# Definition:Angular Measure/Radian

< Definition:Angular Measure(Redirected from Definition:Radian)

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## Definition

The **radian** is a measure of plane angles symbolized either by the word $\radians$ or without any unit.

**Radians** are pure numbers, as they are ratios of lengths. The addition of $\radians$ is merely for clarification.

$1 \radians$ is the angle subtended at the center of a circle by an arc whose length is equal to the radius:

### Value of Radian in Degrees

The value of a radian in degrees is given by:

- $1 \radians = \dfrac {180 \degrees} {\pi} \approx 57 \cdotp 29577 \, 95130 \ 82320 \, 87679 \, 8154 \ldots \degrees$

This sequence is A072097 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Also known as

**Radian measure** is also known as **circular measure**.

## Also see

- Results about
**radians**can be found**here**.

## Technical Note

The $\LaTeX$ code for \(\radians\) is `\radians`

.

## Sources

- 1976: K. Weltner and W.J. Weber:
*Mathematics for Engineers and Scientists*... (previous) ... (next): $1$. Functions: $1.5$ Trigonometric or Circular Functions: $1.5.1$ Unit Circle - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**angular measure** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**angular measure** - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $5$: Eternal Triangles: The origins of trigonometry

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