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 = 57.29577951 deg
1 deg = 0.01745329252 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 57.29577951 = 572.9577951 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 | 57.29577951 deg |
| 2 rad | 114.591559 deg |
| 5 rad | 286.4788976 deg |
| 10 rad | 572.9577951 deg |
| 20 rad | 1145.91559 deg |
| 50 rad | 2864.788976 deg |
| 100 rad | 5729.577951 deg |
| 200 rad | 11459.1559 deg |
| 500 rad | 28647.88976 deg |
| 1000 rad | 57295.77951 deg |
Common radian to degree conversions
- 1 rad = 57.29578 deg
- 2 rad = 114.591559 deg
- 3 rad = 171.887339 deg
- 4 rad = 229.183118 deg
- 5 rad = 286.478898 deg
- 6 rad = 343.774677 deg
- 7 rad = 401.070457 deg
- 8 rad = 458.366236 deg
- 9 rad = 515.662016 deg
- 10 rad = 572.957795 deg
- 12 rad = 687.549354 deg
- 15 rad = 859.436693 deg
- 20 rad = 1,145.91559 deg
- 25 rad = 1,432.394488 deg
- 30 rad = 1,718.873385 deg
- 40 rad = 2,291.831181 deg
- 50 rad = 2,864.788976 deg
- 60 rad = 3,437.746771 deg
- 75 rad = 4,297.183463 deg
- 100 rad = 5,729.577951 deg
- 150 rad = 8,594.366927 deg
- 200 rad = 11,459.155903 deg
- 250 rad = 14,323.944878 deg
- 300 rad = 17,188.733854 deg
- 500 rad = 28,647.889757 deg
- 750 rad = 42,971.834635 deg
- 1,000 rad = 57,295.779513 deg