FS Exam Preparation

Comprehensive preparation for the Fundamentals of Surveying (FS) exam. 7 modules covering all 7 exam domains with 60 in-depth topics.

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Lesson 5

Datums & Datum Conversions

Learning Objectives

After completing this topic, you should be able to:

Define a geodetic datum and its components
Describe the major horizontal datums (NAD 27, NAD 83, WGS 84)
Describe the major vertical datums (NGVD 29, NAVD 88)
Explain why datum transformations are necessary
Understand the difference between geocentric and local datums
Describe the upcoming NSRS modernization (NATRF2022, NAPGD2022)

Overview

A datum is a reference system that defines the position of the coordinate origin, the orientation of the coordinate axes, and the shape and size of the reference surface (ellipsoid for horizontal datums, geoid for vertical datums). Every coordinate or elevation in surveying is referenced to a specific datum, and mixing datums without proper transformation is one of the most common sources of error in geospatial data.

The FS exam tests your understanding of the major datums used in the United States and the basic concepts of datum transformation.

Key Concepts

Figure FS.4.5 — Datum Comparison: NAD 27 vs NAD 83

What Is a Datum?

A horizontal datum defines a reference for latitude and longitude (and horizontal coordinates):

The ellipsoid (shape and size)
The orientation and position of the ellipsoid relative to the earth
The network of control points with published coordinates

A vertical datum defines a reference for elevations:

A specific level surface (approximating mean sea level)
The network of benchmarks with published elevations

Major Horizontal Datums

NAD 27 (North American Datum of 1927):

Based on the Clarke 1866 ellipsoid
Origin point: Meades Ranch, Kansas (the ellipsoid was positioned to best fit North America at this point)
A local datum (not earth-centered)
Coordinates were determined by classical triangulation and traverse
Still found on many older maps, plats, and deeds
The ellipsoid does not fit well away from the origin; distortions accumulate over large distances

NAD 83 (North American Datum of 1983):

Based on the GRS 80 ellipsoid
Earth-centered (geocentric) datum
Determined by satellite (Doppler) observations and classical surveys
The current standard horizontal datum in the United States
Multiple realizations (adjustments): NAD 83 (1986), NAD 83 (HARN), NAD 83 (CORS96), NAD 83 (2011)
Each realization improves the accuracy; coordinates may differ by centimeters between realizations

WGS 84 (World Geodetic System 1984):

The GPS reference datum
Based on the WGS 84 ellipsoid (virtually identical to GRS 80)
Earth-centered, global datum
Maintained by the U.S. Department of Defense
Practically coincident with NAD 83 at the 1-2 meter level, but differs at the centimeter level
WGS 84 is periodically refined to align with ITRF (the most accurate global reference frame)

Differences Between NAD 27 and NAD 83

Figure FS.4.5d — NAD 27 (Clarke 1866, local) vs NAD 83 (GRS 80, geocentric)

The coordinate differences between NAD 27 and NAD 83 for the same physical point can be significant:

Parameter	Typical Difference (Conterminous U.S.)
Latitude	0 to 2 arc seconds (0 to 60 meters)
Longitude	0 to 3 arc seconds (0 to 100 meters)
Northing (State Plane)	0 to 200+ meters
Easting (State Plane)	0 to 200+ meters

These are not small differences. Using NAD 27 coordinates in a NAD 83 system (or vice versa) without transformation produces significant errors.

Common wrong path — treating a NAD 83 "realization" like a datum change. NAD 83 has been adjusted several times: NAD 83(1986), NAD 83(HARN), NAD 83(CORS96), NAD 83(2011), and so on. These are realizations of the same datum, not different datums. The coordinate of a physical monument can differ by several centimeters — occasionally more than a decimeter — between realizations, which is much smaller than the 30+ meters separating NAD 27 from NAD 83, but much larger than the centimeter-level precision expected of modern GNSS control. Students sometimes answer "use NADCON" when the question is really about realization differences within NAD 83. NADCON converts between NAD 27 and NAD 83; realization differences within NAD 83 require a specific realization-to-realization transformation (e.g., HTDP from NGS, or epoch-shift via CORS). Exam questions plant this trap by quoting coordinates with realization tags — read them carefully.

Quick retrieval check — try before reading on.

▶A survey from 2008 reports coordinates on "NAD 83 (HARN)." A current survey reports coordinates on "NAD 83 (2011) epoch 2010.00." Can you directly compare the two coordinate sets for a physical monument that hasn't moved? If not, what tool applies?

No — not directly. Although both are NAD 83, the realizations differ. For a typical CONUS location, NAD 83(HARN) and NAD 83(2011) coordinates for the same monument can differ by centimeters to a decimeter. To compare the two, apply a realization-to-realization transformation. NGS's HTDP (Horizontal Time-Dependent Positioning) tool handles this: input the older realization and epoch, specify the target realization and epoch, and it outputs the adjusted coordinates. NADCON is not the right tool here — NADCON bridges NAD 27 and NAD 83, not realizations within NAD 83. If the monument has moved (tectonic motion, subsidence), even HTDP may not suffice; you'd need observations at both epochs and a model of the physical movement. On the exam, the keyword is "realization" — treat it as a subtle but real shift, not the same as the datum label.

Major Vertical Datums

Figure FS.4.5f — NGVD 29, NAVD 88, NAPGD2022 vertical datums

NGVD 29 (National Geodetic Vertical Datum of 1929):

Based on mean sea level as determined at 26 tide gauge stations in North America
Also called the Sea Level Datum of 1929
The vertical reference for older maps, plats, and surveys
Has known distortions because the geoid and mean sea level do not coincide perfectly

NAVD 88 (North American Vertical Datum of 1988):

Determined by a least-squares adjustment of all leveling data in North America, then held fixed to a single tidal benchmark at Father Point/Rimouski, Quebec (rather than to the mean of 26 tidal gauges as in NGVD 29)
The current standard vertical datum in the United States
More accurate and internally consistent than NGVD 29

Differences between NGVD 29 and NAVD 88:

Typically 0 to 0.5 meters across the conterminous U.S., but can be larger in some areas (NGS VERTCON documentation; Zilkoski, Results of the General Adjustment of NAVD 88, 1992)
The difference varies by location (not a constant offset)
Conversion requires using published datum shifts (VERTCON tool from NGS)

Datum Transformations

Horizontal transformation (NAD 27 to NAD 83):

Figure FS.4.5b — NAD 27 → NADCON → NAD 83 transformation

Uses NADCON (North American Datum Conversion) from NGS
Based on a grid of latitude and longitude shifts
Accuracy: approximately 15 cm (NGS NADCON documentation, geodesy.noaa.gov)

Vertical transformation (NGVD 29 to NAVD 88):

Figure FS.4.5c — NGVD 29 → VERTCON → NAVD 88

Uses VERTCON from NGS
Based on a grid of elevation differences
Accuracy: approximately 2 cm (NGS VERTCON documentation, geodesy.noaa.gov)

General 3D transformations (between global frames):

Seven-parameter (Helmert) transformation: 3 translations, 3 rotations, 1 scale factor
Used to convert between WGS 84, NAD 83, ITRF
The parameters are published by NGS and other agencies

NSRS Modernization

Figure FS.4.5e — NSRS modernization: NATRF2022, NAPGD2022, GEOID2022

NGS is modernizing the National Spatial Reference System:

NATRF2022 (North American Terrestrial Reference Frame of 2022):

Will replace NAD 83 as the horizontal datum
Will be a plate-fixed, ITRF-aligned reference frame
Coordinates will be time-dependent (velocities published for each point to account for tectonic motion)

NAPGD2022 (North American-Pacific Geopotential Datum of 2022):

Will replace NAVD 88 as the vertical datum
Based on a gravimetric geoid model rather than leveling
Will allow GNSS to determine orthometric heights directly (with geoid model)
Eliminates the need for extensive leveling networks

Exam Tips

NAD 27 uses Clarke 1866 (local datum, Meades Ranch origin); NAD 83 uses GRS 80 (geocentric datum)
NAD 27 and NAD 83 coordinates for the same point can differ by tens to hundreds of meters -- never mix them
WGS 84 is practically identical to NAD 83 at the 1-2 meter level; for higher accuracy, they differ
NGVD 29 and NAVD 88 differ by 0 to 0.5+ meters; the difference varies by location
NADCON converts horizontal coordinates between NAD 27 and NAD 83
VERTCON converts elevations between NGVD 29 and NAVD 88
Every coordinate or elevation must specify its datum -- a number without a datum is meaningless
The FS exam may ask about the characteristics of each datum, the differences between them, or why transformation is necessary
Newer NAD 83 realizations (2011, CORS96) are more accurate than the original 1986 adjustment
The upcoming NATRF2022 will be time-dependent to account for tectonic motion

FS Exam Preparation

Module 1: Surveying Processes & Methods

Module 2: Mapping Processes & Methods

Module 3: Boundary Law & Real Property

Module 4: Surveying Principles & Geodesy

Module 5: Survey Computations

Module 6: Business Concepts

Module 7: Applied Math & Statistics