Our **radians to degrees calculator** is a **powerful tool** that converts **angular measurements** from **radians** to **degrees** using **degrees = radians × (180/π)** formula.

- 0 radians = 0 degrees
- π/6 radians = 30 degrees
- π/4 radians = 45 degrees
- π/3 radians = 60 degrees
- π/2 radians = 90 degrees
- π radians = 180 degrees
- 2π radians = 360 degrees

## Radians to Degrees Calculator

Radians converted to | Calculation | Degrees (rounded to 2 decimal places) |
---|---|---|

π/6 | (π/6) × (180/π) | 30.00° |

π/4 | (π/4) × (180/π) | 45.00° |

π/3 | (π/3) × (180/π) | 60.00° |

π/2 | (π/2) × (180/π) | 90.00° |

2π/3 | (2π/3) × (180/π) | 120.00° |

5π/6 | (5π/6) × (180/π) | 150.00° |

3π/4 | (3π/4) × (180/π) | 135.00° |

7π/6 | (7π/6) × (180/π) | 210.00° |

5π/4 | (5π/4) × (180/π) | 225.00° |

4π/3 | (4π/3) × (180/π) | 240.00° |

3π/2 | (3π/2) × (180/π) | 270.00° |

5π/3 | (5π/3) × (180/π) | 300.00° |

7π/4 | (7π/4) × (180/π) | 315.00° |

π | π × (180/π) | 180.00° |

5π/2 | (5π/2) × (180/π) | 450.00° |

3π | 3π × (180/π) | 540.00° |

7π/2 | (7π/2) × (180/π) | 630.00° |

2π | 2π × (180/π) | 360.00° |

## Radians to Degrees Conversion Formula

The **formula** to convert radians to degrees is:

**degrees = radians × (180/π)**

Where:

π (pi)is approximately3.14159180/πis approximately57.2958

**π**: Approximately equal to 3.14159, this is a mathematical constant that relates the circumference of a circle to its diameter.

- Convert
**π/2 radians**to degrees:**degrees = (π/2) × (180/π) = 90°** - Convert
**1 radian**to degrees:**degrees = 1 × (180/π) ≈ 57.2958°**

## How do I Convert Radians to Degrees?

By using formula : **Degrees = Radians × (180 / π)**

**Identify the angle in radians**: Ensure you have the**correct radian measurement**.**Apply the conversion formula**: Multiply the radian value by**(180/π)**.**Simplify the expression**: If the result contains**π**, calculate its**decimal approximation**.**Round if necessary**: Depending on the required**precision**, round the result.

Let’s convert **2π/3 radians** to degrees:

**Angle in radians**:**2π/3****Apply the formula**:**(2π/3) × (180/π)****Simplify**:**2 × 180 / 3 = 360 / 3****Calculate**:**120°**

Therefore, **2π/3 radians** is equal to **120 degrees**.

## How do you convert 1 radian to degrees round your answer to the nearest degree?

To convert **1 radian** to degrees and round to the **nearest degree**:

**Apply the formula**:**1 × (180/π) ≈ 57.2958°****Round to the nearest degree**:**57°**

One **radian** is defined as the angle subtended at the center of a circle by an arc equal in length to the **radius**. This angle is **constant** regardless of the circle’s size.

When we multiply **1 radian** by **(180/π)**, we’re essentially asking: “How many degrees are in the angle that an arc equal to the radius would sweep out?”

The result, **57.2958°**, tells us that a little more than **57°** corresponds to **1 radian**. When we round to the nearest degree, we get **57°**.

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