Primary sources · 4
- [1] NGA.STND.0036_1.0.0_WGS84 — Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems · National Geospatial-Intelligence Agency Standard, Version 1.0.0 · 8 July 2014 (current revision) https://earth-info.nga.mil/index.php?dir=wgs84&action=wgs84
- [2] NIMA TR8350.2 — Predecessor document, third edition, defining the same a and 1/f · National Imagery and Mapping Agency Technical Report · 4 July 1997, amended 2000 https://gis-lab.info/docs/nima-tr8350.2-wgs84fin.pdf
- [3] EGM2008 — Earth Gravitational Model paired with WGS-84 for the geoid surface (separate from the ellipsoid) · Pavlis et al., Journal of Geophysical Research · April 2012 https://doi.org/10.1029/2011JB008916
- [4] EPSG:4326 — Industry-standard coordinate reference system identifier for WGS-84 geographic 2D · IOGP EPSG Geodetic Parameter Dataset · Continuously maintained https://epsg.io/4326
WGS-84 is the reference ellipsoid that every GPS receiver, every modern flight management computer, and every web mapping library treats as "Earth." It is not Earth — Earth is bumpier — but it is a tractable mathematical surface to which all real-world positions are referred.
What WGS-84 actually is
WGS-84 is two things at once. First, it is an ellipsoid of revolution — a mathematical surface defined by a and f that approximates mean sea level to within ~100 metres globally. Second, it is a reference frame: a choice of origin (Earth's centre of mass), an orientation (zero longitude at IERS Reference Meridian, not Greenwich exactly), and a scale (the SI metre).
The defining and derived parameters
WGS-84 picks four defining parameters and derives everything else from them. The defining four are a, 1/f, the Earth's gravitational constant GM, and the angular velocity ω. The ellipsoid you care about for distance and position only needs a and 1/f — GM and ω are needed for satellite orbit mechanics and gravimetry.
| Parameter | Symbol | Value | Status |
|---|---|---|---|
| Semi-major axis | a | 6,378,137.0 m | Defining |
| Inverse flattening | 1/f | 298.257223563 | Defining |
| Earth's gravitational constant | GM | 3.986004418 × 10¹⁴ m³ s⁻² | Defining |
| Earth's angular velocity | ω | 7.2921151467 × 10⁻⁵ rad s⁻¹ | Defining |
| Flattening | f | 0.003352810664747... | Derived (1/(1/f)) |
| Semi-minor axis | b | 6,356,752.314 m | Derived (a · (1−f)) |
| First eccentricity squared | e² | 0.00669437999014 | Derived |
| Equatorial circumference | 2π a | 40,075.017 km | Derived |
| Polar (meridional) circumference | — | 40,007.863 km | Derived |
| Mean radius (arithmetic) | (2a + b)/3 | 6,371,008.8 m | Derived |
Why these specific numbers
WGS-84's a and 1/f were chosen in 1984 by the U.S. Defense Mapping Agency (now NGA) to fit a worldwide set of Doppler satellite-tracking observations collected through the late 1970s. The values closely match the IUGG GRS-80 ellipsoid that civilian geodesy had adopted four years earlier — the two share 1/f = 298.257222101 vs 298.257223563, a difference of less than 0.1 mm at Earth scale.
How GPS depends on WGS-84
The GPS broadcast ephemeris — the per-satellite orbital parameters transmitted by each satellite to the receiver — is referenced to WGS-84. The receiver computes satellite positions from those ephemerides, performs trilateration, and returns coordinates also referenced to WGS-84. A mismatch between the ellipsoid the satellites use and the ellipsoid the receiver assumes would inject a systematic position error of several metres.
| Ellipsoid | a (m) | 1/f | Used by |
|---|---|---|---|
| WGS-84 (1984) | 6,378,137.0 | 298.257223563 | GPS, Google Maps, Aviation FMS |
| GRS-80 (1980) | 6,378,137.0 | 298.257222101 | NAD83, ITRF — civilian geodesy |
| Airy 1830 | 6,377,563.396 | 299.3249646 | OSGB36 — Great Britain Ordnance Survey |
| Clarke 1866 | 6,378,206.4 | 294.9786982 | NAD27 — North America pre-1986 |
| Krassowsky 1940 | 6,378,245.0 | 298.3 | Soviet/Russian SK-42 |
The geoid is not the ellipsoid
A common confusion: WGS-84 the ellipsoid is a smooth mathematical surface; the geoid is the irregular surface of equal gravitational potential that mean sea level approximates. Heights labelled "above sea level" typically refer to the geoid, while raw GPS heights refer to the ellipsoid. The difference (the geoid undulation) ranges from −106 m near the Maldives to +85 m near Iceland.