Angle Converter

What is an Angle?

An angle is a measure of rotation between two lines or rays that share a common endpoint (vertex). Angles are fundamental in geometry, trigonometry, navigation, engineering, and many other fields. They can be measured in various units, with degrees being the most common in everyday use, and radians being the standard unit in mathematics and physics.

Major Angle Units

• Degree (°): 1/360 of a full rotation. Most commonly used unit in everyday life.
• Radian (rad): The SI unit of angle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. 2π radians = 360°.
• Gradian (grad): 1/400 of a full rotation. Also called gon or grad. Used in surveying.
• Turn (rev): One complete rotation. 1 turn = 360° = 2π radians.
• Arcminute ('): 1/60 of a degree. Used in astronomy and navigation.
• Arcsecond ("): 1/60 of an arcminute or 1/3600 of a degree. Used for precise measurements.
• Milliradian (mrad): 1/1000 of a radian. Used in military and shooting.

Conversion Formulas

The key conversion formulas between angle units are:

• Degrees to Radians: radians = degrees × π/180
• Radians to Degrees: degrees = radians × 180/π
• Degrees to Gradians: gradians = degrees × 10/9
• Degrees to Turns: turns = degrees / 360
• Degrees to Arcminutes: arcminutes = degrees × 60
• Degrees to Arcseconds: arcseconds = degrees × 3600

Interesting Angle Facts

Did you know that the concept of 360 degrees in a circle comes from the ancient Babylonians, who used a base-60 number system? The word "degree" comes from the Latin "degredus" meaning "step". In mathematics, π radians (approximately 3.14159) equals exactly 180 degrees. A right angle is exactly 90 degrees or π/2 radians, forming the basis of rectangular coordinate systems.

Real-World Applications

Angles are used in countless real-world applications: architecture and construction (building angles), navigation (compass bearings), astronomy (celestial coordinates), engineering (mechanical design), computer graphics (3D rendering), sports (projectile angles), and even in everyday activities like driving (steering angles) and photography (camera angles). Understanding angle conversions is essential for working across different fields and measurement systems.