Radian to Degree Conversion Chart
| Radian (rad) | Degree (deg) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 0.0175 rad | 1.0027 deg | Base Angular Increment Unit Degree Deflection | 0.0175 × 57.2958 = 1.0027 deg |
| 0.0873 rad | 5.0019 deg | Small Angle Approximation Mechanical Slope Gradient | 0.0873 × 57.2958 = 5.0019 deg |
| 0.2618 rad | 15 deg | One Hour Earth Axial Rotation Time Angle | 0.2618 × 57.2958 = 15.0000 deg |
| 0.5236 rad | 30.0001 deg | Exact Pi Over Six Radians Special Right Triangle | 0.5236 × 57.2958 = 30.0001 deg |
| 0.7854 rad | 45.0001 deg | Exact Pi Over Four Radians Isosceles Right Triangle | 0.7854 × 57.2958 = 45.0001 deg |
| 1 rad | 57.2958 deg | One Natural Radian Arc-Length Radius Equality Standard | 1 × 57.2958 = 57.2958 deg |
| 1.0472 rad | 60.0002 deg | Exact Pi Over Three Radians Equilateral Triangle Angle | 1.0472 × 57.2958 = 60.0002 deg |
| 1.5708 rad | 90.0002 deg | Exact Pi Over Two Radians Right Angle Perpendicular | 1.5708 × 57.2958 = 90.0002 deg |
| 2.0944 rad | 120.0003 deg | Two Pi Over Three Radians Hexagonal Interior Angle | 2.0944 × 57.2958 = 120.0003 deg |
| 2.3562 rad | 135.0004 deg | Three Pi Over Four Radians Regular Octagon Angle | 2.3562 × 57.2958 = 135.0004 deg |
| 2.618 rad | 150.0004 deg | Five Pi Over Six Radians Obtuse Triangle Coordinate | 2.618 × 57.2958 = 150.0004 deg |
| 3.1416 rad | 180.0005 deg | Exact Pi Radians Straight Angle Semicircular Arc | 3.1416 × 57.2958 = 180.0005 deg |
| 3.927 rad | 225.0006 deg | Five Pi Over Four Radians Third Quadrant Vector | 3.927 × 57.2958 = 225.0006 deg |
| 4.7124 rad | 270.0006 deg | Three Pi Over Two Radians Three-Quarter Circle Turn | 4.7124 × 57.2958 = 270.0006 deg |
| 6.2832 rad | 360.0019 deg | Exact Two Pi Radians Full Geometric Circle Revolution | 6.2832 × 57.2958 = 360.0019 deg |
Radian to Degree Formula & Unit Definitions
The conversion formula is θ_deg = θ_rad × (180 / π). One radian equals approximately 57.295779513 degrees (or exactly 180 / π degrees). To convert radians to degrees, multiply the radian value by 180 and divide by π (or multiply by ~57.29578). To convert degrees back into radians, multiply by π and divide by 180 (or divide by 57.29578).
Quick Estimation: Multiply radians by 57.3 for a quick mental estimate. Key benchmarks: 1 rad ≈ 57.3°; 0.5 rad ≈ 28.6°; 1.57 rad (π/2) ≈ 90°; 3.14 rad (π) ≈ 180°.
Radian Unit (rad)
Coherent SI Plane Angle- Creator & Origin: Introduced in print by mathematician James Thomson in 1873 and recognized as the official SI angular unit.
- Standard Definition: The circular angle subtending an arc equal in length to the circle radius (2π rad = 1 full revolution).
- Everyday Focus: Calculus equations, orbital mechanics, angular momentum, digital robotics kinematics, and DSP filter phase.
Degree Angle (°)
Sexagesimal Circle Division- Creator & Origin: Ancient Babylonian sexagesimal division of the celestial solar orbit into 360 equal parts.
- Standard Definition: Defined as 1/360 of a complete circle or rotation, with 90° representing a perpendicular right angle.
- Everyday Focus: Aviation flight headings, naval charts, compass bearings, carpentry miter cuts, and camera fields of view.
Frequently Asked Questions
Q.How many degrees are in one radian?
One radian equals approximately 57.29578 degrees (exactly 180/π degrees).
Q.What is the reverse conversion from degrees to radians?
To convert back, use the Degree to Radian Converter where 1° equals approximately 0.017453 rad.
Q.How many degrees is 3.14159 radians?
3.14159 radians (π radians) equals exactly 180 degrees.
Q.How many degrees is 1.5708 radians?
1.5708 radians (π/2 radians) equals exactly 90 degrees.
Q.What formula converts radians to degrees?
Multiply radians by 180 and divide by π: Degrees = Radians × (180 / π).