambda _{0})\cos \varphi _{1}\\y&=R(\varphi -\varphi _{0})\end{aligned}}}$

The plate carrée (French, for flat square),^[3] is the special case where ${\displaystyle \varphi _{1}}$ is zero. This projection maps x to be the value of the longitude and y to be the value of the latitude,^[4] and therefore is sometimes called the latitude/longitude or lat/lon(g) projection. Despite sometimes being called "unprojected", it is actually projected.

When the ${\displaystyle \varphi _{1}}$ is not zero, such as Marinus's ${\displaystyle \varphi _{1}=36}$,^[5] or Ronald Miller's ${\displaystyle \varphi _{1}=(37.5,43.5,50.5)}$,^[6] the projection can portray particular latitudes of interest at true scale.

While a projection with equally spaced parallels is possible for an ellipsoidal model, it would no longer be equidistant because the distance between parallels on an ellipsoid is not constant. More complex formulae can be used to create an equidistant map whose parallels reflect the true spacing.

Reverse

${\displaystyle {\begin{aligned}\lambda &={\frac {x}{R\cos \varphi _{1}}}+\lambda _{0}\\\varphi &={\frac {y}{R}}+\varphi _{0}\end{aligned}}}$

Alternative names

In spherical panorama viewers, usually:

• ${\displaystyle \lambda }$ is called "yaw";^[7]
• ${\displaystyle \varphi }$ is called "pitch";^[8]

where both are defined in degrees.