How to Convert Angle Units
Convert between different angle units instantly. Our converter handles degrees, radians, gradians, and more-essential for mathematics, engineering, navigation, and geometry.
Understanding Angle Units
Angles measure the rotation between two lines meeting at a point. Degrees (°) divide a circle into 360 parts. Radians measure angles using the radius of a circle-a full circle is 2π radians. Gradians divide a circle into 400 parts.
Angle Conversion Formulas
Key relationships: 360° = 2π radians = 400 gradians. Therefore: 1° = π/180 radians ≈ 0.01745 rad, 1 radian = 180/π ≈ 57.3°.
Example:
Convert 45° to radians: 45 × (π/180) = π/4 ≈ 0.785 radians. Convert π/2 radians to degrees: (π/2) × (180/π) = 90°.
Common Use Cases
Real-world applications for this calculator
Mathematics & Programming
Most programming languages use radians for trigonometric functions, requiring conversion from degrees.
Navigation
Convert compass headings and bearings between different angle systems.
Construction & Engineering
Convert slope angles and roof pitches between degrees and other units.
Tips
- Common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π.
- When using calculators or code, check if trig functions expect degrees or radians.
- π radians = 180° is the key relationship to remember.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180. For example, 90° = 90 × (π/180) = π/2 radians ≈ 1.571 radians.
How do I convert radians to degrees?
Multiply radians by 180/π. For example, π radians = π × (180/π) = 180°. One radian ≈ 57.3°.
Why do mathematicians use radians?
Radians simplify many mathematical formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians. Arc length = radius × angle only works with radians.
What is a gradian?
A gradian (or gon) divides a right angle into 100 parts, making a full circle 400 gradians. It's sometimes used in surveying because it simplifies percentage grade calculations.