What Is an Angle Converter?
An angle converter transforms angular measurements between degrees, radians, gradians, and turns. It is essential for mathematics, physics, engineering, and navigation where different angular units are used.
How to Use This Angle Converter
- Enter the angle value to convert.
- Select the source unit (e.g., degrees).
- Choose the target unit (e.g., radians) and view the result.
Key Concepts
A full circle = 360 degrees = 2π radians = 400 gradians = 1 turn. Key conversions: 1 radian = 180/π ≈ 57.2958 degrees. 1 degree = π/180 ≈ 0.01745 radians. Radians are the natural unit for calculus and trigonometric functions. Gradians divide a right angle into 100 parts, making them useful in surveying.
Frequently Asked Questions
Why do mathematicians prefer radians?
Radians simplify calculus formulas. The derivative of sin(x) is cos(x) only when x is in radians. In degrees, you would need a conversion factor of π/180.
What is a gradian?
A gradian (also called a gon) divides a right angle into 100 parts, so a full circle = 400 gradians. It simplifies percentage-based slope calculations in surveying.
How do I convert degrees to radians in my head?
Multiply degrees by π/180. Common values: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π.