How Angle Converter Works
The degree is the base unit here, with a full circle equal to 360 degrees. One radian — the angle where the arc length equals the radius — is about 57.29578 degrees (180/π), and one gradian, used in some surveying contexts, is exactly 0.9 degrees (a full circle is 400 gradians). Your input is multiplied by its own factor to get degrees, then divided by each other unit's factor to produce the rest of the results.
How to Use This Tool
- Enter the angle value you want to convert.
- Choose the unit it's currently in — degrees, radians or gradians.
- The results box shows that angle converted into every other unit, updating as you type.
- Select Reset to clear the field and start over.
Example
A straight angle, 180 degrees, equals π radians — about 3.14159 rad (180 ÷ 57.29578) — and exactly 200 gradians (180 ÷ 0.9).
Helpful Tips
- Radians are the standard unit in most programming languages' math libraries (Math.sin, Math.cos, etc.), so convert to radians before feeding an angle into code that expects them.
- Gradians divide a right angle into 100 units instead of 90, which can simplify some surveying and engineering calculations that rely on decimal fractions of a circle.
Frequently Asked Questions
Why is a radian such an unusual-looking number of degrees?
A radian is defined geometrically — the angle subtended when the arc length equals the circle's radius — rather than by dividing a circle into a round number of parts. That geometric definition works out to about 57.29578 degrees, or 180/π exactly.
When would I use gradians instead of degrees or radians?
Gradians are mostly used in surveying, some European mapping systems, and older scientific calculators (labeled "grad" or "gon"), where dividing a right angle into 100 parts makes certain calculations more convenient than degrees' 90.
How many radians are in a full circle?
A full circle is 2π radians, roughly 6.28319 radians, corresponding to 360 degrees or 400 gradians — all three represent the same complete rotation, just measured in different-sized units.
Do I need to convert to radians for trigonometry?
It depends on the tool — most programming languages and many calculators expect radians for trigonometric functions, while degrees are more common in everyday geometry and navigation, so this converter helps bridge between the two.
This tool runs entirely in your browser. Your input is not uploaded to any server.