$\varphi$, $\lambda$ are latitude and longitude in radiant, respectively.
Surface area
https://onlinelibrary.wiley.com/doi/full/10.1111/tgis.12636
Distances / cell sizes
$f = \frac{a-b}{a}$
$e^2 = f(2 - f)$
where $a$ is the semi-major axis, $b$ the semi-minor axis, and $f$ the flattening.
For the WGS84 ellipsoid:
$a = 6378137$
$b = 6356752.314245$
Meridional radius:
$M(\varphi)=\frac{1-e^2}{a^2} N(\varphi)^3$
Prime vertical radius:
$N(\varphi)=\frac{a}{\sqrt{1-e^2\sin^2\varphi}}.$
Distances:
$\Delta X = \Delta\lambda N(\varphi\prime)\cos(\varphi\prime)$
$\Delta Y = \Delta\varphi M(\varphi\prime)$
Where $\varphi\prime$ is the mean for the given range (in our case, the center of the given cell)
Reference
Compare results with Karneys's solution, for both distances and areas.
For the tiny distances here (likely a few hundred meters max), it should be accurate to under a millimeter.
Surface area
https://onlinelibrary.wiley.com/doi/full/10.1111/tgis.12636
Distances / cell sizes
where$a$ is the semi-major axis, $b$ the semi-minor axis, and $f$ the flattening.
$a = 6378137$
$b = 6356752.314245$
For the WGS84 ellipsoid:
Meridional radius:
Prime vertical radius:
Distances:
Where
Reference
Compare results with Karneys's solution, for both distances and areas.
For the tiny distances here (likely a few hundred meters max), it should be accurate to under a millimeter.