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Latitude & Longitude to Cartesian (XYZ) Converter

Convert Geodetic coordinates (Latitude, Longitude, Altitude) to Earth-Centered Earth-Fixed (ECEF) Cartesian coordinates (X, Y, Z) using WGS84 standards.

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Category Geometry & Planimetry

Input Coordinates

-90° (South) to 90° (North)
-180° (West) to 180° (East)
meters
Height above the ellipsoid surface

Cartesian Coordinates (ECEF)

X 0.000 m
Y 0.000 m
Z 0.000 m
Y Z X
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About

This tool transforms Geodetic coordinates (Latitude φ, Longitude λ, and Height h) into Earth-Centered, Earth-Fixed (ECEF) Cartesian coordinates (X, Y, Z). This conversion is fundamental in Global Positioning Systems (GPS), geodesy, and navigation logic.

Unlike simple spherical models, this calculator utilizes the WGS84 Ellipsoid model, which accounts for the Earth's oblateness (flattening at the poles). This ensures high-precision results suitable for engineering and scientific applications. The output represents the 3D position relative to the Earth's center of mass.

coordinate-converter geodesy ecef gps wgs84 cartesian

Formulas

The transformation from Geodetic to Cartesian coordinates requires calculating the radius of curvature in the prime vertical, denoted as N(φ).

N(φ) = a√1 − e2 sin2φ
X = (N + h) cosφ cosλ
Y = (N + h) cosφ sinλ
Z = ((1 − e2)N + h) sinφ

Legend:

  • φ = Latitude (converted to radians)
  • λ = Longitude (converted to radians)
  • h = Height above ellipsoid (meters)
  • a = Semi-major axis of the ellipsoid
  • e2 = First eccentricity squared (2f − f2)

Reference Data

Ellipsoid ModelSemi-Major Axis (a)Inverse Flattening (1/f)Use Case
WGS846378137.0 m298.257223563Global GPS Standard
GRS806378137.0 m298.257222101North American Datum (NAD83)
Airy 18306377563.4 m299.3249646Ordnance Survey (UK)
Clarke 18666378206.4 m294.9786982Old North American Datum (NAD27)
Sphere6371000.0 m∞Rough Estimates

Frequently Asked Questions

Cartesian coordinates originate from the center of the Earth. Increasing altitude moves the point further from the center in all three dimensions (X, Y, and Z), depending on your latitude and longitude vectors. It is a linear radial expansion.
WGS84 is the standard for GPS, while GRS80 is used for the North American Datum 1983 (NAD83). They differ slightly in the flattening factor, resulting in a difference of about 0.1mm in positions, which is negligible for most non-scientific applications.
Yes. For Latitude, negative values represent the Southern Hemisphere. For Longitude, negative values represent the Western Hemisphere (West of the Prime Meridian).
The output X, Y, Z coordinates are in meters (m) relative to the Earth's center of mass.