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Radians and degrees are units used to measure angles. Degrees are the more common unit, where a circle is divided into 360 equal parts. Radians are an alternative unit based on the radius of a circle, with 2π radians in a full circle. They’re used in mathematics, physics, and engineering to describe rotations and angles.

## How to convert radians to degrees

To convert radians to degrees, you can use the following formula:

**Degrees = Radians × (180 / π)**

Where:

- Degrees is the angle in degrees.
- Radians is the angle in radians.
- π (pi) is a mathematical constant approximately equal to 3.14159.

**Example – Convert 6 radian to degree**

**Ans.** Degrees = 6 × (180 / π)

= 6 x (180 / 3.14159)

= 6 x 57.295

= 343.77

### Radians to degrees conversion table

Radians (rad) |
Radians (rad) |
Degrees (°) |

0 rad | 0 rad | 0° |

π/6 rad | 0.5235987756 rad | 30° |

π/4 rad | 0.7853981634 rad | 45° |

π/3 rad | 1.0471975512 rad | 60° |

π/2 rad | 1.5707963268 rad | 90° |

2π/3 rad | 2.0943951024 rad | 120° |

3π/4 rad | 2.3561944902 rad | 135° |

5π/6 rad | 2.6179938780 rad | 150° |

π rad | 3.1415926536 rad | 180° |

3π/2 rad | 4.7123889804 rad | 270° |

2π rad | 6.2831853072 rad | 360° |

## FAQs on Radians to Degrees conversion

### How do you convert radians to degrees?

To convert radians to degrees, you can use the following formula: Degrees = Radians × (180/π). Multiply the radians value by 180 and divide by π (approximately 3.14159) to get the equivalent value in degrees.

### What is the degree measure of π in radians?

The degree measure of π (pi) in radians is 180 degrees. This means that one full circle, which is 360 degrees, corresponds to 2π radians.

### What is the formula for converting 1 radian to degrees?

The formula for converting 1 radian to degrees is: Degrees = 1 radian × (180/π), which simplifies to approximately 57.2958 degrees.

### What is 2π/3 in degrees?

The value of 2π/3 radians in degrees is approximately 120 degrees.

### What is 2π/8 in degrees?

The value of 2π/8 radians in degrees is 45 degrees. This simplifies to 1/8 of a full circle.

### What is 3π/4 radians in degrees?

The value of 3π/4 radians in degrees is approximately 135 degrees. This corresponds to three-fourths of a full circle.

### What is 7π/4 radians in degrees?

The value of 7π/4 radians in degrees is approximately 315 degrees. This is more than a full circle (2π radians) by 1/4 of a circle.

### What is 15π/4 radians in degrees?

The value of 15π/4 radians in degrees is 135 degrees. This is because 15π/4 radians is equivalent to three and three-fourths of a full circle.