degree [deg] to radian [rad] Converter
Quick Reference
1 degree (deg) = 0.01745329252 radian (rad)
1 radian (rad) = 57.29577951 degree (deg)
How to Convert degree to radian
1 deg = 0.017453292519943295 rad
1 rad = 57.29577951308232 deg
To convert degree to radian, divide the value by 57.29577951 (equivalently, multiply by 0.01745329252). To convert radian back to degree, multiply by 57.29577951.
Example: convert 10 deg to rad:
10 deg = 10 x 0.017453292519943295 = 0.17453292519943295 rad
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
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 to radian Conversion Table
| degree [deg] | radian [rad] |
|---|---|
| 1 deg | 0.017453292519943295 rad |
| 2 deg | 0.03490658503988659 rad |
| 5 deg | 0.08726646259971647 rad |
| 10 deg | 0.17453292519943295 rad |
| 20 deg | 0.3490658503988659 rad |
| 50 deg | 0.8726646259971648 rad |
| 100 deg | 1.7453292519943295 rad |
| 200 deg | 3.490658503988659 rad |
| 500 deg | 8.726646259971648 rad |
| 1000 deg | 17.453292519943297 rad |