# Radians to Gradians Conversion

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

**Results in Gradians:**

^{g}

## How to Convert Radians to Gradians

To convert a radian measurement to a gradian measurement, multiply the angle by the conversion ratio. One radian is equal to 63.661977 gradians, so use this simple formula to convert:

The angle in gradians is equal to the radians multiplied by 63.661977.

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

^{g}

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

## Radians

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.

## 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.^{[2]}

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.

## Radian to Gradian Conversion Table

Radians | Gradians |
---|---|

1 rad | 63.66^{g} |

2 rad | 127.32^{g} |

3 rad | 190.99^{g} |

4 rad | 254.65^{g} |

5 rad | 318.31^{g} |

6 rad | 381.97^{g} |

7 rad | 445.63^{g} |

8 rad | 509.3^{g} |

9 rad | 572.96^{g} |

10 rad | 636.62^{g} |

11 rad | 700.28^{g} |

12 rad | 763.94^{g} |

13 rad | 827.61^{g} |

14 rad | 891.27^{g} |

15 rad | 954.93^{g} |

16 rad | 1,019^{g} |

17 rad | 1,082^{g} |

18 rad | 1,146^{g} |

19 rad | 1,210^{g} |

20 rad | 1,273^{g} |

21 rad | 1,337^{g} |

22 rad | 1,401^{g} |

23 rad | 1,464^{g} |

24 rad | 1,528^{g} |

25 rad | 1,592^{g} |

26 rad | 1,655^{g} |

27 rad | 1,719^{g} |

28 rad | 1,783^{g} |

29 rad | 1,846^{g} |

30 rad | 1,910^{g} |

31 rad | 1,974^{g} |

32 rad | 2,037^{g} |

33 rad | 2,101^{g} |

34 rad | 2,165^{g} |

35 rad | 2,228^{g} |

36 rad | 2,292^{g} |

37 rad | 2,355^{g} |

38 rad | 2,419^{g} |

39 rad | 2,483^{g} |

40 rad | 2,546^{g} |

## References

- International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
- 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