# Radians vs. Degrees

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 |

Download and print Angular Velocity chart

### Example - Angular velocity 100 rad/s

An angular velocity of * 100 rad/s * can as indicated in the chart above be estimated to aprox. * 950 rpm * and * 5700 deg/s * .

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