Orthometric Height – Elevation Above Geoid in Surveying: Complete Glossary and Technical Reference

Orthometric height is a cornerstone concept in geodesy, surveying, civil engineering, and all fields that require accurate and consistent elevation data. Understanding the difference between orthometric, ellipsoidal, and geoid heights—and how to correctly convert between them—is critical for anyone working with mapping, land development, infrastructure, or environmental analysis.

Orthometric Height

Orthometric height (H) is the vertical distance from a point on the Earth’s surface to the geoid—a theoretical surface that closely aligns with global mean sea level and is defined by the Earth’s gravity field. This height is measured along the direction of gravity (the plumb line) and reflects the true potential energy of water flow, making it the most practical and widely used definition of “elevation above sea level” in mapping, construction, and hydrology.

Orthometric heights are the values shown on topographic maps, benchmarks, and legal land descriptions, and are essential for designing drainage, roadways, railways, and any infrastructure where the movement of water is a factor.

Direct measurement of orthometric height is achieved through spirit leveling, a highly accurate but labor-intensive process that measures the elevation difference between points using a level and graduated rods. Over large areas, however, spirit leveling is inefficient, so modern practice often relies on Global Navigation Satellite System (GNSS) technology to provide ellipsoidal heights, which are then converted to orthometric heights using a geoid model.

The fundamental relationship is:

H = h – N

where:

• h is the ellipsoidal height (from GNSS),
• N is the geoid height (from a geoid model),
• H is the orthometric height (elevation above the geoid/mean sea level).

Orthometric height provides a consistent, gravity-based reference for comparing elevations at any scale. For example, the published height of Mount Everest (8,848.86 meters) is its orthometric height—its elevation above the geoid, not the ellipsoid.

Geoid Height (Geoid Undulation)

Geoid height (N), also known as geoid undulation or geoid separation, is the vertical distance between the reference ellipsoid (a smooth mathematical approximation of Earth’s shape) and the geoid at a specific location.

• If N is positive, the geoid lies above the ellipsoid.
• If N is negative, the geoid lies below the ellipsoid.

For example, in the continental United States, geoid heights typically range from about –27 meters to –38 meters (the geoid is below the WGS84 ellipsoid).

Geoid height is vital for converting GNSS-derived ellipsoidal heights to orthometric heights. Accurate geoid models (such as EGM2008 globally or GEOID18 in the U.S.) are used to determine N at any location, enabling the calculation of elevation above mean sea level.

The undulating nature of the geoid is caused by variations in Earth’s gravity field, resulting from mountains, valleys, and subsurface density differences. These undulations can exceed 100 meters worldwide.

Modern geoid models are developed from satellite altimetry, gravimetric surveys, and terrestrial data, and are updated regularly to improve precision.

Ellipsoidal Height

Ellipsoidal height (h) is the vertical distance from a point on the Earth’s surface to the reference ellipsoid (e.g., WGS84, GRS80).

• GNSS and GPS receivers provide ellipsoidal heights by default.
• Ellipsoidal heights ignore gravity variations and geoid undulations, so they do not directly represent “elevation above sea level.”
• Conversion to orthometric height (the value used in engineering and mapping) requires application of the geoid correction (N).

Ellipsoidal heights are essential for precise geodetic calculations, satellite navigation, and global reference frameworks, but cannot be used as “above sea level” elevations without geoid correction.

Geoid

The geoid is the equipotential surface of Earth’s gravity field that best represents mean sea level globally. It is the only surface to which the force of gravity is everywhere perpendicular, making it the natural reference for measuring orthometric heights.

• The geoid is an irregular shape that reflects the real distribution of mass within the Earth.
• It is not a simple geometric surface like a sphere or ellipsoid.
• The geoid is determined by a combination of satellite, airborne, and terrestrial gravity measurements.

The geoid serves as the zero elevation surface for most national and regional vertical datums, and is the reference for all orthometric heights.

Reference Ellipsoid

A reference ellipsoid is a mathematically defined, oblate spheroid that approximates the Earth’s overall shape. Key parameters:

• Semi-major axis (equatorial radius)
• Flattening (degree of polar “squashing”)

Common ellipsoids:

• WGS84: Used globally, especially for GPS.
• GRS80: Used in North America (NAD83).
• International 1924: Used in historical European mapping.

All GNSS/GPS positions are referenced to a specific ellipsoid, affecting computed coordinates and heights.

Vertical Datum

A vertical datum is the reference surface from which elevations are measured. Major types:

• Geoid-based datums (e.g., NAVD88, EGM2008): Reference the geoid.
• Ellipsoid-based datums (e.g., WGS84): Reference the ellipsoid.
• Tidal datums: Use local mean sea level at a specific tide gauge.

Using the correct vertical datum is essential for consistent elevation data across regions and projects.

Mean Sea Level (MSL)

Mean Sea Level (MSL) is the average height of the ocean’s surface over time, used as a practical approximation for the geoid in many local and regional vertical datums.

• MSL is not level globally—it varies due to ocean currents, gravity anomalies, and atmospheric effects.
• In mapping, “elevation above mean sea level” typically means “height above the geoid.”

Geoid Model

A geoid model mathematically represents the undulations of the geoid relative to a reference ellipsoid. It provides geoid heights (N) as a grid, enabling users to convert GNSS ellipsoidal heights to orthometric heights.

• Leading global geoid models: EGM96, EGM2008.
• U.S. national model: GEOID18.
• Geoid models are updated as new satellite and terrestrial gravity data become available.

Height System Relationships

The relationship between ellipsoidal height (h), geoid undulation (N), and orthometric height (H):

H = h – N

All three quantities must refer to the same location and use compatible datums and models.

Practical Applications

Surveying

Surveyors use orthometric heights for all projects requiring accurate elevation data. Traditional leveling networks and benchmarks are based on orthometric heights, referenced to a vertical datum (like NAVD88).

Workflow:

1. Collect ellipsoidal heights (h) with GNSS.
2. Retrieve geoid heights (N) from a geoid model.
3. Compute orthometric heights (H = h – N) for maps, designs, and legal documentation.

GPS/GNSS Data Collection

GNSS receivers provide latitude, longitude, and ellipsoidal height. To obtain “elevation above sea level,” always apply a geoid correction. Omitting this step can introduce errors of 10–50 meters or more, depending on location.

Drone Mapping and Photogrammetry

Drones record ellipsoidal heights in image metadata. For engineering or environmental deliverables, these must be converted to orthometric heights using a geoid model, ensuring products align with mapping and construction standards.

Process:

• Get local geoid height (N).
• Apply the offset to image altitudes.
• Validate with ground control points (GCPs) of known orthometric height.

Hydrology and Floodplain Mapping

Orthometric heights are vital for water flow modeling, floodplain delineation, and environmental risk analysis. Since water flows “down” orthometric surfaces, accurate heights ensure reliable predictions and designs.

Regional Vertical Datums and Geoid Models

United States

• North American Vertical Datum of 1988 (NAVD88) is the standard system.
• GEOID18 is the current geoid model for GNSS-to-orthometric conversions.

Europe

Various national datums based on local mean sea level observations:

• NAP (Netherlands)
• TAW (Belgium)
• Conversion between datums is necessary for cross-border projects.

Global

• EGM96 and EGM2008 are global geoid models referenced to the WGS84 ellipsoid, widely used for international navigation and mapping.

Conversion Methods

To convert ellipsoidal height (h) to orthometric height (H):

1. Identify reference surfaces: Know your ellipsoid and geoid model.
2. Collect ellipsoidal height (h): From GNSS or dataset.
3. Obtain geoid height (N): Use a geoid model or calculator.
4. Calculate: H = h – N.
5. Document: Reference all models and datums.
6. Validate: Compare results to local benchmarks if possible.

Common Misunderstandings

• Confusing ellipsoidal and orthometric heights: Always convert GNSS heights to orthometric using a geoid model.
• Mixing datums: Don’t combine data from different vertical datums without proper transformation.
• Using outdated models: Always use current geoid models.
• Assuming mean sea level is flat: MSL varies regionally due to gravity and oceanographic effects.

Key Terms Defined

In summary: Orthometric height is the true “elevation above sea level” used in surveying, engineering, and mapping. It is measured above the geoid, requires correction from GNSS ellipsoidal heights using a geoid model, and is vital for all applications where accurate elevation matters.

If you’re working with elevation data, always ensure you understand the difference between orthometric, ellipsoidal, and geoid heights—and use the correct conversion methods and models for your region and project.