How to convert degrees to radians. Use the interactive display. Change the value of the angle in degrees and then this will be converted to radians.

## Summary/Background

Radians and
degrees are two alternative units for measuring angle. There are 360 degrees or
2 \pi radians in a full turn. The radian measure is
used at advanced level and beyond in mathematics through out calculus
(differentiation and integration).

360 \text{ degrees} = 2\pi \text{ radians}

1 \text{ degree} = \displaystyle \frac{\pi}{180} \text{ radians}

1 \text{ radian} = \displaystyle \frac{180}{\pi} \text{ degrees}

360 \text{ degrees} = 2\pi \text{ radians}

1 \text{ degree} = \displaystyle \frac{\pi}{180} \text{ radians}

1 \text{ radian} = \displaystyle \frac{180}{\pi} \text{ degrees}

## Software/Applets used on this page

## Glossary

### calculus

the study of change; a major branch of mathematics that includes the study of limits, derivatives, rates of change, gradient, integrals, area, summation, and infinite series. Historically, it has been referred to as "the calculus of infinitesimals", or "infinitesimal calculus".

There are widespread applications in science, economics, and engineering.

There are widespread applications in science, economics, and engineering.

### radian

a measure of angle equal to the size of the angle subtended at the centre of a circle of radius r by an arc of length r.

### union

The union of two sets A and B is the set containing all the elements of A and B.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AP Calculus AB (USA) | 1 | Trigonometry | Radians |

AP Calculus BC (USA) | 1 | Trigonometry | Radians |

AQA A-Level (UK - Pre-2017) | C2 | Trigonometry | Radians |

AQA A2 Maths 2017 | Pure Maths | Trigonometry and Radians | Radians |

AQA AS/A2 Maths 2017 | Pure Maths | Trigonometry and Radians | Radians |

CBSE XI (India) | Sets and Functions | Trigonometric Functions | Radians |

CCEA A-Level (NI) | C2 | Trigonometry | Radians |

CIE A-Level (UK) | P1 | Trigonometry | Radians |

E Trigonometry | E1 Radians | Radians | |

Edexcel A-Level (UK - Pre-2017) | C2 | Trigonometry | Radians |

Edexcel A2 Maths 2017 | Pure Maths | Using Radians | Radians |

Edexcel AS/A2 Maths 2017 | Pure Maths | Using Radians | Radians |

I.B. Higher Level | 3 | Trigonometry | Radians |

I.B. Standard Level | 3 | Trigonometry | Radians |

Methods (UK) | M2 | Trigonometry | Radians |

OCR A-Level (UK - Pre-2017) | C2 | Trigonometry | Radians |

OCR A2 Maths 2017 | Pure Maths | Radians | Radians |

OCR MEI A2 Maths 2017 | Pure Maths | Radians | Radians |

OCR-MEI A-Level (UK - Pre-2017) | C2 | Trigonometry | Radians |

Pre-Calculus (US) | C4 | Trigonometry | Radians |

Pre-U A-Level (UK) | 2 | Trigonometry | Radians |

Scottish (Highers + Advanced) | HM1 | Trigonometry | Radians |

Scottish Highers | M1 | Trigonometry | Radians |

Universal (all site questions) | T | Trigonometry | Radians |

WJEC A-Level (Wales) | C2 | Trigonometry | Radians |