# Gradians to Degrees Conversion

Enter the angle in gradians below to get the value converted to degrees.

**Results in Degrees:**

^{g}= 0.9°

1

^{g}= 0° 54′ 0″

## How to Convert Gradians to Degrees

To convert a gradian measurement to a degree measurement, multiply the angle by the conversion ratio.

Since one gradian is equal to 0.9 degrees, you can use this simple formula to convert:

The angle in degrees is equal to the gradians multiplied by 0.9.

**For example,**here's how to convert 5 gradians to degrees using the formula above.

^{g}= (5 × 0.9) = 4.5°

Gradians and degrees are both units used to measure angle. Keep reading to learn more about each unit of measure.

## Gradians

A gradian is equal to 1/400 of a revolution or circle, or 9/10°.
The grad, or gon, is more precisely defined as π/200, or 1.570796 × 10^{-2} radians.^{[1]}

This unit simplifies the measurements of right angles, as 90° is equal to 100 gradians.

Gradians | Degrees |
---|---|

0 grad | 0° |

100 grad | 90° |

200 grad | 180° |

300 grad | 270° |

400 grad | 360° |

A gradian is sometimes also referred to as a grad, gon, or grade. Gradians can be abbreviated as * ^{g}*, and are also sometimes abbreviated as

*gr*or

*grd*. For example, 1 gradian can be written as 1

^{g}, 1 gr, or 1 grd.

In formal expressions, the slash, or solidus (/), is used to separate units used to indicate division in an expression.

## Degrees

A degree is a measure of angle equal to 1/360th of a revolution, or circle.^{[2]} 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.

## Gradian to Degree Conversion Table

Gradians | Degrees (decimal) | Degrees (minutes & seconds) |
---|---|---|

1^{g} |
0.9" | 0° 54′ 0″ |

2^{g} |
1.8" | 1° 48′ 0″ |

3^{g} |
2.7" | 2° 42′ 0″ |

4^{g} |
3.6" | 3° 36′ 0″ |

5^{g} |
4.5" | 4° 30′ 0″ |

6^{g} |
5.4" | 5° 24′ 0″ |

7^{g} |
6.3" | 6° 18′ 0″ |

8^{g} |
7.2" | 7° 12′ 0″ |

9^{g} |
8.1" | 8° 6′ 0″ |

10^{g} |
9" | 9° 0′ 0″ |

11^{g} |
9.9" | 9° 54′ 0″ |

12^{g} |
10.8" | 10° 48′ 0″ |

13^{g} |
11.7" | 11° 42′ 0″ |

14^{g} |
12.6" | 12° 36′ 0″ |

15^{g} |
13.5" | 13° 30′ 0″ |

16^{g} |
14.4" | 14° 24′ 0″ |

17^{g} |
15.3" | 15° 18′ 0″ |

18^{g} |
16.2" | 16° 12′ 0″ |

19^{g} |
17.1" | 17° 6′ 0″ |

20^{g} |
18" | 18° 0′ 0″ |

21^{g} |
18.9" | 18° 54′ 0″ |

22^{g} |
19.8" | 19° 48′ 0″ |

23^{g} |
20.7" | 20° 42′ 0″ |

24^{g} |
21.6" | 21° 36′ 0″ |

25^{g} |
22.5" | 22° 30′ 0″ |

26^{g} |
23.4" | 23° 24′ 0″ |

27^{g} |
24.3" | 24° 18′ 0″ |

28^{g} |
25.2" | 25° 12′ 0″ |

29^{g} |
26.1" | 26° 6′ 0″ |

30^{g} |
27" | 27° 0′ 0″ |

31^{g} |
27.9" | 27° 54′ 0″ |

32^{g} |
28.8" | 28° 48′ 0″ |

33^{g} |
29.7" | 29° 42′ 0″ |

34^{g} |
30.6" | 30° 36′ 0″ |

35^{g} |
31.5" | 31° 30′ 0″ |

36^{g} |
32.4" | 32° 24′ 0″ |

37^{g} |
33.3" | 33° 18′ 0″ |

38^{g} |
34.2" | 34° 12′ 0″ |

39^{g} |
35.1" | 35° 6′ 0″ |

40^{g} |
36" | 36° 0′ 0″ |

## References

- Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI),
*National Institute of Standards and Technology*, https://physics.nist.gov/cuu/pdf/sp811.pdf - Collins Dictionary, Definition of 'degree', https://www.collinsdictionary.com/us/dictionary/english/degree

## More Gradian & Degree Conversions

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