radian

American  

[rey-dee-uhn] / ˈreɪ di ən /

noun

Mathematics.

1. the measure of a central angle subtending an arc equal in length to the radius: equal to 57.2958°. rad

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radian British  

/ ˈreɪdɪən /

noun

1.  rad.  an SI unit of plane angle; the angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius. 1 radian is equivalent to 57.296 degrees and π/2 radians equals a right angle

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radian Scientific  

/ rā′dē-ən /

1. A supplementary unit of the International System used in angular measure. One radian is equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle, approximately 57°17′44.6″.

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Etymology

Origin of radian

First recorded in 1875–80; radi(us) + -an

Explanation

In math, a radian is the angle created when the arc length of a circle is equal to the radius of that circle. If you have a slice of pizza that's as long as the length of its crust, the angle created by the pointy end of the pizza slice is a radian. Imagine taking the radius of a circle — the line going from the center to the perimeter — and wrapping it around the outside. The angle this creates is a radian. You'll need to understand radians to study advanced math like trigonometry or calculus. The concept of a radian as a unit of measure was developed in 1714, but the word wasn't coined until the nineteenth century, from radius.

Example Sentences

See Examples For:

radian

We create Figure 10 by choosing several input values close to with half of them less than and half of them greater than Note that we need to be sure we are using radian mode.

From Textbooks ● Dec. 1, 2021

We say the angle corresponding to the arc of length 1 has radian measure 1.

From Textbooks ● Mar. 30, 2016

The radian measure would be the arc length divided by the radius.

From Textbooks ● Feb. 13, 2015

For calculators or software that use only radian mode, we can find the sine of for example, by including the conversion factor to radians as part of the input:

From Textbooks ● Feb. 13, 2015

If we allow the arc between A and B to be the diameter of the moon, it is by astronomical calculation about .009 radian, or .009 CO.

From A Quantitative Study of the Nocturnal Migration of Birds. Vol.3 No.2 by George H. Lowery.