# Radians Conversion

The radian is a unit used to measure angle. Use one of the conversion calculators below to convert to another unit of measure, or read on to learn more about radians.

## Radian Conversion Calculators

Choose a unit of angle to convert to.

## Radian Definition and Usage

A radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc.^{[1]} 1 radian is equal to 180/π, or about 57.29578°. There are about 6.28318 radians in a circle.

The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as *rad*, and are also sometimes abbreviated as * ^{c}*,

*r*, or

*. For example, 1 radian can be written as 1 rad, 1*

^{R}^{c}, 1 r, or 1

^{R}.

Radians are often expressed using their definition. The formula to find radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Thus, radians may also be expressed as the formula of arc length over the radius.

### Background and Origin

The radian was designed in 1714 by Roger Cotes, but it wasnâ€™t named and defined in publication until 1873. It was designed as a more natural measure of angle as an alternative to the degree.

### Uses

Radians are the defacto unit for measuring angles in calculus and physics. Radians are more easily expressed in formulae and are a more natural mathematical unit, hence the appeal in these fields.

## Radians Measurement Conversion Table

radians | milliradians | degrees | minutes of arc | seconds of arc | gradians | revolutions | circles | mils (NATO) |
---|---|---|---|---|---|---|---|---|

1 rad | 1,000 mrad | 57.29578° | 3,438' | 206,265" | 63.661977^{g} |
0.159155 r | 0.159155 cir | 1,019 mil |

2 rad | 2,000 mrad | 114.591559° | 6,875' | 412,530" | 127.323954^{g} |
0.31831 r | 0.31831 cir | 2,037 mil |

3 rad | 3,000 mrad | 171.887339° | 10,313' | 618,794" | 190.985932^{g} |
0.477465 r | 0.477465 cir | 3,056 mil |

4 rad | 4,000 mrad | 229.183118° | 13,751' | 825,059" | 254.647909^{g} |
0.63662 r | 0.63662 cir | 4,074 mil |

5 rad | 5,000 mrad | 286.478898° | 17,189' | 1,031,324" | 318.309886^{g} |
0.795775 r | 0.795775 cir | 5,093 mil |

6 rad | 6,000 mrad | 343.774677° | 20,626' | 1,237,589" | 381.971863^{g} |
0.95493 r | 0.95493 cir | 6,112 mil |

7 rad | 7,000 mrad | 401.070457° | 24,064' | 1,443,854" | 445.633841^{g} |
1.114085 r | 1.114085 cir | 7,130 mil |

8 rad | 8,000 mrad | 458.366236° | 27,502' | 1,650,118" | 509.295818^{g} |
1.27324 r | 1.27324 cir | 8,149 mil |

9 rad | 9,000 mrad | 515.662016° | 30,940' | 1,856,383" | 572.957795^{g} |
1.432394 r | 1.432394 cir | 9,167 mil |

10 rad | 10,000 mrad | 572.957795° | 34,377' | 2,062,648" | 636.619772^{g} |
1.591549 r | 1.591549 cir | 10,186 mil |

11 rad | 11,000 mrad | 630.253575° | 37,815' | 2,268,913" | 700.28175^{g} |
1.750704 r | 1.750704 cir | 11,205 mil |

12 rad | 12,000 mrad | 687.549354° | 41,253' | 2,475,178" | 763.943727^{g} |
1.909859 r | 1.909859 cir | 12,223 mil |

13 rad | 13,000 mrad | 744.845134° | 44,691' | 2,681,442" | 827.605704^{g} |
2.069014 r | 2.069014 cir | 13,242 mil |

14 rad | 14,000 mrad | 802.140913° | 48,128' | 2,887,707" | 891.267681^{g} |
2.228169 r | 2.228169 cir | 14,260 mil |

15 rad | 15,000 mrad | 859.436693° | 51,566' | 3,093,972" | 954.929659^{g} |
2.387324 r | 2.387324 cir | 15,279 mil |

16 rad | 16,000 mrad | 916.732472° | 55,004' | 3,300,237" | 1,019^{g} |
2.546479 r | 2.546479 cir | 16,297 mil |

17 rad | 17,000 mrad | 974.028252° | 58,442' | 3,506,502" | 1,082^{g} |
2.705634 r | 2.705634 cir | 17,316 mil |

18 rad | 18,000 mrad | 1,031° | 61,879' | 3,712,767" | 1,146^{g} |
2.864789 r | 2.864789 cir | 18,335 mil |

19 rad | 19,000 mrad | 1,089° | 65,317' | 3,919,031" | 1,210^{g} |
3.023944 r | 3.023944 cir | 19,353 mil |

20 rad | 20,000 mrad | 1,146° | 68,755' | 4,125,296" | 1,273^{g} |
3.183099 r | 3.183099 cir | 20,372 mil |

## References

- International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf