radian [rad] to degree [deg] Converter
Quick Reference
1 radian (rad) = 57.29577951 degree (deg)
1 degree (deg) = 0.01745329252 radian (rad)
How to Convert radian to degree
1 rad = 57.29577951308232 deg
1 deg = 0.017453292519943295 rad
To convert radian to degree, multiply the value by 57.29577951. To convert degree back to radian, divide by 57.29577951.
Example: convert 10 rad to deg:
10 rad = 10 x 57.29577951308232 = 572.9577951308232 deg
radian
Definition: A radian is the standard unit of angular measure, used in many areas of mathematics. One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
History/origin: The concept of radian measure was developed in the mid-18th century. Roger Cotes was one of the first to recognize the naturalness of using the radius as the unit of angle measurement. The term 'radian' first appeared in print on 1873, in examination questions set by James Thomson at Queen's College, Belfast.
Current use: Radians are widely used in mathematics, physics, and engineering, particularly in calculus, trigonometry, and signal processing. They simplify many formulas and are the standard unit for angular measurement in scientific and mathematical contexts.
degree
Definition: A degree (symbol: °) is a unit of angular measure, representing 1/360 of a full rotation. It is a common unit for measuring angles, particularly in geometry and navigation.
History/origin: The division of a circle into 360 degrees is attributed to the ancient Babylonians, who used a base-60 (sexagesimal) numeral system. They may have chosen 360 because it is close to the number of days in a year.
Current use: Degrees are widely used in everyday contexts for measuring angles, such as in maps, compasses, and architectural drawings. They are also commonly used in mathematics and science, although radians are preferred in many theoretical contexts.
radian to degree Conversion Table
| radian [rad] | degree [deg] |
|---|---|
| 1 rad | 57.29577951308232 deg |
| 2 rad | 114.59155902616465 deg |
| 5 rad | 286.4788975654116 deg |
| 10 rad | 572.9577951308232 deg |
| 20 rad | 1145.9155902616465 deg |
| 50 rad | 2864.7889756541163 deg |
| 100 rad | 5729.5779513082325 deg |
| 200 rad | 11459.155902616465 deg |
| 500 rad | 28647.88975654116 deg |
| 1000 rad | 57295.77951308232 deg |