Enter either radian or degree and calculate the equivalent

## Formula to convert between Radians and Degrees

### How many Radians to Degrees?

### How many Degrees in a Radian?

- To convert radian to degrees, multiple radian value with 180 / π
- Therefore, 0.5 radians = 28.65 degrees.

## What are Radians and Degrees?

- Radians and Degrees are units of measurement of an angle. The SI Unit of an angle is 'Radians'.
- A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
- A degree is defined as the angle subtended at the center of a circle by an arc whose length is equal to 1/360th of the circumference of the circle. The full circle is 360 degrees
- A radian is a bigger unit than a degree. 1 radian is equal to 57.2958 degrees.
- Symbol of a degree is 'θ'. Symbol of a Radian is 'rad'
- Degrees are simpler and easy to visualize with a circle of 360 degrees. Degrees are used in any exterior activities such as surveying, construction work, drawing arcs and circles on paper using protractor and in maps and clocks
- Radians are more precise than degrees and used in calculations such as in trignometry, physics angular and rotational motion.

## How is Pi related to Radians and Degrees?

- The ratio of Circumference of a Circle to the Diameter (C/D) is a fixed value and it is always equal to 22/7 which is 3.14159. This fixed value for C/D = 3.141 holds good for any type of circle
- This ratio is defined as Pi represented by the symbol π which represents the value 3.14.
- We know that the diameter of any circle is twice of the radius.

Therefore, Circumference/Diameter = Circumference/(2 * Radius) = π - Circumference = 2* π * Radius = 2πR
- As we know a Radian is defined as the angle formed by the arc of a circle with the radius.

A circumference is a full arc of 360 degrees. Therefore, radian of a full circle = circumference/radius = 2*π = 2 * 3.14 = 6.14 radians - The angle formed by the full circle is 360 degrees. Therefore 360 degrees = 2π radians. which forms the basis for the conversion between the 2 units

## Degrees to Radians Table

Angle in Degree (deg) | In Radians (rad) |
---|---|

1 degree | 0.017 rad |

2 degrees | 0.034 rad |

5 degrees | 0.087 rad |

10 degrees | 0.174 rad |

30 degrees | 0.523 rad |

45 degrees | 0.785 rad |

57.3 degrees | 1 rad |

60 degrees | 1.047 rad |

90 degrees | 1.57 rad |

135 degrees | 2.3561 rad |

180 degrees | 3.14 rad |

240 degrees | 4.2 rad |

270 degrees | 4.71 rad |

360 degrees | 6.28 rad |

450 degrees | 7.85 rad |

540 degrees | 9.42 rad |

630 degrees | 10.99 rad |

720 degrees | 12.56 rad |

810 degrees | 14.13 rad |

900 degrees | 15.7 rad |

990 degrees | 17.27 rad |

1080 degrees | 18.84 rad |

1170 degrees | 20.42 rad |

1260 degrees | 21.99 rad |

1350 degrees | 23.56 rad |

1440 degrees | 25.13 rad |

1530 degrees | 26.7 rad |

1620 degrees | 28.27 rad |

1710 degrees | 29.84 rad |

1800 degrees | 31.41 rad |

1890 degrees | 32.98 rad |

1980 degrees | 34.55 rad |

2070 degrees | 36.12 rad |

2160 degrees | 37.69 rad |

2250 degrees | 39.26 rad |

2340 degrees | 40.84 rad |

2430 degrees | 42.41 rad |

2520 degrees | 43.98 rad |

2610 degrees | 45.55 rad |

2700 degrees | 47.12 rad |

2790 degrees | 48.69 rad |

2880 degrees | 50.26 rad |

2970 degrees | 51.83 rad |

3060 degrees | 53.4 rad |

3150 degrees | 54.977 rad |

3240 degrees | 56.54 rad |

3330 degrees | 58.11 rad |

3420 degrees | 59.69 rad |

3510 degrees | 54.97 rad |

3600 degrees | 62.83 rad |

## Radians to Degrees Table

Pi Radians (rad) | In Degrees (deg) |
---|---|

Quarter Pi / 0.25 rad | 45 degrees |

Half Pi / 0.5 rad | 90 degrees (Quarter Circle) |

1 rad | 180 degrees (Half Circle) |

2 rad | 360 degrees (One Circle) |

3 rad | 540 degrees (One and Half Circle) |

4 rad | 720 degrees (Two Circle) |

5 rad | 900 degrees (Two and Half Circle) |

6 rad | 1080 degrees (Three Circle) |

7 rad | 1260 degrees (Three and Half Circle) |

8 rad | 1440 degrees (Four Circle) |

9 rad | 1620 degrees (Four and Half Circle) |

10 rad | 1800 degrees (Five Circle) |

## FAQ on Rad-Degree conversions

1 circle = 360 degrees.

A circle multiplied by 360 gives the angle in degrees.

2 circle = 720 degrees.

10 circle = 3600 degrees.

6.28 radians

pi radians is 180 degrees

2 pi radians is 360 degrees

The unit circle is a circle with a radius of 1 unit.

An angle of 1 radian subtends an arc length of 1 unit on the unit circle.

This makes the unit circle a convenient tool for visualizing angles in radians.

Since Unit circle is a circle of radius = 1 unit.

It is 2 Pi or 6.28 radians.

A degree is a unit of measurement of an angle.

One rotation around a circle is equal to 360 degrees.

Theta (θ) is simply a variable to indicate an angle and is typically used in mathematical equations.

. It can be represented in radians or in degrees.

It is 1.0471 rad which means 60 degrees