Polar radius

Earth radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). This length is also used as a unit of distance, especially in astronomy and geology, where it is usually denoted by R_⊕.

This article deals primarily with spherical and ellipsoidal models of Earth. See Figure of Earth for a more complete discussion of the models. Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km to 6,384 km (3,947–3,968 mi). Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 km (3,959 mi).

While "radius" normally is a characteristic of perfect spheres, the term as used in this article more generally means the distance from some "center" of Earth to a point on the surface or on an idealized surface that models Earth. It can also mean some kind of average of such distances, or of the radius of a sphere whose curvature matches the curvature of the ellipsoidal model of Earth at a given point.

Aristotle, writing in On the Heavens around 350 BC, reports that "the mathematicians" guess the circumference of the Earth to be 400,000 stadia. Due to uncertainty about which stadion variant Aristotle meant, scholars have interpreted Aristotle's figure to be anywhere from highly accurate to almost double the true value. The first known scientific measurement and calculation of the radius of the Earth was performed by Eratosthenes about 240 BC. Estimates of the accuracy of Eratosthenes’s measurement range from within 0.5% to within 17%. As with Aristotle's report, uncertainty in the accuracy of his measurement is due to modern uncertainty over which stadion definition he used.

Earth's rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere. Local topography increases the variance, resulting in a surface of profound complexity. Our descriptions of the Earth's surface must be simpler than reality in order to be tractable. Hence, we create models to approximate characteristics of the Earth's surface, generally relying on the simplest model that suits the need.

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