geoprimsField-grade geospatial math

NAD83 vs. WGS 84 explained

Datums, realizations, and epochs, and why a meter separates two systems people treat as the same.

For surveyors · updated 2026-09-23

NAD 83 and WGS 84 are two different geodetic datums. They started out almost the same in the 1980s, but today they differ by more than a meter across the United States, and the gap grows every year. A latitude and longitude means nothing precise until you know which datum, and which version of it, it is on.

The short reason: WGS 84 is tied to the whole Earth, and NAD 83 is tied to the North American plate. The plate moves, so the two slowly pull apart.

What a datum is, and what a realization is

A datum says where the coordinate grid sits on the Earth: where its center is, how it is turned, and what ellipsoid it uses. NAD 83 and WGS 84 use nearly the same ellipsoid, so the difference between them is not about shape. It is about where the frame is anchored.

Each datum has been updated several times. Each update is a realization, and it has its own tag:

Datum Current realization Anchored to
WGS 84 G2296, used by NGA since January 7, 2024 The whole Earth; aligned with ITRF2020
NAD 83 NAD 83(2011), epoch 2010.00 The North American plate

NGS also keeps NAD 83(PA11) for the Pacific plate and NAD 83(MA11) for the Mariana plate. The HTDP revision log from the National Geodetic Survey (NGS) treats WGS 84 (G2296) as equal to ITRF2020, the international frame. NGA says the WGS 84 frame is aligned with the ITRF to within a centimeter.

Why the gap keeps growing

A coordinate in a plate-fixed frame like NAD 83(2011) stays put while the ground under it moves with the plate. A coordinate in an Earth-fixed frame like WGS 84 or ITRF2020 changes as the plate drifts. That is why an ITRF or WGS 84 coordinate needs an epoch: the date it was true.

The plate motion tool shows the drift. With the ITRF2020 plate model, a point in central Kansas moves 14.57 mm a year west and 3.41 mm a year south. From 2010.0 to 2026.7 that adds up to 0.2498 m.

The same drift shows up in the datum difference. At that Kansas point the gap between WGS 84 (G2296) and NAD 83(2011) was 1.161 m at epoch 2010.0 and is 1.3573 m at epoch 2026.7.

How it is worked out

NGS publishes the relationship as a 14-parameter Helmert transformation in its HTDP software: three shifts, three rotations, a scale change, and a yearly rate for each. The steps are:

  1. Turn latitude, longitude, and ellipsoidal height into Earth-centered X, Y, Z.
  2. Work out the seven parameters at your epoch from their rates.
  3. Rotate, scale, and shift X, Y, Z into the other frame.
  4. Turn the result back into latitude, longitude, and height.

The NAD 83 transformation tool follows HTDP’s route through ITRF94 and reports the difference as east, north, and up.

A worked example

A point in central Kansas at 38.5° N, 98° W, 500 m ellipsoidal height, given in WGS 84 (G2296) at epoch 2026.7 and moved to NAD 83(2011):

Result Value
East 1.2039 m
North −0.6267 m
Horizontal difference 1.3573 m, toward 117.5°
Up 1.0234 m
NAD 83(2011) height 501.0234 m

The same point on NAD 83(2011) plots about 1.36 m east-southeast of its WGS 84 spot, and its ellipsoidal height is about 1 m larger. The size and direction change across the country. At epoch 2026.7 the horizontal difference is 1.5763 m in San Francisco and 1.2588 m in New York.

Old datums: NAD 27 and NADCON5

NAD 27 is a much older datum, built outward from Meades Ranch in Kansas. Its errors vary from place to place, so a single set of parameters cannot convert it. NGS publishes grids of shifts instead, called NADCON 5.0. At Meades Ranch the NADCON5 tool moves a NAD 27 position 29.815 m, toward 272.1°, to reach NAD 83(1986).

Outside North America, older datums such as ED50 are often converted with published Helmert parameters. The legacy datum tool moves a point in Paris 138.7 m from ED50 to WGS 84, and warns that this transformation is good only to about 10 m.

Rules of thumb

Common mistakes

Where the numbers come from

The transformation parameters are those in NGS’s HTDP 3.6.0. The NAD 83 frames and their 2010.00 epoch are described in NGS Technical Report 65, and the NAD 27 grids in NGS Technical Report 63. Each tool shows its steps under “How we got this.” Start with the NAD 83 transformation tool for modern GNSS data, and the NADCON5 tool for anything on NAD 27.

Try it: Transform between NAD 83 and ITRF or WGS 84

The calculator below is the real tool, running its worked example. Change any value; nothing leaves your device.

1.3573m

The frames differ here by 1.3573 m horizontally, toward 117.5°.

East shift
North shift
Up shift
Shift direction
Latitude
Longitude
Provenance
Computed by
geodesy.datum.nad83 1.0.0, core 0.1.0
Model
NGS HTDP 3.6.0 14-parameter transformations through ITRF94, applied as HTDP does; WGS 84 (G2296, G2139, G1762) taken as ITRF2020, ITRF2014, and ITRF2008
Accuracy
Matches NGS HTDP 3.6.0 within 1 mm; the transformation itself is good to about 1–2 cm in the conterminous United States
Notes
None
Cites
National Geodetic Survey, NOAA, Horizontal Time-Dependent Positioning (HTDP) software, version 3.6.0

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Sources

Every number on this page comes from the tools above, which cite their sources on their own pages under "How we got this." Found a mistake? Use "Report a problem" at the bottom of the page.