# Degrees Conversion

The degree 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 degrees.

## Degree Conversion Calculators

Choose a unit of angle to convert to.

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

**Related Calculators**

## Degree Definition and Usage

A degree is a measure of angle equal to 1/360th of a revolution, or circle.^{[1]} The number 360 has 24 divisors, making it a fairly easy number to work with.
There are also 360 days in the Persian calendar year, and many theorize that early astronomers used 1 degree per day.

The degree is an SI accepted unit for angle for use with the metric system. A degree is sometimes also referred to as a degree of arc, arc degree, or arcdegree. Degrees can be abbreviated as *°*, and are also sometimes abbreviated as *deg*. For example, 1 degree can be written as 1° or 1 deg.

Degrees can also be expressed using minutes and seconds as an alternative to using the decimal form. Minutes and seconds are expressed using the prime (′) and double-prime (″) characters, although a single-quote and double-quote are often used for convenience.

One minute is equal to 1/60th of a degree and one second is equal to 1/60th of a minute.

Protractors are commonly used to measure angles in degrees. They are semi-circle or full-circle devices with degree markings allowing a user to measure an angle in degrees. Learn more about how to use a protractor or download a printable protractor.

### Background and Origin

Although the true origin of the degree is not certain, it likely originated in Babylonian astronomy. Babylonian, and later Greek, astronomers observed that stars advance about 1/360th of their circular path in the sky every night. They also divided the ecliptic, or circle representing the path of the sun, into 360 parts.

Another common theory is that degrees originated out of the Persian calendar, which is made up of 360 days in the year. 360 is also very close to the 365 actual days in a year and 354 average number of days in the luni-solar year.

Regardless of the origin, the number 360 is an easy number to use mathematically, which makes it appealing to use. The appeal comes from the fact that the number 360 has 24 divisors.

### Uses

Degrees are a very widely used unit of angular measure, and are used in managed fields. Though the degree is not an SI unit, it is accepted for use as a measure of angle.

## Degrees Measurement Conversion Table

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

1° | 0.017453 rad | 17.453293 mrad | 60' | 3,600" | 1.111111^{g} |
0.002778 r | 0.002778 cir | 17.777778 mil |

2° | 0.034907 rad | 34.906585 mrad | 120' | 7,200" | 2.222222^{g} |
0.005556 r | 0.005556 cir | 35.555556 mil |

3° | 0.05236 rad | 52.359878 mrad | 180' | 10,800" | 3.333333^{g} |
0.008333 r | 0.008333 cir | 53.333333 mil |

4° | 0.069813 rad | 69.81317 mrad | 240' | 14,400" | 4.444444^{g} |
0.011111 r | 0.011111 cir | 71.111111 mil |

5° | 0.087266 rad | 87.266463 mrad | 300' | 18,000" | 5.555556^{g} |
0.013889 r | 0.013889 cir | 88.888889 mil |

6° | 0.10472 rad | 104.719755 mrad | 360' | 21,600" | 6.666667^{g} |
0.016667 r | 0.016667 cir | 106.666667 mil |

7° | 0.122173 rad | 122.173048 mrad | 420' | 25,200" | 7.777778^{g} |
0.019444 r | 0.019444 cir | 124.444444 mil |

8° | 0.139626 rad | 139.62634 mrad | 480' | 28,800" | 8.888889^{g} |
0.022222 r | 0.022222 cir | 142.222222 mil |

9° | 0.15708 rad | 157.079633 mrad | 540' | 32,400" | 10^{g} |
0.025 r | 0.025 cir | 160 mil |

10° | 0.174533 rad | 174.532925 mrad | 600' | 36,000" | 11.111111^{g} |
0.027778 r | 0.027778 cir | 177.777778 mil |

11° | 0.191986 rad | 191.986218 mrad | 660' | 39,600" | 12.222222^{g} |
0.030556 r | 0.030556 cir | 195.555556 mil |

12° | 0.20944 rad | 209.43951 mrad | 720' | 43,200" | 13.333333^{g} |
0.033333 r | 0.033333 cir | 213.333333 mil |

13° | 0.226893 rad | 226.892803 mrad | 780' | 46,800" | 14.444444^{g} |
0.036111 r | 0.036111 cir | 231.111111 mil |

14° | 0.244346 rad | 244.346095 mrad | 840' | 50,400" | 15.555556^{g} |
0.038889 r | 0.038889 cir | 248.888889 mil |

15° | 0.261799 rad | 261.799388 mrad | 900' | 54,000" | 16.666667^{g} |
0.041667 r | 0.041667 cir | 266.666667 mil |

16° | 0.279253 rad | 279.25268 mrad | 960' | 57,600" | 17.777778^{g} |
0.044444 r | 0.044444 cir | 284.444444 mil |

17° | 0.296706 rad | 296.705973 mrad | 1,020' | 61,200" | 18.888889^{g} |
0.047222 r | 0.047222 cir | 302.222222 mil |

18° | 0.314159 rad | 314.159265 mrad | 1,080' | 64,800" | 20^{g} |
0.05 r | 0.05 cir | 320 mil |

19° | 0.331613 rad | 331.612558 mrad | 1,140' | 68,400" | 21.111111^{g} |
0.052778 r | 0.052778 cir | 337.777778 mil |

20° | 0.349066 rad | 349.06585 mrad | 1,200' | 72,000" | 22.222222^{g} |
0.055556 r | 0.055556 cir | 355.555556 mil |

## References

- Collins Dictionary, Definition of 'degree', https://www.collinsdictionary.com/us/dictionary/english/degree