Angle Converter
Convert between deg/rad/grad.
Input
Result
What is an Angle Converter?
An Angle Converter is a free online tool that converts angle measurements between degrees (°), radians (rad), and gradians (gon). It is essential for mathematics, trigonometry, engineering, navigation, and computer graphics where different angle units are used.
How to calculate angle conversion manually (the formula)
To convert degrees to radians, multiply by π/180 (radians = degrees × π / 180). To convert radians to degrees, multiply by 180/π (degrees = radians × 180 / π). To convert degrees to gradians, multiply by 200/180. To convert gradians to degrees, multiply by 180/200.
Example calculation
Convert 90° to radians: 90 × π / 180 = π/2 = 1.5708 rad. Convert π radians to degrees: π × 180 / π = 180°. Convert 200 grad to degrees: 200 × 180 / 200 = 180°.
Common mistakes
- Using degrees in trigonometric functions without converting — Most programming languages and calculators expect radians, not degrees. Always convert unless using degree mode.
- Forgetting the π factor — The conversion between degrees and radians always involves π. A common mistake is multiplying or dividing by 180 without including π.
- Confusing gradians with degrees — A right angle is 100 gradians but 90 degrees. Assuming they are the same leads to significant errors.
Frequently asked questions
What is an Angle Converter?
An Angle Converter is a tool that converts angle measurements between degrees, radians, and gradians.
How do I convert degrees to radians?
To convert degrees to radians, multiply the angle in degrees by π/180. For example, 180° × π/180 = π radians.
What is the formula for converting radians to degrees?
To convert radians to degrees, multiply the angle in radians by 180/π. For example, π radians × 180/π = 180°.
How many radians are in a full circle?
A full circle contains 2π radians, which is approximately 6.28319 radians.
What is a gradian?
A gradian (or gon) divides a right angle into 100 units. There are 400 gradians in a full circle, 100 gradians in a right angle.