# Circles to Radians Converter

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

**Results in Radians:**

Do you want to convert radians to circles?

## How to Convert Circles to Radians

To convert a measurement in circles to a measurement in radians, multiply the angle by the following conversion ratio: 6.283185 radians/circle.

Since one circle is equal to 6.283185 radians, you can use this simple formula to convert:

The angle in radians is equal to the angle in circles multiplied by 6.283185.

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

### How Many Radians Are in a Circle?

There are **6.283185** radians in a circle, which is why we use this value in the formula above.

1 cir = 6.283185 rad

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

## What is a Circle?

A circle is the equivalent of 1 revolution around a circle, or 360°.

A circle is sometimes also referred to as a revolution. Circles can be abbreviated as *cir*; for example, 1 circle can be written as 1 cir.

A circle is more commonly used to describe a round, symmetrical shape with no corners or edges than it is to describe plane angle. The shape is described by its radius and circumference.

Learn more about circles.

## 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.

## Circle to Radian Conversion Table

Circles | Radians |
---|---|

1 cir | 6.2832 rad |

2 cir | 12.57 rad |

3 cir | 18.85 rad |

4 cir | 25.13 rad |

5 cir | 31.42 rad |

6 cir | 37.7 rad |

7 cir | 43.98 rad |

8 cir | 50.27 rad |

9 cir | 56.55 rad |

10 cir | 62.83 rad |

11 cir | 69.12 rad |

12 cir | 75.4 rad |

13 cir | 81.68 rad |

14 cir | 87.96 rad |

15 cir | 94.25 rad |

16 cir | 100.53 rad |

17 cir | 106.81 rad |

18 cir | 113.1 rad |

19 cir | 119.38 rad |

20 cir | 125.66 rad |

21 cir | 131.95 rad |

22 cir | 138.23 rad |

23 cir | 144.51 rad |

24 cir | 150.8 rad |

25 cir | 157.08 rad |

26 cir | 163.36 rad |

27 cir | 169.65 rad |

28 cir | 175.93 rad |

29 cir | 182.21 rad |

30 cir | 188.5 rad |

31 cir | 194.78 rad |

32 cir | 201.06 rad |

33 cir | 207.35 rad |

34 cir | 213.63 rad |

35 cir | 219.91 rad |

36 cir | 226.19 rad |

37 cir | 232.48 rad |

38 cir | 238.76 rad |

39 cir | 245.04 rad |

40 cir | 251.33 rad |

## 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

## More Circle & Radian Conversions

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