Angle Converter
Convert angles between degrees, radians, gradians and turns
Converted angle
How we calculated it
About the Angle Converter
Angle Converter changes angular measurements between degrees, radians, gradians and other supported units. It is useful in geometry, trigonometry, engineering and software where formulas may require a specific angle convention.
Degrees and radians describe the same rotation using different scales. Trigonometric functions in programming languages often expect radians even when the original problem is written in degrees.
How to Use the Angle Converter
- Enter the angular value.
- State whether the number is in degrees, radians, gradians or another supported angle unit.
- Choose the angle convention required by the formula or application.
- Convert before passing the value into trigonometric functions that assume a particular unit.
How the Calculation Works
Angular units describe the same rotation with different full-turn scales. A complete turn is 360 degrees, 2π radians and 400 gradians, so conversion is based on the ratio between those reference values rather than on a physical change in the angle.
Degrees to radians uses radians = degrees×π/180, while radians to degrees uses degrees = radians×180/π. Conversions involving gradians or turns use the same full-rotation equivalence, with the calculator preserving the direction and magnitude of the original rotation.
Worked example
Angle Converter Worked Example
135° to radians
135×π/180 = 3π/4 ≈ 2.35619 radians.
Result guide
Understanding Your Angle Converter Result
The converted angle describes the same rotation. Numerical trigonometric results will be wrong if an angle is fed into a function under the wrong unit assumption. Angles can also be normalized after conversion when an application expects one turn range, such as 0° to 360° or −π to π. That normalization is a representation choice rather than part of the basic unit conversion, so preserve the original direction before wrapping the angle.
Before you rely on the answer
Assumptions and Limitations
- The angle is an ordinary scalar rotation.
- π is used consistently in degree-radian conversion.
- The target application’s angle convention is known.
Practical tip
Using This Result in Practice
When working in code, label variables with the unit or convert at the boundary. Many geometry bugs come from passing degree values into a radians-based math function.
Related calculations
Useful Calculations to Continue With
If the angle defines a portion of a circle and you need area, use the Circle Sector Calculator.
If the angle and radius are known and you need curved distance, use the Arc Length Calculator.
Common questions
Angle Converter FAQ
How many radians are in 180 degrees?
π radians.
How many degrees are in one radian?
Approximately 57.2958°.
Why do programming trig functions often use radians?
Radians are the natural mathematical angle measure used in calculus and many standard libraries.