# Convert Angle from Degrees to Radians

To convert an angle from degrees to radians, multiply the angle by the constant τ (tau) divided by 360°. For example, to convert 30° to radians multiply by τ (approximately 6.283) and then divide by 360° which gives us the angle of τ/12 radians.

## Explanation

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

## Examples

### Convert 30 Degrees To Radians

To convert the angle of 30 degrees to radians multiply by the ratio of τ (6.283) radians divided by 360°.

### Convert 60 Degrees To Radians

To convert the angle of 60 degrees to radians multiply by the ratio of τ (6.283) radians divided by 360°.

## 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 |