# Convert Angle from Radians to Degrees

To convert an angle from radians to degrees multiply by the common ratio of 360° divided by τ (6.283) radians.

## Explanation

Observe that a full rotation in radians is τ radians and a full rotation in degrees is 360°. The constant τ is a naturally occuring number approximately equal to 6.2831853071. To convert an angle from radians to degrees, we multiply by 360° over τ. The radians units cancel leaving us with the angle in degrees.

## Examples

### Convert 1 Radian to Degrees

To convert an angle from radians to degrees multiply by the common ratio of 360° divided by τ (6.283) radians.

### Convert 2 Radians to Degrees

To convert an angle from radians to degrees multiply by the common ratio of 360° divided by τ (6.283) radians.

## Common Conversions

See the table below for common conversions.

degrees | radians |
---|---|

0° | 0 |

30° | τ/12 |

45° | τ/8 |

60° | τ/6 |

90° | τ/4 |

120° | τ/3 |

135° | 3τ/8 |

150° | 5τ/12 |

180° | τ/2 |

210° | 7τ/12 |

225° | 5τ/8 |

240° | 4τ/6 |

270° | 3τ/4 |

300° | 5τ/6 |

315° | 7τ/8 |

330° | 11τ/12 |

360° | τ |

## Links

Angle | concept

Degrees | concept

Radians | concept

Circle | concept