Datums & heights · 4 min read

GRS 80 and WGS 84: the reference ellipsoids and why they are nearly identical

GRS 80 and WGS 84 share a semi-major axis and differ in flattening only in the ninth digit. The practical difference is a tenth of a millimeter.

GRS 80 is the ellipsoid underlying NAD 83. WGS 84 is the ellipsoid underlying the reference frame that GPS broadcasts its orbits in. They have the same semi-major axis and flattenings that agree to eight significant figures, which leads to a reasonable question: are they the same ellipsoid, and if not, does the difference matter?

The answers are no and no. They are formally different, the difference in the polar radius is about a tenth of a millimeter, and it is entirely negligible for surveying. What is emphatically not negligible is the difference between the datums built on them, which is a different matter and is where real coordinate discrepancies of one to two meters come from.

The defining constants

GRS 80 and WGS 84 compared
ParameterGRS 80WGS 84
Semi-major axis a6 378 137 m6 378 137 m
Reciprocal flattening 1/f298.257222101298.257223563
Semi-minor axis b (derived)6 356 752.3141 m6 356 752.3142 m
How flattening is fixedDerived from the dynamic form factor J2Adopted directly as a defining constant
Adopted byInternational Union of Geodesy and Geophysics, 1979US Department of Defense, first version 1984

The reciprocal flattenings differ by 0.000001462. Propagated to the polar semi-minor axis, that produces a difference of roughly 0.1 mm. No survey instrument, and no realistic combination of them, resolves that.

Why the difference exists at all

GRS 80 is defined by four constants: the semi-major axis, the geocentric gravitational constant, the dynamic form factor J2 which describes the Earth equatorial bulge, and the angular velocity of rotation. Flattening is not one of the defining constants; it is computed from J2 through a series expansion, and the published value 1/f = 298.257222101 is the result of that computation.

WGS 84 started from the same idea but expressed the second-degree zonal term as a normalized spherical harmonic coefficient, then rounded that coefficient before deriving flattening from it. The rounding is the entire origin of the discrepancy. Later, rather than silently changing a published constant, WGS 84 promoted its flattening to a defining constant in its own right. The gravitational constants of the two systems also differ slightly, which matters for orbit computation and not for a boundary survey.

Where the meter-level difference really comes from

NAD 83 was fixed in the 1980s using the best available determination of the geocentre at the time. Later satellite geodesy showed that determination was off: the NAD 83 origin sits roughly 2.2 m from the true center of mass of the Earth. Because the offset is a translation of the whole frame, it shows up as a systematic difference of one to two meters in horizontal position between NAD 83 and the modern global frames, varying with location.

So if a handheld receiver reporting WGS 84 gives a position a meter and a half from your NAD 83 control, the ellipsoid is not the reason. The frame origin is. Correcting it requires a datum transformation, not an ellipsoid parameter change.

WGS 84 has realizations too

WGS 84 is often spoken of as though it were a single fixed thing. It is not. It has been redetermined repeatedly as the tracking network and the processing improved, and the successive versions are identified by GPS week numbers — G1150, G1674, G1762, G2139 and later. Each realization is aligned more closely to the contemporary international terrestrial reference frame, and the current ones agree with it at the centimetre level.

For most surveying purposes it is safe to treat a current WGS 84 realization and the contemporary international frame as equivalent. It is never safe to treat either of them as equivalent to NAD 83.

What this means for your work

  • Do not attempt to correct between GRS 80 and WGS 84 as ellipsoids. The difference is a tenth of a millimeter and any transformation you apply will be noise you introduced yourself.
  • Do transform between NAD 83 and a global frame when meter-level agreement matters. That is a real, systematic, one-to-two-meter difference.
  • Autonomous handheld positions are broadcast in a WGS 84 realization. Treating those numbers as NAD 83 imports the frame offset silently.
  • When a network provider or a correction service quotes a datum, ask which realization and which epoch, not just which ellipsoid.
  • The modernized frame replacing NAD 83 is designed to be genuinely geocentric, which removes this particular offset for good.

The short version: GRS 80 and WGS 84 are the same shape for every practical purpose, and the meter you are chasing is a frame problem, not a shape problem.

Questions

Are GRS 80 and WGS 84 the same ellipsoid?

Not formally. They share a semi-major axis of 6 378 137 m but their reciprocal flattenings differ — 298.257222101 versus 298.257223563 — because WGS 84 derived flattening from a rounded harmonic coefficient. The resulting difference in the polar radius is about 0.1 mm, which is negligible for any survey.

So why do my WGS 84 and NAD 83 coordinates differ by more than a meter?

Because of the datum, not the ellipsoid. The NAD 83 origin is offset from the true geocentre by roughly 2.2 m, which shows up as a systematic one to two meter horizontal difference from modern global frames. Fixing it requires a datum transformation.

Which ellipsoid does State Plane use?

State Plane Coordinate System zones defined on NAD 83 are computed on the GRS 80 ellipsoid. Older SPCS 27 zones were computed on Clarke 1866, which is one of the reasons NAD 27 and NAD 83 State Plane coordinates are not interchangeable.

Sources

  • NOAA / National Geodetic Survey — GRS 80 parameters as adopted for NAD 83, and the relationship between NAD 83 and the international terrestrial reference frames.