Degree to Radian Conversion Chart
| Degree (deg) | Radian (rad) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 1 deg | 0.0175 rad | Base Angular Increment Unit Degree Deflection | 1 × 0.017453 = 0.0175 rad |
| 5 deg | 0.0873 rad | Small Angle Approximation Mechanical Slope Gradient | 5 × 0.017453 = 0.0873 rad |
| 15 deg | 0.2618 rad | One Hour Earth Axial Rotation Time Angle | 15 × 0.017453 = 0.2618 rad |
| 30 deg | 0.5236 rad | Exact Pi Over Six Radians Special Right Triangle | 30 × 0.017453 = 0.5236 rad |
| 45 deg | 0.7854 rad | Exact Pi Over Four Radians Isosceles Right Triangle | 45 × 0.017453 = 0.7854 rad |
| 60 deg | 1.0472 rad | Exact Pi Over Three Radians Equilateral Triangle Angle | 60 × 0.017453 = 1.0472 rad |
| 90 deg | 1.5708 rad | Exact Pi Over Two Radians Right Angle Perpendicular | 90 × 0.017453 = 1.5708 rad |
| 120 deg | 2.0944 rad | Two Pi Over Three Radians Hexagonal Interior Angle | 120 × 0.017453 = 2.0944 rad |
| 135 deg | 2.3562 rad | Three Pi Over Four Radians Regular Octagon Angle | 135 × 0.017453 = 2.3562 rad |
| 150 deg | 2.618 rad | Five Pi Over Six Radians Obtuse Triangle Coordinate | 150 × 0.017453 = 2.618 rad |
| 180 deg | 3.1416 rad | Exact Pi Radians Straight Angle Semicircular Arc | 180 × 0.017453 = 3.1416 rad |
| 225 deg | 3.927 rad | Five Pi Over Four Radians Third Quadrant Vector | 225 × 0.017453 = 3.927 rad |
| 270 deg | 4.7124 rad | Three Pi Over Two Radians Three-Quarter Circle Turn | 270 × 0.017453 = 4.7124 rad |
| 315 deg | 5.4978 rad | Seven Pi Over Four Radians Fourth Quadrant Diagonal | 315 × 0.017453 = 5.4978 rad |
| 360 deg | 6.2832 rad | Exact Two Pi Radians Full Geometric Circle Revolution | 360 × 0.017453 = 6.2832 rad |
Degree to Radian Formula & Unit Definitions
The exact mathematical relationship is defined by θ_rad = θ_deg × (π / 180). One degree equals exactly π / 180 radians (approximately 0.0174532925 radians). To convert degrees to radians, multiply degrees by π and divide by 180 (or multiply by ~0.017453). To perform the reciprocal conversion from radians back into degrees, multiply radians by 180 / π (approximately 57.29578).
Quick Estimation: Divide degrees by 57.3 for a quick approximation, or recall key circle benchmarks: 30° = π/6 ≈ 0.524 rad; 45° = π/4 ≈ 0.785 rad; 90° = π/2 ≈ 1.571 rad; 180° = π ≈ 3.142 rad.
Degree Angle (°)
Sexagesimal Circle Division- Creator & Origin: Originated in ancient Babylonian astronomy (c. 2000 BCE) dividing a complete circular year into 360 equal parts.
- Standard Definition: Defined as exactly 1/360 of a full geometric rotation or circle (360° = 2π rad).
- Everyday Focus: Navigation compass bearings, architectural construction angles, right-angle geometry, and machine tool setups.
Radian Unit (rad)
Coherent SI Plane Angle- Creator & Origin: Coined by James Thomson in 1873 and adopted as the coherent dimensionless SI unit for plane angular measure.
- Standard Definition: The angle subtended at the center of a circle by an arc whose length equals the circle radius (s = rθ).
- Everyday Focus: Calculus derivatives, harmonic wave physics, angular velocity (rad/s), and game engine graphics rotation matrices.
Frequently Asked Questions
Q.How many radians are in one degree?
One degree equals approximately 0.01745329 radians (exactly π/180 rad).
Q.What is the reverse conversion from radians to degrees?
To convert back, use the Radian to Degree Converter where 1 rad equals approximately 57.2958°.
Q.How many radians is 180 degrees?
180 degrees equals exactly π radians (approximately 3.14159265 radians).
Q.How many radians is 90 degrees?
90 degrees equals exactly π/2 radians (approximately 1.5707963 radians).
Q.What formula converts degrees to radians?
Multiply degrees by π and divide by 180: Radians = Degrees × (π / 180).