radian

drawing illustrating radian

For the meaning of any metric prefix, 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.) 

Convert between radians and degrees

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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. History of Mathematics (2nd ed., 1919), page 484.

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

 

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