What is the Degrees to Radians Converter?
This tool converts between degrees (°) and radians (rad) — the two standard units for measuring angles. Degrees are used in everyday geometry and navigation, while radians are the standard in mathematics, physics, and engineering.
The conversion is based on the fundamental relationship: π radians = 180 degrees.
How to Use This Converter
- Enter a value: Type the number you want to convert. Start with 180 to see π radians.
- Select direction: Choose ° or rad as your starting unit.
- Read the result: The converted value appears instantly.
The Conversion Formula
Since π rad = 180°:
- Degrees to radians: value × (π / 180) = result in radians
- Radians to degrees: value × (180 / π) = result in degrees
Common Angles
0° = 0 rad, 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 270° = 3π/2 rad, 360° = 2π rad.
Real-World Applications
Trigonometry, calculus, physics (wave motion, rotational mechanics), computer graphics, and game development all use radians. Converting between degrees and radians is essential for students, engineers, and programmers.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180. For example, 90° × π/180 = π/2 rad ≈ 1.5708 rad.
How do I convert radians to degrees?
Multiply radians by 180/π. For example, π rad × 180/π = 180°.
What is 1 radian in degrees?
1 radian ≈ 57.2958°.
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