# Radians to Gradians Converter

Enter the angle in radians below to get the value converted to gradians. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)

**Results in Gradians:**

^{g}

Do you want to convert gradians to radians?

## How to Convert Radians to Gradians

To convert a measurement in radians to a measurement in gradians, multiply the angle by the following conversion ratio: 63.661977 gradians/radian.

Since one radian is equal to 63.661977 gradians, you can use this simple formula to convert:

gradians = radians × 63.661977

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

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

^{g}

### How Many Gradians Are in a Radian?

There are **63.661977** gradians in a radian, which is why we use this value in the formula above.

1 rad = 63.661977^{g}

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

## What Is a Radian?

A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.^{[1]} 1 radian is equal to 180/π degrees, 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 an angle in 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.

Radians are also considered to be a "unitless" unit. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.

For example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. If θ were in degrees, however, then s would have units of degree-meters.

Learn more about radians.

## What Is a Gradian?

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 the expressions of units, the slash, or solidus (/), is used to express a change in one or more units relative to a change in one or more other units.

Learn more about gradians.

## 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/documents/20126/41483022/SI-Brochure-9-EN.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

## More Radian & Gradian Conversions

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