This angle converter translates between degrees, radians, and gradians instantly in both directions.
Conversion
Angle Conversion Calculator
Convert between degrees, radians and gradians.
Calculator
About this calculator
Formula notes
radians = degrees × π / 180; gradians = degrees × 10/9; a full circle is 360° = 2π rad = 400 gon.
Worked examples
- Example: 180° = π ≈ 3.142 rad = 200 gradians, as the default conversion shows.
- An angle of 150 degrees equals 5pi/6 radians and approximately 166.667 gradians.
How to use it
- Enter the angle in any one unit.
- Read the other units filled in automatically.
- Use radians for calculus and gradians for surveying.
Frequently asked questions
Why do formulas use radians instead of degrees?
Radian-based derivatives of sin and cos stay clean (d/dx sin x = cos x) without extra factors.
What is a gradian used for?
It divides a right angle into 100 parts, which some surveying and engineering fields prefer.
Limits and interpretation
- The converter changes angular units but does not normalize direction into a preferred range such as 0 to 360 degrees.
- Rounded decimal radians can hide exact pi-based values, so preserve symbolic forms when exact geometry matters.