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Radian - Degree Converter

Enter either radian or degree and calculate the equivalent

## How many Degrees in a Radian? How many Radians to Degrees?

### Degrees to Radians Formula

### Radians to Degrees Formula

- To convert radian to degrees, multiple radian value with 180 / π
- This would give you a result of 0.5 radians = 28.65 degrees.

## Definition of 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
- 1 radian is equal to 57.2958 degrees.
- Symbol of a degree is 'θ'. Symbol of a Radian is 'rad'

## 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

## Why do we need to convert between Degrees and Radians?

- Degrees are easier to understand and better for visualization.
- Degrees are used in surveying, construction, housework, art and craft, carpentry, navigation guide and it is also part of gadgets such as compass, clocks, maps and protractor. ,
- Radians are more precise and derived based on ratio of arc on circumference to radius. It is most suitable for calculations though not easy to visualize
- Radians are used in mathematics such as in trignometry and calculus, physics such as in rotational movement/angular motion and in programming.
- While using any trignometric and calculus equations, we need to convert degrees to radians as all these equations are in radians
- If we have a radian value but we need to use that to visualize or apply it physically in practice for any visual activity, we have to convert rad to degrees.

## 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

Both Radian and Degree are units of measurement of an angle.

Radian is the SI unit for angle.

Radian is defined as the distance travelled in an arc divided by the radius angle in radians

(theta)= (distance travelled / radius )

Θ = s/r.

Degree measures the angle of displacement from original to new position

1 circle = 360 degrees.

A circle multiplied by 360 gives the angle in degrees.

2 circle = 720 degrees.

10 circle = 3600 degrees.

Multiply radian by 57.29 degrees to convert from radian to degree

Multiply degree by 0.0174 to convert degree to radian.

180 degrees is 3.14 radians.

6.28 radians

pi radians is 180 degrees

360 deg

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.

The length of an arc divided by radius is a radian measure.

1 radian measure is a unit cicle of arc length 1 and radius of 1.

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.

Radian is a bigger unit than Degree.

1 Radian = 57.3 degrees

3.14 Radian (1 Pi) = 180 degrees

6.28 Radian (2 Pi) = 360 degrees

Angle of full circle = 360 degrees. Radian of full circle = (distance covered by arc/ Radius) = Perimeter of the circle / Radius = 2 Pi * R / R = 2 * Pi . This implies, 2 * Pi Radians = 360 Degrees Therefore, 1 Radian = 57.3 Degrees 1 Degree = 0.017 Radians

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.

Pi (π) is the ratio of circumference to the diameter π = C/D It has a constant value of 3.1415 (equal to 22/7) Radian is the ratio of arc length to the radius and it can be expressed in terms of Pi. 2 * Pi Radians = 360 Degrees

It is 1.0471 rad which means 60 degrees