Use Degrees to Radians to convert angle measurements Degrees to Radians and vice versa.

The measure of an angle in radians is equal to the ratio of (the length of the arc intercepted by the angle) to (radius of the circle). Since the radian is a pure number, the "unit" [rad] cannot be written. In other words, when no angle unit is specified, the given numerical value is implicitly expressed in radians. If [rad] is sometimes added, it is to help people who are not familiar with the field. In words: "The measure of an angle in radians is equal to the length of the arc intercepted by the angle on the trigonometric circle."

The Degree is a measure of the angles of the plane which corresponds to 0-360 of a circle. Each degree can be divided into minutes and seconds. The degree has its origin in Babylon, whose numbering system was in base sixty. At that time, it was believed that the sun revolved around the Earth. Calculations indicate that it took exactly 360 days for the Sun to make a complete revolution. So, with each passing day, the Sun covered part of this path. This arc, which corresponds to the path of the Sun following its orbit for one day, was equaled by an angle, the apex of which was the center of our planet. This angle became a unit of measurement and was called a degree or angle of a degree. Although it was later shown that it was the Earth that revolved around the Sun and not the other way around, this way of measuring angles has remained until today. Another heritage of the Babylonians is the division of time into hours, minutes and seconds, which is also done on a similar scale

To convert degrees to radians we multiply the measure of the angle by π, then we divide the result by 180 °.

Example: converting 20 ° to radians:

20 ° = 20 ° × π / 180 ° = 0.349065

To convert radians to degrees multiply the angle measurement by 180 °, then divide the result by π.

Example: converting 0.30 to degrees:

0.30 = 0.30 × 180 ° / π = 17.18873 °

If π appears in the expression for the angle, we replace π by 180 °.

To convert degrees to radians, multiply the angle measurement by π, then divide the result by 180 °.

A radian is a unit of measurement for measuring angles, such as the degree, minute of arc, grade, or thousandth. An angle of 1 radian is an angle that defines an arc of a circle with a length equal to the radius of the circle.

name of the angle | value in radians | value in degrees |

zero angle | 0 rad | 0° |

milliradian | 1 mrad | 0°3′26″15‴ |

π/6 rad | 30 ° | |

π/4 rad | 45° | |

π/3 rad | 60 ° | |

radian | 1 rad | 57°17′44″48‴ |

right angle | π/2 rad | 90° |

2π/3 rad | 120 ° | |

3π/4 rad | 135° | |

flat angle | π rad | 180° |

5π/4 rad | 225° | |

3π/2 rad | 270° | |

7π/4 rad | 315° | |

full angle | 2π rad | 360° |

For an angle of value less than 0.17 radians (ie ~ 10 °), the error is less than 1%;

For an angle of value less than 0.05 radians (i.e. ~ 3 °), the error is less than 0.1% 3.

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