Convert between degrees, radians, gradians, and turns. 360° = 2π radians = 400 gradians = 1 turn. Radians are used in mathematics and physics. Degrees are used in everyday navigation and geometry. Gradians (also called grads) are used in surveying. π radians = 180°.
📂 Converters
📐 Angle Converter
Convert angles between degrees, radians, gradians, and turns. Essential for students, engineers, and programmers working with trigonometry and geometry.
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Free angle converter. No sign-up needed.
🤔 How Does This Work?
All angles first converted to degrees
1 radian = 180/π degrees ≈ 57.2958°
1 gradian = 0.9 degrees
1 turn = 360 degrees
❓ Frequently Asked Questions
What are radians?▼
Radians measure angles as the ratio of arc length to radius. One radian is the angle where the arc length equals the radius. A full circle = 2π radians ≈ 6.283 radians. Radians are the natural unit for angles in mathematics — calculus and physics formulas use radians because trigonometric derivatives are simplest in radians.
When do I use degrees vs radians?▼
Use degrees for: everyday angles, navigation, surveying, construction, basic geometry. Use radians for: calculus and higher mathematics, physics equations (angular velocity, circular motion), computer programming trig functions (Math.sin() in most languages uses radians). Converting: degrees × π/180 = radians. Radians × 180/π = degrees.
Radians measure angles as the ratio of arc length to radius. One radian is the angle where the arc length equals the radius. A full circle = 2π radians ≈ 6.283 radians. Radians are the natural unit for angles in mathematics — calculus and physics formulas use radians because trigonometric derivatives are simplest in radians.
When do I use degrees vs radians?▼
Use degrees for: everyday angles, navigation, surveying, construction, basic geometry. Use radians for: calculus and higher mathematics, physics equations (angular velocity, circular motion), computer programming trig functions (Math.sin() in most languages uses radians). Converting: degrees × π/180 = radians. Radians × 180/π = degrees.