Radian to Degree Converter
Convert radian to degree instantly. 1 radian = 57.29578 degree.
Radian to Degree Table
| Radian | Degree |
|---|---|
| 1 rad | 57.29578 ° |
| 5 rad | 286.478898 ° |
| 10 rad | 572.957795 ° |
| 30 rad | 1718.873385 ° |
| 45 rad | 2578.310078 ° |
| 90 rad | 5156.620156 ° |
| 180 rad | 10313.240312 ° |
| 360 rad | 20626.480625 ° |
Related Conversions
Quick Answer
Formula: Degree = Radian × 57.3
Multiply any radian value by 57.3 to get degree.
Reverse: Radian = Degree × 0.01745
Worked Examples
Radian to Degree Conversion Table
Common radian values — factor: 1 rad = 57.3 °
| Radian (rad) | Degree (°) | Context |
|---|---|---|
| 0.001 rad | 0.0573 ° | ~0.057° |
| 0.01 rad | 0.573 ° | ~0.573° |
| 0.1 rad | 5.73 ° | ~5.73° |
| 0.5236 rad | 30 ° | 30° |
| 0.7854 rad | 45 ° | 45° |
| 1 rad | 57.3 ° | ~57.3° |
| 1.571 rad | 90 ° | 90° right angle |
| 2 rad | 114.6 ° | ~114.6° |
| 3.142 rad | 180 ° | 180° π |
| 4 rad | 229.2 ° | ~229° |
| 4.712 rad | 270 ° | 270° 3π/2 |
| 6.283 rad | 360 ° | 360° 2π |
| 10 rad | 573 ° | ~573° |
| 20 rad | 1146 ° | ~1,146° |
| 100 rad | 5730 ° | ~5,730° |
Mental Math Tricks
Radians × 180/π = degrees. Round to × 57.3 for quick estimates.
π/6=30°, π/4=45°, π/3=60°, π/2=90°, π=180°, 2π=360°.
Degrees × π/180 = radians.
Who Uses This Conversion?
Uses radians for calculus — derivatives of sin/cos are clean only in radians.
Applies radians in wave equations, angular momentum, and rotational dynamics.
Uses Math.sin(), Math.cos() which require radians in virtually all languages.
Describes phase angles, frequency in rad/s, and Fourier transforms in radians.
Models angular velocity in rad/s and phase margins in radians.
Programs joint angles and end-effector orientation using radians in ROS and MATLAB.
Related Conversions
Frequently Asked Questions
About Radian and Degree
Radian (rad)
The radian is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. It was formally adopted by the SI system in 1995, though it had been used in mathematics since the 18th century.
Radians simplify calculus and physics: derivatives of trigonometric functions, wave equations, and angular velocity formulas are all cleaner in radians. One full circle = 2π radians ≈ 6.2832 rad.
Interesting fact: The name 'radian' was coined by physicist James Thomson in 1873. At exactly 1 radian, the arc length equals the radius — the elegant geometric relationship that makes radians so mathematically natural.
Degree (°)
The degree (°) divides a full circle into 360 equal parts. This system traces back to ancient Babylonian astronomy, which used a base-60 (sexagesimal) number system. The choice of 360 is practical: it is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, and 120.
Degrees remain the dominant angle unit in everyday life, navigation, surveying, and most engineering disciplines. Compass bearings, latitude and longitude, and architectural drawings all use degrees.
Interesting fact: The Babylonians may have chosen 360 because they approximated the solar year as 360 days, making each day of travel correspond to one degree of the Sun's apparent annual motion around the sky.
About Radian to Degree Conversion
Converting radian to degree is essential in mathematics, physics, engineering, and surveying. Degrees are used in everyday contexts and navigation; radians are the standard in calculus and physics; gradians are common in European surveying. Having accurate conversions ensures correct results across disciplines.
Key reference: a right angle (90°) = 90 °. A full circle (360°) = 360 °. Reverse: 1 ° = 0.01745 rad. Exact factor: 1 rad = 57.3 °.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.