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

---

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

---

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″.

---

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

An angle with a degree measure of 180° has a radian measure of π rad.

From Textbooks • Mar. 30, 2016

Since an angle of 360° corresponds to the circumference of a circle, or an arc of length 2π, we conclude that an angle with a degree measure of 360° has a radian measure of 2π.

From Textbooks • Mar. 30, 2016

The radian measure of angle θ is the length of the arc it subtends on the unit circle.

From Textbooks • Mar. 30, 2016

Note that when an angle is described without a specific unit, it refers to radian measure.

From Textbooks • Feb. 13, 2015

The torsion couple per radian was determined by preliminary experiments.

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 4 "Grasshopper" to "Greek Language" by Various