# Radians

## The radian - unit of angle measure - and angular velocity

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The radian is the SI derived unit of an angle where

*θ* = d / r (1)

*where *

*θ* = radian

*d = circular distance measured along the arc (m, in)*

*r = radius in circle (m, in)*

Since the length of a circle is *2 π r,* and the radius of the circle is *r* - the radians in a complete circle can be calculated to

* θ = *2 π r / r

*= 2 π*

*=~* 6.283185

One radian can be expressed in degrees as

*1 rad = 360 ^{o} / (2 π) = ~ 57.29578^{o } (2a)*

One radian can be expressed in revolutions as

*1 rev = 1 / (2 π) = ~ 0.16 (2a)*

One degree can be expressed in radians as

*1 ^{o} = 2 π / 360^{o} = ~ 0.01745 radian (2c)*

Note! - radians are used by default in angular expressions in most computer languages.

The radian is defined as the angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle.

degrees | 0^{o} | 15^{o} | 30^{o} | 45^{o} | 60^{o} | 75^{o} | 90^{o} | 180^{o} | 270^{o} | 360^{o} |
---|---|---|---|---|---|---|---|---|---|---|

radians | 0 | π/12 | π/6 | π/4 | π/3 | 5π/12 | π/2 | π | 3π/2 | 2π |

0 | 0.26 | 0.52 | 0.79 | 1.05 | 1.31 | 1.57 | 3.14 | 4.71 | 6.28 |

### Radians to Degrees Converter

### Degrees to Radians Converter

### Angular Velocity

Converting angular velocity *(ω)* to other units

*ω =*1 rad/s = 9.55 r/min (rpm) = 0.159 r/s (rps) (3)

#### RPM to Radians and Degrees per Second Converter

Revolutions (rpm) | Angular Velocity | |
---|---|---|

(rad/s) | (deg/s) | |

0 | 0.0 | 0 |

10 | 1.0 | 60 |

20 | 2.1 | 120 |

30 | 3.1 | 180 |

40 | 4.2 | 240 |

50 | 5.2 | 300 |

60 | 6.3 | 360 |

70 | 7.3 | 420 |

80 | 8.4 | 480 |

90 | 9.4 | 540 |

100 | 10.5 | 600 |

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