The Geoid Explained

A bowling ball dropped onto a sloped lawn rolls downhill. But what is “downhill”? Not the direction toward the centre of Earth, exactly — that direction is the gravitational pull, which varies in strength and direction depending on local mass distribution. Not perpendicular to the reference ellipsoid either — the ellipsoid is a mathematical idealisation that ignores Earth's actual interior. “Downhill” is the direction perpendicular to the geoid — the equipotential surface of Earth's gravity field. Water flows along geoid contours. Buildings stand perpendicular to it. Civil engineering, hydrology, and any sea-level-relative work all reference the geoid.

The /learn/what-is-a-geodetic-datum pillar introduces the geoid as one of the four components of a datum. This article goes deep on what the geoid is, why it's irregular, how modern geoid models are built, and why orthometric heights matter.

What the geoid is

The geoid is an equipotential surface of Earth's gravity field. At every point on the geoid, the gravitational potential is the same value, and the local gravity vector points perpendicular to the surface.

If Earth were a perfect sphere of uniform density, the geoid would be a perfect sphere. It isn't — Earth is slightly flattened by rotation, and mass inside Earth is unevenly distributed. The geoid reflects both effects: it's roughly the shape of an ellipsoid of revolution, with bumps and dips of up to ~85 m where the local gravity is anomalous.

The geoid is the surface that the global ocean would settle into if tides, winds, currents, salinity gradients, and other dynamic effects vanished. In practice, mean sea level (averaged over years) closely approximates the geoid over open oceans; on land, the geoid extends conceptually beneath the surface, threading through hills and mountains as the surface that water would form if the land were transparent to it.

Why the geoid is irregular

Earth's interior is not uniform. The core, mantle, and crust all have different densities; within each layer, mass distribution varies regionally. Major contributors to geoid irregularity:

• Continental crust is less dense than oceanic crust, but thicker; the net gravitational effect varies regionally.
• Mountain ranges add mass above the geoid but typically have low-density “roots” that partly compensate (isostasy). The net effect on the geoid varies from range to range.
• Ocean trenches are deficits of mass; the geoid sags above them.
• Mantle density variations — including subducting slabs of former ocean floor — pull the geoid up or down depending on the density contrast.
• The Indian Ocean Geoid Low — a 105+ metre depression in the geoid southwest of India — is still under active scientific investigation as of the late 2020s; the leading hypothesis is ancient subducted material in the deep mantle.

The geoid undulation N — the height of the geoid above the reference ellipsoid (positive) or below (negative) — has a global range of about 191 m (from −106 m near Sri Lanka to +85 m near Iceland). Locally, the undulation typically varies by tens of metres across continental scales.

Geoid undulation around the world

A few representative values from EGM2008:

| Region | Approx. geoid undulation (N) | | ---------------------------------- | ---------------------------- | | Indian Ocean Geoid Low (off Sri Lanka) | −106 m | | Caribbean | −40 m | | Continental US (CONUS) | −20 to −30 m | | Atlantic Ocean (mid-latitude) | −10 to +20 m | | Western Europe | +40 to +50 m | | Iceland | +60 to +85 m | | Indonesia / Philippines | +60 to +75 m | | North-east Atlantic (near Iceland) | +85 m |

For sea-level-relative work in CONUS, the geoid is roughly 25 m below the WGS 84 ellipsoid — so a GPS ellipsoidal height of 100 m corresponds to an orthometric (sea-level) height of about 125 m. In Iceland the situation flips: an ellipsoidal height of 100 m corresponds to an orthometric height of about 15 m.

The /tools/elevation tool returns orthometric heights (referenced to the geoid via the dataset's vertical datum); the underlying coordinate is in WGS 84 horizontal.

Modern global and regional geoid models

The geoid is computed by combining satellite gravity observations with terrestrial measurements:

• NASA's GRACE and GRACE-FO missions (2002–present) track the changing distance between two satellites in nearly identical orbits. When the lead satellite passes over a mass concentration, it's pulled slightly ahead; the changing satellite-to-satellite distance reveals the local gravity field. GRACE produces monthly snapshots of Earth's gravity at ~300 km resolution.
• ESA's GOCE mission (2009–2013) carried a gravity gradiometer that measured the gravity field at higher spatial resolution (~100 km) than GRACE achieves.
• Terrestrial gravity surveys add fine-scale detail by measuring gravity directly at points on land or shipborne at sea.
• Satellite altimetry (Jason, Sentinel-3, others) measures the ocean's mean surface to centimetres, helping constrain the marine geoid.

The combined data products include:

• EGM2008 (NGA, 2008) — the canonical global geoid model since 2008. Spherical harmonic expansion to degree 2,190 (~10 km resolution).
• EGM96 (NGA, 1996) — an earlier model, still seen in legacy systems.
• GEOID18 (NGS, 2018) — current US geoid model. Used to convert between ellipsoidal and orthometric heights for NAD 83(2011) / NAVD 88.
• GEOID2022 (NGS, planned mid-2020s) — the modernised US geoid model that will accompany NATRF2022 / NAPGD2022 in the upcoming NSRS modernization.
• EGG2015 and similar regional models for Europe and elsewhere.

Each model is parameterised as a set of spherical harmonic coefficients; software libraries (PROJ, GeographicLib) include EGM2008 by default and add regional refinements where needed.

Converting between heights — worked example

A GPS receiver in lower Manhattan reports an ellipsoidal height of h = 28.5 m above the WGS 84 ellipsoid. The geoid model GEOID18 reports a geoid undulation at that location of approximately N = −33.4 m (the geoid is 33.4 m below the ellipsoid in mid-Manhattan).

The orthometric height (sea-level height) is:

H = h − N
H = 28.5 − (−33.4)
H = 28.5 + 33.4
H = 61.9 m

So the GPS receiver, sitting at a place that's 61.9 m above mean sea level, reports an ellipsoidal height of only 28.5 m because the geoid is significantly below the ellipsoid in this region. The conversion is a subtraction; the value of N comes from the geoid model.

For the same calculation in Iceland, where the geoid is roughly 80 m above the ellipsoid:

h (ellipsoidal) = 200 m
N (geoid undulation) = +80 m
H (orthometric) = 200 − 80 = 120 m

A GPS reading of 200 m in Iceland corresponds to an actual sea-level height of only 120 m. Without the geoid-model correction, the height claim is off by 80 m.

The /tools/elevation tool returns orthometric heights for any point — applying the appropriate geoid model under the hood so the value displayed is sea-level-relative.

Why orthometric heights matter

The geoid's practical importance is that water flows along geoid contours (or more precisely, perpendicular to the local gravity vector). Three classes of work require orthometric heights specifically:

1. Hydrology and water management. Determining flow direction in rivers, drainage of farmland, design of irrigation systems, sizing of culverts and storm drains. Ellipsoidal heights would produce wrong drainage maps because the geoid undulation varies regionally.
2. Civil engineering. Roads, railways, runways, bridges, and sewer systems all reference orthometric heights so they grade consistently along the geoid. A road designed on ellipsoidal heights would have inconsistent grades relative to gravity.
3. Sea-level monitoring. Long-term sea-level change is measured relative to a vertical datum tied to the geoid. The distinction matters for climate-change research and coastal planning.

For navigation, recreation, and most everyday GPS use, the ellipsoidal-vs-orthometric distinction is invisible because consumer GPS doesn't expose ellipsoidal height (most devices apply a geoid model and report orthometric height) and the 20-metre offset is below typical positioning noise. But for infrastructure work, the distinction is foundational.

Common misconceptions

“The geoid is sea level.” Close but not identical. Mean sea level (averaged over many years) approximates the geoid over open oceans, but ocean currents, salinity, temperature gradients, and atmospheric pressure variations cause the actual mean sea surface to differ from the geoid by up to ~2 m. The geoid is the idealised sea-level surface; actual mean sea level is a measurement of it with dynamic-ocean corrections.

“The geoid is a sphere.” The geoid is approximately ellipsoidal in overall shape (matching Earth's rotation- flattened figure), with regional bumps and dips of up to ~85 m on top. It is decidedly not spherical — even the “mean geoid” (the best-fit ellipsoid to the geoid surface) is the WGS 84 ellipsoid, not a sphere.

“GPS gives elevation above sea level.” Raw GPS gives ellipsoidal height. Consumer devices typically apply a geoid model (EGM96 or EGM2008 are common) to convert to orthometric height before display, but the conversion is not always exact and not always disclosed. For survey-grade work, the device's geoid model has to be the right one for the region (GEOID18 in the US is more accurate locally than the global EGM2008).

“The geoid changes shape over time.” Tiny but measurable changes occur as mass redistributes — melting ice sheets, groundwater depletion, glacial isostatic adjustment from the last ice age. GRACE has measured these changes for over 20 years; the centimetre-per-decade scale matters for climate research but is invisible to everyday positioning.

“The geoid is the same everywhere on the planet.” There is one global geoid surface, but its shape varies regionally by up to ~191 m total. Regional geoid models (GEOID18, EGG2015, others) refine the global geoid (EGM2008) with local terrestrial gravity data so the model is more accurate in its region.

“You can use any geoid model interchangeably.” EGM96 to EGM2008 to GEOID18 can differ by tens of centimetres at a given location. For sub-decimetre work, the specific model matters and should be recorded as part of the height's metadata. For metre-scale work, any modern global model is sufficient.