Historical Oblate Spheroid Parameters Calculator Given the Geographic Coordinates and Elevation of Any Point Relative to the Surface of Any of Several Historical Reference Spheroid Models
Latitude  (−Neg = South)   ,  Longitude  (−Neg = West) ±Deg.dddddddddd   or   ±Deg  min  sec.ssss	Sea-Level Elevation  in meters or feet (m,   ft)
Select a spheroid model to compute the rectangular 3D  XYZ-coordinates of the point based on the geographic coordinates and elevation given above and the equations following below.
GRS 80 | WGS 84 Ellipsoid Model Parameters Used worldwide by the ITRS - International Terrestrial Reference System and the GPS - Global Positioning System Equatorial radius R = 6378137.0000 m = 3963.190592 mi Polar radius r = 6356752.3142 m = 3949.902764 mi Flattening f = 0.003352810665 = 1/298.2572235605 Eccentricity e = 0.081819190843 e² = 0.006694379990 Equatorial Quarter = 10018754.1713 m = 6225.3652 mi Meridional Quarter = 10001965.7293 m = 6214.9333 mi Circumference at Equator = 40075016.6856 m = 24901.460897 mi Circumference of Meridian = 40007862.9173 m = 24859.733480 mi Circumference Difference = 67153.7683 m = 41.727417 mi __________________________________________________________________ Location Coordinates and Sea Level Elevation of Point Latitude = +053° 36' 43.1653" N = +53.6119903611° Longitude = -001° 39' 51.9920" W = -1.6644422222° Height/Elev = +299.8000 m = +983.60 ft = +983 ft and 7.1 in __________________________________________________________________ Corresponding Rectangular 3D XYZ-Coordinates of Point at Given Location and Elevation. x = +3790644.8998 m = +2355.397541 mi y = -110149.2097 m = -68.443546 mi z = +5111482.9706 m = +3176.128268 mi _________________________________________________________________
BASIC ELLIPSOID FORMULAS AND RELATIONSHIPS APPLIED HERE Given the general static ellipsoid parameters: R = Equatorial radius of ellipsoid = Length of semi-major axis r = Polar radius of ellipsoid = Length of semi-minor axis where,  r ≤ R If ((R = r)), then the form is a perfect sphere, otherwise it is an ellipsoid or oblate spheroid to some degree, generally wider between two opposite equatorial points due to a slight equatorial bulge, than between the opposite polar points. NOTE: In the equations, any units of measure may be used for (R, r), such as feet, meters, kilometers, miles, etc., just as long as the same units are used consistently throughout. The values of (x, y, z) will be expressed in the same units as the parameters (R, r). Computing 3D Rectangular XYZ-Coordinates For a Point on a Reference Ellipsoid Surface The reference ellipsoid parameters, location and elevation of the point are: R = Equatorial radius. r = Polar radius. Lat = Geographic latitude of point on ellipsoid surface. Lon = Geographic longtitude of point on ellipsoid surface (Negative = West). $h$ = Height or elevation of point relative to ellipsoid surface. From the given parameters, the 3D XYZ-coordinates of the point, relative to the surface of the reference ellipsoid, are computed from the equations given below. Let: $f=\frac{R-<!--\; -\; -->r}{R}$ = Polar flattening factor of ellipsoid. $e=\sqrt{1-{\left(\frac{r}{R}\right)}^2}$ $\rho =\frac{R}{1-<!--\; -\; -->e²·<!--\; ·\; -->sin²(\mathrm{Lat<!--\; \varphi \; -->})}$ = Radius vector from ellipsoid center to surface at latitude $\left(\mathrm{Lat<!--\; \varphi \; -->}\right)$. Then: $x=(h+\rho )·<!--\; ·\; -->cos(\mathrm{Lat<!--\; \varphi \; -->})·<!--\; ·\; -->cos(\mathrm{Lon<!--\; \lambda \; -->})$ $y=(h+\rho )·<!--\; ·\; -->cos(\mathrm{Lat<!--\; \varphi \; -->})·<!--\; ·\; -->sin(\mathrm{Lon<!--\; \lambda \; -->})$ $z=(h+\rho ·<!--\; ·\; -->(1-<!--\; -\; -->e²))·<!--\; ·\; -->sin(\mathrm{Lat<!--\; \varphi \; -->})$
Reference: The Earth Ellipsoid https://en.wikipedia.org/wiki/Earth_ellipsoid
A PHP Science Program by Jay Tanner - Revised: 2023 March 01 Wednesday at 11:53:49 PM GMT