# Gradians to Radians Conversion

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

**Results in Radians:**

^{g}= 0.015708 rad

## How to Convert Gradians to Radians

To convert a gradian measurement to a radian measurement, multiply the angle by the conversion ratio. One gradian is equal to 0.015708 radians, so use this simple formula to convert:

The angle in radians is equal to the gradians multiplied by 0.015708.

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

^{g}= (5 × 0.015708) = 0.07854 rad

Gradians and radians 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.

## 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.^{[2]} 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.

## Gradian to Radian Conversion Table

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

1^{g} |
0.015708 rad |

2^{g} |
0.031416 rad |

3^{g} |
0.047124 rad |

4^{g} |
0.062832 rad |

5^{g} |
0.07854 rad |

6^{g} |
0.094248 rad |

7^{g} |
0.109956 rad |

8^{g} |
0.125664 rad |

9^{g} |
0.141372 rad |

10^{g} |
0.15708 rad |

11^{g} |
0.172788 rad |

12^{g} |
0.188496 rad |

13^{g} |
0.204204 rad |

14^{g} |
0.219911 rad |

15^{g} |
0.235619 rad |

16^{g} |
0.251327 rad |

17^{g} |
0.267035 rad |

18^{g} |
0.282743 rad |

19^{g} |
0.298451 rad |

20^{g} |
0.314159 rad |

21^{g} |
0.329867 rad |

22^{g} |
0.345575 rad |

23^{g} |
0.361283 rad |

24^{g} |
0.376991 rad |

25^{g} |
0.392699 rad |

26^{g} |
0.408407 rad |

27^{g} |
0.424115 rad |

28^{g} |
0.439823 rad |

29^{g} |
0.455531 rad |

30^{g} |
0.471239 rad |

31^{g} |
0.486947 rad |

32^{g} |
0.502655 rad |

33^{g} |
0.518363 rad |

34^{g} |
0.534071 rad |

35^{g} |
0.549779 rad |

36^{g} |
0.565487 rad |

37^{g} |
0.581195 rad |

38^{g} |
0.596903 rad |

39^{g} |
0.612611 rad |

40^{g} |
0.628319 rad |

## 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 - 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