GNSS Positioning Calculator

ECEF to Geodetic Coordinate Conversion

X, Y, Z [m] are the components of a position in the global Earth-Centered, Earth-Fixed (ECEF) cartesian coordinate system. The converter transforms these to geodetic coordinates (latitude, longitude, ellipsoidal height) on the WGS84 reference ellipsoid, and vice versa. You can also enter coordinates in degrees-minutes-seconds (DMS) notation.

Height [m] is the ellipsoidal height above the WGS84 ellipsoid, not to be confused with orthometric height (above mean sea level).

Use the address search to look up any place by name and automatically fill in its coordinates, or click My location to use your device's GPS.

Azimuth, Elevation & Slant Range (AER)

θ [°] is the elevation angle of the target position as seen from the reference position, measured from the local horizontal plane.

φ [°] is the azimuth angle, measured clockwise from North in the local horizontal plane.

ρ [m] is the slant range — the straight-line distance between the two positions.

East-North-Up (ENU) Coordinates

The ENU local coordinate system expresses the difference between two ECEF positions in a frame aligned with the reference position's local horizon:

ΔE [m] East component, ΔN [m] North component, and ΔU [m] Up component.

Distances & Bearings

Orthodromic distance is the shortest path between two points on the ellipsoid surface (great-circle distance), computed using the Vincenty inverse formula on the WGS84 ellipsoid.

Loxodromic distance (rhumb line) is the distance along a path of constant bearing. It is always equal to or longer than the orthodromic distance.

Euclidean distance is the straight-line 3D distance between the two ECEF positions (through the Earth).

The initial and final bearings are the headings at the start and end of the great-circle arc. The rhumb bearing is the constant heading along the loxodromic path. The midpoint is the geographic center of the great-circle arc, and the horizon distances indicate how far each position can see to the geometric horizon based on its height.

Coordinate Formats

Each position card also displays the coordinates in several additional representations:

UTM (Universal Transverse Mercator) projects the position onto a flat metric grid defined by a zone number (1–60) and hemisphere. Easting and northing are given in metres. UTM is the standard format for topographic maps and land surveying.

Maidenhead is a compact grid-square locator widely used in amateur radio. A 6-character code (e.g. JN58td) identifies an area of roughly 5 × 2.5 km.

Geohash is an alphanumeric string that encodes a position by recursively halving the coordinate space. It is used in databases and web applications for spatial indexing. The 8-character default gives sub-metre precision.

Related Tools

• GPS Time Converter — convert between GPS, UTC, Julian Date and other time scales
• NMEA Log Viewer — plot GNSS tracks from NMEA log files on a map
• NTRIP Client — browse correction streams and monitor live RTCM data
• Signal Spectrum — interactive PSD chart of all GNSS L-band signals

Positioning FAQ

What is ECEF?

ECEF (Earth-Centered, Earth-Fixed) is a 3D cartesian coordinate system with its origin at the Earth's center of mass. The X axis points to the intersection of the prime meridian and equator, Z points to the North Pole, and Y completes the right-handed system. GPS satellites broadcast positions in ECEF.

How do I convert ECEF to latitude and longitude?

An iterative or closed-form algorithm converts X, Y, Z coordinates to geodetic latitude, longitude and ellipsoidal height on a reference ellipsoid (usually WGS84). Enter your ECEF values in the calculator above for an instant conversion.

What is WGS84?

WGS84 (World Geodetic System 1984) is the reference ellipsoid and coordinate system used by GPS. It defines the size and shape of the Earth model (semi-major axis 6 378 137 m, flattening 1/298.257223563) used for all coordinate conversions on this page.

What is the difference between ellipsoidal height and sea level altitude?

Ellipsoidal height is the distance above the WGS84 ellipsoid, which is a mathematical surface. Mean sea level (orthometric height) follows the geoid, an irregular equipotential surface. The two can differ by up to ±100 m depending on location.

What are azimuth and elevation?

Azimuth is the horizontal angle from North, measured clockwise (0–360°). Elevation is the vertical angle above the local horizon (0° = horizon, 90° = zenith). Together with slant range they form the AER coordinate system, commonly used for satellite tracking and antenna pointing.

What is the ENU coordinate system?

ENU (East-North-Up) is a local tangent-plane coordinate system centered at a reference point. East points along the local parallel, North along the local meridian, and Up is normal to the ellipsoid. It is used to express relative positions in an intuitive, human-readable frame.

What is the difference between orthodromic and loxodromic distance?

Orthodromic (great-circle) distance is the shortest path between two points on the ellipsoid surface. Loxodromic (rhumb line) distance follows a path of constant bearing, which is longer but simpler to navigate. For short distances the difference is negligible.

What is UTM?

UTM (Universal Transverse Mercator) is a map projection that divides the Earth into 60 zones of 6° longitude each. Within each zone, positions are expressed as easting and northing in metres. UTM is widely used in surveying, mapping and military applications because it provides a flat, metric grid with minimal distortion.

What is a Maidenhead grid locator?

The Maidenhead Locator System divides the Earth into grid squares identified by alternating letters and digits (e.g. JN58td). It is primarily used by amateur radio operators to describe station locations concisely. Each 6-character locator identifies an area of roughly 5 × 2.5 km.

What is a geohash?

A geohash is a compact string that encodes a geographic location by recursively subdividing the world into a grid. Longer strings mean higher precision. Geohashes are used in databases and web applications for efficient spatial indexing and proximity searches.

What is the geometric horizon distance?

The geometric horizon distance is how far an observer can see to the horizon from a given height above the ellipsoid, assuming standard atmospheric refraction (k = 0.13). It depends only on the observer's altitude and the Earth's radius.