Angle Converter
Convert angles between degrees, radians, gradians, and turns.
Converter guide
About Angle Converter
The angle converter changes a value among degrees, radians, gradians, and turns. Angles describe rotation, and different fields use different units: degrees are common in everyday geometry, while radians are standard in many formulas and programming libraries.
How to use this converter
- 1Enter the angle value, including a negative value if the rotation direction calls for it.
- 2Choose the source unit and the target unit from the selectors. Confirm that you picked the intended unit symbols.
- 3Read the converted value and keep enough decimal places for your calculation. Convert back if you need to check a rounded result.
Conversion method and technical details
The converter maps each unit through degrees: one full turn is 360°, one radian is 180/π degrees, and one gradian is 0.9°. Therefore degrees = radians×180/π, and radians = degrees×π/180. A full turn represents one complete rotation.
Worked real-world example
A right angle is 90° or π/2 radians, 100 gradians, and one quarter of a turn. These are the same rotation expressed with different scales.
Common scenarios and use cases
Convert values for geometry, navigation, graphics, engineering, and code. Check what unit a formula expects before substituting an angle, especially when using trigonometric functions.
For a dependable comparison, confirm both unit labels, keep the original measurement with the converted value, and use the precision required by the task. The converter changes the representation of a value; it does not measure the item or decide which standard your project requires.
Important details and limitations
The converter handles numeric unit conversion and does not determine an angle from a diagram or direction. Rounded decimal outputs may lose precision, and angle wrapping conventions such as 0–360° are not applied to every value.
Check the output unit as well as the number. If the result will be reused in another calculation, retain full precision where possible and round only at the end. For measurements governed by a technical specification, use the standard and tolerance required by that document.
Frequently asked questions
How many radians are in a full turn?
2π radians, which is approximately 6.28318.
Can I convert a negative angle?
Yes. Negative values are supported and represent rotation in the opposite direction under common conventions.
Why does a radian result contain π?
Radians relate arc length to radius, so exact angle values often use π rather than a terminating decimal.
Why can the converted number look much larger or smaller?
Different units use different scales. A measurement can have a larger number in a smaller unit and still describe the same quantity. Check the source and target unit labels before comparing values.
How many decimal places should I keep?
Keep enough precision for the job and avoid rounding values between steps. Round the final displayed answer to match the specification, document, or measuring tool you are using.