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radian

drawing illustrating radian

For the meaning of any metric prefix to radian, go here.

Since the late 19ᵗʰ century, a unit used to measure plane angles in SI and elsewhere, equal to the angle between two radii of a circle that cut off a piece of the circumference whose length is equal to the length of the radius. Symbol, rad.

Since the circumference of a circle is pi times the diameter, or two radii, one radian is 360 divided by 2 pi degrees, or approximately 57° 17′ 45″ (about 57.295 779 513°).

According to Florian Cajori,¹ the term “radian” was first used in print by James Thomson in 1873. (Thomson was a brother of Lord Kelvin.)

A variety of symbols have been used for the radian, including, in a raised position like an exponent, R, r, (r) and c. In 1929 Cajori wrote “Evidently there is, as yet, no approach to uniformity in the designation of radians.”²

1. Florian Cajori.
A History of Mathematics, 2nd ed.
New York: Macmillan, 1919),
Page 484.

2. Florian Cajori.
A History of Mathematical Notations. Volume 2.
La Salle, Illinois: Open Court, 1929.
Page 148.