Degree to Radian Converter
Convert degree to radian instantly. 1 degree = 0.017453 radian.
Degree to Radian Table
| Degree | Radian |
|---|---|
| 1 ° | 0.017453 rad |
| 5 ° | 0.087266 rad |
| 10 ° | 0.174533 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 90 ° | 1.570796 rad |
| 180 ° | 3.141593 rad |
| 360 ° | 6.283185 rad |
Related Conversions
Quick Answer
Formula: Radian = Degree × 0.01745
Multiply any degree value by 0.01745 to get radian.
Reverse: Degree = Radian × 57.3
Worked Examples
Degree to Radian Conversion Table
Common degree values — factor: 1 ° = 0.01745 rad
| Degree (°) | Radian (rad) | Context |
|---|---|---|
| 1 ° | 0.01745 rad | 1° |
| 5 ° | 0.08727 rad | 5° |
| 10 ° | 0.1745 rad | 10° |
| 15 ° | 0.2618 rad | Clock hour |
| 30 ° | 0.5236 rad | Clock half-hour |
| 45 ° | 0.7854 rad | Half right angle |
| 60 ° | 1.047 rad | Equilateral triangle |
| 90 ° | 1.571 rad | Right angle |
| 120 ° | 2.094 rad | Obtuse |
| 135 ° | 2.356 rad | 3/8 turn |
| 180 ° | 3.142 rad | Straight line |
| 270 ° | 4.712 rad | 3/4 turn |
| 360 ° | 6.283 rad | Full circle |
| 720 ° | 12.57 rad | Two rotations |
| 1080 ° | 18.85 rad | Three rotations |
Mental Math Tricks
Degrees × π/180 = radians. Exact. Use 0.01745 as a quick multiplier.
30°=π/6, 45°=π/4, 60°=π/3, 90°=π/2, 180°=π, 360°=2π — memorize these.
Radians × 180/π = degrees.
Who Uses This Conversion?
Measures horizontal and vertical angles in degrees for land surveys and boundary marking.
Specifies roof pitches, staircase angles, and geometric building features in degrees.
Uses compass bearings and course headings expressed in degrees for maritime and aviation.
Learns sine, cosine, and tangent functions using degree inputs on a calculator.
Specifies shaft rotation, cam profiles, and gear engagement angles in degrees.
Reports wind direction in degrees from north (0°–360°) for weather forecasts.
Related Conversions
Frequently Asked Questions
About Degree and Radian
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.
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.
About Degree to Radian Conversion
Converting degree to radian 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°) = 1.571 rad. A full circle (360°) = 6.283 rad. Reverse: 1 rad = 57.3 °. Exact factor: 1 ° = 0.01745 rad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.