WGS 84 Parameters
The four defining parameters of the World Geodetic System 1984 (semi-major axis, reciprocal flattening, geocentric gravitational constant, mean angular velocity), every derived ellipsoid value, normal gravity at equator and pole, and the realization history from original 1987 through WGS 84 (G2139) 2021. Cited to NGA STND 0036 and NIMA TR 8350.2.
Curated by Steve K.. Published . Last updated . Licensed CC BY 4.0.
The World Geodetic System 1984 (WGS 84) is the reference frame that defines geographic coordinates for the Global Positioning System, almost every web map, the Military Grid Reference System, the Universal Transverse Mercator grid, and most modern geospatial software. It comprises a reference ellipsoid (the mathematical shape that approximates Earth), a geocentric coordinate frame, an Earth gravity model (currently EGM2008), and a series of realizations — physical sets of station coordinates that anchor the frame to the ground.
Every value below is taken from NGA STND 0036 (the current canonical specification, 2014) or the earlier NIMA TR 8350.2 (Third Edition Amendment 2, 2004). The four defining parameters are exact by definition; derived parameters and physical constants are given to the precision published by NGA.
Defining parameters
These four numbers completely define the WGS 84 ellipsoid and its rotation. Everything else on this page is derived from them.
| Symbol | Name | Value | Units |
|---|---|---|---|
| a | Semi-major axis (equatorial radius) | 6 378 137.0 | m (exact) |
| 1/f | Reciprocal flattening | 298.257 223 563 | dimensionless (exact) |
| GM | Geocentric gravitational constant (incl. atmosphere) | 3.986 004 418 × 10¹⁴ | m³ s⁻² |
| ω | Nominal mean angular velocity | 7.292 115 × 10⁻⁵ | rad s⁻¹ |
Notes. a and 1/f are exact by definition; they are not measurements. The geocentric gravitational constant GM is published with the mass of the atmosphere included (~3.5 × 10⁸ m³/s² of the total); for satellite dynamics that need GMof the solid Earth only, subtract the atmosphere term. The angular velocity ω is the conventional mean value; instantaneous ω varies on the order of 10⁻⁸ due to Earth's rotation irregularities.
Derived ellipsoid parameters
Everything in this section follows from a and 1/f by closed-form formulas.
| Symbol | Name | Value | Formula |
|---|---|---|---|
| f | Flattening | 3.352 810 664 75 × 10⁻³ | 1 / (1/f) |
| b | Semi-minor axis (polar radius) | 6 356 752.314 245 | a (1 − f) |
| e² | First eccentricity squared | 6.694 379 990 14 × 10⁻³ | f (2 − f) = (a² − b²)/a² |
| e | First eccentricity | 0.081 819 190 842 62 | √e² |
| e′² | Second eccentricity squared | 6.739 496 742 28 × 10⁻³ | e² / (1 − e²) |
| E | Linear eccentricity | 521 854.009 7 | √(a² − b²) |
| c | Polar radius of curvature | 6 399 593.625 8 | a² / b |
Units for b, E, and c are metres. The non-dimensional quantities f, e², e, and e′² have no units.
The three “mean radii” of WGS 84
Three useful single-number summaries of an oblate ellipsoid. They differ by a few kilometres because the ellipsoid is not a sphere. Pick the one that matches your application.
| Symbol | Name | Value (m) | Use when… |
|---|---|---|---|
| R₁ | Mean of the three semi-axes | 6 371 008.7714 | Simple averaging; published “mean Earth radius” |
| R₂ | Authalic sphere radius (equal surface area) | 6 371 007.1810 | Surface-area calculations on a sphere |
| R₃ | Volumetric sphere radius (equal volume) | 6 371 000.7900 | Volume / mass calculations on a sphere |
For navigation and distance work that can tolerate a spherical-Earth approximation (the haversine formula on a sphere), the conventional choice is R₁ = 6,371,008.7714 m, often rounded to 6 371 008 m or 6 371 km. The sub-metre differences between R₁, R₂, and R₃ matter only for precise surface-area or volume work.
Normal gravity (Somigliana formula)
Theoretical gravity on the WGS 84 ellipsoid follows the Somigliana closed-form formula γ(φ) = γe (1 + k sin²φ) / √(1 − e² sin²φ), where φ is geodetic latitude. The constants below are taken from NGA STND 0036 Table 3.6.
| Symbol | Name | Value | Units |
|---|---|---|---|
| γₑ | Theoretical gravity at equator | 9.780 325 3359 | m s⁻² |
| γₚ | Theoretical gravity at pole | 9.832 184 9379 | m s⁻² |
| k | Somigliana's constant | 1.931 852 652 41 × 10⁻³ | dimensionless |
| m | ω² a² b / GM (formula constant) | 3.449 786 506 84 × 10⁻³ | dimensionless |
| C̄2,0 | Normalized dynamic form factor | −4.841 651 437 908 15 × 10⁻⁴ | dimensionless |
These are theoretical (normal) gravity values on the ellipsoid — they do not account for the geoid undulation, terrain, or local mass anomalies. For observed gravity, the difference between normal gravity and measured gravity is the gravity anomaly, and is supplied by EGM2008 (or the more recent EGM2020 candidate models).
Realization history
WGS 84 has been realized seven times. Each realization is a set of ground-station coordinates that anchor the otherwise-mathematical frame to the physical Earth. The G code is the GPS week number on which the realization was introduced; the epoch is the date for which the published station coordinates are valid (plate motion means coordinates drift away from the epoch over time).
| Realization | Introduced | Epoch | Aligned to |
|---|---|---|---|
| WGS 84 (original) | January 1987 | — | NSWC-9Z2 Doppler datum |
| WGS 84 (G730) | 1994.0 | ITRF92 | |
| WGS 84 (G873) | 1997.0 | ITRF94 | |
| WGS 84 (G1150) | 2001.0 | ITRF2000 | |
| WGS 84 (G1674) | 2005.0 | ITRF2008 | |
| WGS 84 (G1762) | 2005.0 | IGb08 | |
| WGS 84 (G2139) | 2016.0 | IGS14 / ITRF2014 |
The current realization is WGS 84 (G2139), active since 3 January 2021 and aligned to IGS14 (the International GNSS Service realization of ITRF2014) at epoch 2016.0. For sub-cm work — geodetic surveying, satellite orbit determination, plate-motion studies — explicitly state the realization and the epoch. For navigation and consumer mapping, “WGS 84” without further qualification is accepted.
WGS 84 vs GRS 80
The Geodetic Reference System 1980 (GRS 80), defined by the International Association of Geodesy in 1980 and described in Moritz (2000), is nearly identical to the WGS 84 ellipsoid and is the basis of NAD 83 (North America), ETRS89 (Europe), and JGD2000 (Japan), among others. The difference is small enough to ignore in any practical application but worth knowing.
| Parameter | WGS 84 | GRS 80 | Difference |
|---|---|---|---|
| a (m) | 6 378 137.0 | 6 378 137.0 | identical |
| 1/f | 298.257 223 563 | 298.257 222 101 | ~1.5 × 10⁻⁶ in 1/f, ≈ 0.1 mm at the pole |
| GM (m³ s⁻²) | 3.986 004 418 × 10¹⁴ | 3.986 005 × 10¹⁴ | ~6 × 10⁸ m³ s⁻², below modern measurement precision |
| ω (rad s⁻¹) | 7.292 115 × 10⁻⁵ | 7.292 115 × 10⁻⁵ | identical (nominal) |
The ellipsoidal-height difference between WGS 84 and GRS 80 at the same geodetic coordinates is sub-millimetre and is dwarfed by the difference between the corresponding datums (e.g. WGS 84 vs NAD 83 differs by roughly 1 to 2 metres in North America because of the different frame definitions, not the ellipsoid). See WGS 84 vs NAD 83 for the practical conversion.
When to use which
- GPS, navigation, GIS, web mapping → WGS 84. Almost universal.
- UTM and MGRS → WGS 84 ellipsoid, even though the grid math itself is independent of the datum.
- Surveying in North America → NAD 83 (GRS 80 ellipsoid). Be explicit about which realization (NAD 83(2011), NAD 83(NA2011), NAD 83(MA11), etc.).
- Surveying in Europe → ETRS89 (GRS 80 ellipsoid).
- Sub-centimetre geodetic work → ITRF directly, with explicit epoch.
- Pre-1987 historical data → the local datum it was published in (NAD 27, ED 50, Tokyo, etc.) and convert with NGS NCAT or PROJ.
The Distance Calculator in this project uses Vincenty's formulae on the WGS 84 ellipsoid; the UTM Converter and MGRS Converter assume WGS 84 inputs. To convert a WGS 84 coordinate to or from a local datum, use NGS NCAT or PROJ — that is outside the scope of this reference.
Related
- WGS 84 Explained— The pillar article on what WGS 84 is, how GPS adopted it, and why it is the default reference frame for nearly every web map.
- What Is a Geodetic Datum?— The conceptual foundation: ellipsoid plus origin plus orientation plus realization equals datum.
- Ellipsoid vs Geoid— Why the WGS 84 ellipsoid is the mathematical reference and the geoid is the physical mean-sea-level surface — they can differ by ±100 m.
- WGS 84 vs NAD 83— The two datums most commonly confused, and how to convert between them.
- Coordinate Format Cheatsheet— The eight common coordinate formats — all of which (DD, DMS, DDM, UTM, MGRS) are stated relative to WGS 84 unless otherwise noted.
Sources
- NGA — NGA.STND.0036_1.0.0_WGS84 — Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems (Edition 1, v1.0.0, 2014-07-08) · https://earth-info.nga.mil/php/download.php?file=coord-wgs84 · Accessed .
- NIMA — NIMA TR 8350.2 — Department of Defense World Geodetic System 1984 (Third Edition Amendment 2, 2004-06-23) · https://earth-info.nga.mil/php/download.php?file=coord-wgs84 · Accessed .
- IERS — IERS Conventions (2010) — Petit, G. & Luzum, B. (eds.), IERS Technical Note 36 · https://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn36.html · Accessed .
- Moritz — Moritz, H. (2000). Geodetic Reference System 1980. Journal of Geodesy, 74(1), 128–133 · https://link.springer.com/article/10.1007/s001900050278 · Accessed .
- NGA — EGM2008 — The Earth Gravitational Model 2008 (Pavlis, Holmes, Kenyon, Factor) — uses the WGS 84 reference ellipsoid · https://earth-info.nga.mil/php/download.php?file=egm-08 · Accessed .
- NGS — NGA / NGS WGS 84 (G2139) Bulletin — Cooperative bulletin announcing the G2139 realization aligned to IGS14 (Jan 2021) · https://earth-info.nga.mil/ · Accessed .
Cite this article
APA format:
Steve K. (2026). WGS 84 Parameters. Coordinately. https://coordinately.org/reference/wgs84-parameters
BibTeX:
@misc{coordinately_wgs84parameters_2026,
author = {K., Steve},
title = {WGS 84 Parameters},
year = {2026},
publisher = {Coordinately},
url = {https://coordinately.org/reference/wgs84-parameters},
note = {Accessed: 2026-06-05}
}