Why the Earth Is Not a Sphere

A common simplification calls Earth “round.” A more precise statement: Earth is almost round — an oblate spheroid shaped by the balance of gravity and rotation. From space the flattening is invisible because it's only 0.34 % of the radius. For coordinate work, it's essential. Every modern reference frame uses an ellipsoid rather than a sphere precisely because the flattening produces metre-scale errors at typical distances if you ignore it.

This article unpacks why the Earth has the shape it does, how that shape was first measured in the 1730s, and why coordinate systems all use the ellipsoidal model rather than the sphere. The /learn/what-is-a-geodetic-datum pillar covers ellipsoids as part of geodetic datums.

The equatorial bulge

Earth rotates once every ~23 hours 56 minutes (a sidereal day). The rotation creates a centrifugal effect: every mass element on Earth experiences an outward push perpendicular to the rotation axis, strongest at the equator and zero at the poles. Over billions of years, this rotation has shaped Earth into an equilibrium oblate spheroid — gravity pulling everything toward the centre, balanced against rotation pushing equatorial mass outward.

The result:

• Equatorial radius: a = 6,378.137 km (WGS 84)
• Polar radius: b = a(1 − f) ≈ 6,356.752 km
• Difference: about 21.4 km
• Flattening: f = 1/298.257223563 (WGS 84)

The flattening number — 1/298 — means the polar radius is shorter than the equatorial by one part in 298. In percentage terms, 0.34 %. Small but real.

The bulge isn't just a static shape: it shifts slightly over time. Mass redistribution from melting ice sheets, post-glacial rebound, and groundwater depletion all change the moment of inertia and the equilibrium shape. Modern satellite gravity missions (NASA GRACE / GRACE-FO; ESA GOCE) track these changes at the millimetre-per-year scale.

The numbers in detail

Per NGA WGS 84:

| Parameter | Value | | ---------------------------- | ---------------------------------- | | Semi-major axis (equatorial) | a = 6,378,137.0 m | | Semi-minor axis (polar) | b ≈ 6,356,752.3142 m | | Flattening | f = 1/298.257223563 | | First eccentricity squared | e² = 6.69437999014 × 10⁻³ | | Mean radius | R = (2a + b)/3 ≈ 6,371,008.8 m | | Surface area | ~510,072,000 km² | | Mass | M ≈ 5.972 × 10²⁴ kg | | Standard gravitational parameter | GM = 3.986004418 × 10¹⁴ m³/s² |

These are the WGS 84 ellipsoid's defining numbers — the mathematical surface that approximates the physical Earth's shape closely enough for sub-metre coordinate work globally.

Why the shape was first measured this way

The shape of the Earth was a subject of intense scientific controversy in the early 18th century. Isaac Newton, working from his theory of gravitation in the Principia (1687), predicted that a rotating self-gravitating fluid should be oblate — bulged at the equator, flattened at the poles. Independently, Christiaan Huygens reached the same conclusion using a slightly different argument.

But the French Cassini family of astronomers — Giovanni Domenico Cassini and his son Jacques — measured a French meridian arc and arrived at the opposite conclusion: the Earth was prolate, elongated at the poles and flatter at the equator. Their result appeared as authoritative as Newton's prediction, and the two camps disagreed bitterly through the 1720s and 1730s.

To settle the debate, the French Academy of Sciences in 1735 dispatched two expeditions:

• Lapland expedition (1736–1737), led by Pierre-Louis Maupertuis, measured a meridian arc near 66°N.
• Peru expedition (1735–1744), led by Charles-Marie de La Condamine, measured an arc near the equator in what is now Ecuador.

The two arcs differed in length per degree of latitude. The Lapland degree was longer than the Peruvian degree — confirming Newton's prediction. A degree of latitude is longer near the poles because the Earth's surface curves more gently there (the polar radius of curvature is larger than the equatorial).

By 1744 the matter was settled: Earth is an oblate spheroid. The Cassini measurements had been distorted by accumulated errors across long surveying chains; the precision-engineered expeditionary instruments resolved the question definitively.

This was geodesy's first triumph as an experimental science.

Why this matters for coordinates

Every modern coordinate reference system uses an ellipsoidal Earth model, not a spherical one. The reason: the difference matters.

A degree of latitude on a sphere is roughly 111.32 km everywhere. On the WGS 84 ellipsoid:

• At the equator: 110.574 km per degree
• At 45°: 111.132 km per degree
• At the poles: 111.694 km per degree

The variation is about 1.1 km from equator to pole, or 1 %. For distance calculations:

• Vincenty's formula on the WGS 84 ellipsoid achieves millimetre accuracy globally.
• Haversine on a sphere achieves about 0.5 % accuracy on average, worse near the poles.

For survey-scale work, sub-metre engineering, and any application where positional accuracy is the deliverable, the ellipsoidal model is non-negotiable. For visual web mapping at typical zoom levels, a spherical model (e.g., Web Mercator's spherical formulas) is acceptable because the pixel resolution exceeds the sphere-vs-ellipsoid error.

The /tools/distance-calculator uses Vincenty on WGS 84 by default; the haversine fallback is reserved for cases where Vincenty fails to converge near antipodes.

A concrete illustration of the ellipsoidal-vs-spherical discrepancy: the great-circle distance from New York to London on a sphere of radius 6,371 km is approximately 5,572 km; the Vincenty geodesic distance on the WGS 84 ellipsoid is approximately 5,585 km. The 13 km difference (about 0.23 %) is small in fractional terms but well over the kilometre scale — enough to matter for fuel planning on commercial flights, for precision navigation, and for any work that quotes distance to better than a percent.

Beyond the oblate spheroid: the geoid

The ellipsoid is one model. The actual Earth is more complex still. The geoid — the equipotential gravity surface that approximates mean sea level — deviates from the ellipsoid by up to ~85 m in either direction. So even the oblate-spheroid model is a simplification of the irregular physical Earth.

For coordinate work, three nested models are needed:

1. Sphere — for visualisations and rough calculations (accuracy ~0.5 %).
2. Ellipsoid — for almost everything modern: GPS, surveying, navigation, mapping (accuracy sub-metre).
3. Geoid — for vertical references, sea-level work, hydrology (accuracy sub-decimetre with modern models).

The /learn/ellipsoid-vs-geoid article covers the comparison between the latter two in detail.

Other rotating bodies

Earth's oblate-spheroid shape isn't unique. Other rotating self-gravitating bodies show analogous flattening, with magnitudes depending on rotation rate, mass, and internal structure:

| Body | Rotation period | Flattening | | ------- | ---------------- | ------------ | | Jupiter | 9 h 56 min | 1 / 15.4 | | Saturn | 10 h 33 min | 1 / 10.2 | | Uranus | 17 h 14 min | 1 / 43.6 | | Neptune | 16 h | 1 / 58.5 | | Earth | 23 h 56 min | 1 / 298.3 | | Mars | 24 h 37 min | 1 / 169.8 | | Sun | ~25 days | 1 / ~100,000 | | Moon | 27 days | 1 / 825 |

The gas giants are visibly oblate in any direct image — Jupiter's 1/15.4 flattening corresponds to a polar diameter ~9,000 km shorter than its equatorial diameter, easily seen through a backyard telescope. Mars is more spherical than Earth despite having similar rotation: its lower mass and thinner crust make for less gravitational equilibration. The Moon's synchronous rotation relative to Earth gives it a tidally-frozen near-spherical shape.

Every modern geodetic system for the other planets uses their respective oblate spheroid: Mars uses the IAU 2000 Mars ellipsoid; the Moon uses lunar reference frames. The principles are the same; the parameters differ.

Common misconceptions

“Earth is a perfect sphere.” It is not. The flattening is 1/298, real and measurable. The sphere is a useful approximation for rough work but introduces systematic errors of up to 0.5 % in distance calculations.

“Earth is pear-shaped.” A 1958 satellite measurement suggested a slight north–south asymmetry; the southern hemisphere appeared marginally fatter. Subsequent satellite gravity missions (GRACE, GOCE) have quantified this: there is a small north–south asymmetry, but it's about 50 m on top of the 6,378 km radius — roughly one part in 100,000. It does not make the Earth “pear-shaped” in any meaningful sense; it's a minor higher-order effect on top of the oblate-spheroid shape.

“The bulge means the equator is further from the centre than Everest.” Mount Chimborazo (a volcano in Ecuador near the equator) is, in fact, the highest point on Earth measured from the centre. Its summit is roughly 6,384 km from the geocentre, compared to Everest's ~6,382 km — Chimborazo wins by ~2 km because it sits on the equatorial bulge. Everest is higher above mean sea level, but Chimborazo is further from the centre. Both statements are correct; they measure different things.

“The flattening is too small to matter.” For visualisation at globe scale, true. For everything sub-metre, false. A 1 % error in distance accumulates to tens of metres on continent-scale paths. Every modern GIS, GPS, and surveying system models the Earth as an ellipsoid because the alternative is wrong.

“Newton settled this with the Principia in 1687.” Newton predicted oblate flattening, but the empirical confirmation required the 1736–1744 expeditions to Lapland and Peru. Theory and observation arrived at the answer separately; the convergence is what closed the chapter. The history of geodesy is full of such theory-observation interplay.

“Earth's rotation is what causes the bulge.” It is — but only in equilibrium. A non-rotating Earth would be a sphere; the rotation pushes mass outward at the equator until gravity, internal pressure, and centrifugal effect balance. The 21.4 km bulge is the equilibrium answer. Earth has been rotating for billions of years, so it's effectively in steady-state.

“If Earth weren't rotating, GPS would still need an ellipsoid.” No — a hypothetical non-rotating Earth would relax into a sphere (modulo geoid undulations from mass distribution). The reference ellipsoid models the rotation-induced flattening. Without rotation, the “ellipsoid” would degenerate to a sphere, and the flattening parameter would be zero. Earth's rotation is the reason the geodetic discipline needs an ellipsoid in the first place.