Angle Converter
Convert between degrees, radians, gradians, and turns instantly
Enter an angle value to see conversions
Try the examples below to get started
Quick Examples
What is Angle Conversion?
Angle conversion is the process of converting measurements of angles from one unit to another. Different fields of mathematics, science, and engineering use various units to measure angles, and being able to convert between them is essential for accurate calculations and communication.
The most common angle units include degrees (°), radians (rad), gradians (grad), and turns (or revolutions). Each unit has its specific applications and advantages depending on the context in which it's used.
Understanding Angle Units
Degrees (°)
The most commonly used unit in everyday applications. A full circle contains 360 degrees. This system dates back to ancient Babylonian mathematics and is widely used in navigation, geography, and general measurements.
Radians (rad)
The standard unit in mathematics and physics. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle contains 2π radians (approximately 6.28319 radians).
Gradians (grad)
Also called "gons," gradians divide a circle into 400 equal parts. This metric-based system is used primarily in surveying and some European countries. A right angle equals 100 gradians.
Turns (Revolutions)
A turn represents one complete rotation around a circle. It's intuitive and often used in computer graphics, animation, and describing rotational motion. One turn equals 360 degrees or 2π radians.
Common Use Cases
Mathematics & Calculus
Radians are essential for calculus, trigonometry, and advanced mathematics because they simplify derivative and integral formulas.
Navigation & Geography
Degrees are the standard for latitude, longitude, compass bearings, and celestial navigation.
Engineering & Surveying
Gradians are sometimes used in civil engineering and land surveying, particularly in Europe.
Computer Graphics & Animation
Turns and radians are commonly used in CSS, game development, and 3D graphics for intuitive rotation specifications.
Conversion Formulas
Degrees ↔ Radians
Radians = Degrees × (π / 180)
Degrees = Radians × (180 / π)
Degrees ↔ Gradians
Gradians = Degrees × (10 / 9)
Degrees = Gradians × (9 / 10)
Degrees ↔ Turns
Turns = Degrees / 360
Degrees = Turns × 360
Frequently Asked Questions
Why do mathematicians prefer radians?
Radians are the natural unit for angles in calculus and higher mathematics because they simplify formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians. This makes calculations more elegant and efficient.
What's the difference between arcminutes and degrees?
Arcminutes and arcseconds are subdivisions of degrees. One degree equals 60 arcminutes ('), and one arcminute equals 60 arcseconds ("). They're used for precise angle measurements in astronomy, navigation, and surveying.
When should I use gradians instead of degrees?
Gradians are primarily used in surveying and civil engineering in some countries. The system was designed to be more decimal-friendly (with right angles being exactly 100 gradians). However, degrees remain more common globally.
How accurate are the conversions?
Our converter uses JavaScript's native Math functions with double-precision floating-point arithmetic, providing accuracy up to 15-17 significant digits. Results are displayed with 8 decimal places for most units, which is sufficient for virtually all practical applications.
Is my data secure when using this tool?
Yes! All conversions are performed entirely in your browser using client-side JavaScript. No data is sent to any server, ensuring complete privacy and security of your calculations.