Understanding Angular Measurements
Angles can be measured in several systems. Degrees divide a full rotation into 360 parts, radians relate arc length to radius (a full circle is 2π radians), and gradians divide a right angle into 100 parts. Each system has its advantages depending on the application.
In programming and scientific computing, most math functions expect angles in radians. Navigation and everyday use prefer degrees. Surveying sometimes uses gradians. Arcminutes and arcseconds provide finer divisions of degrees, essential in astronomy, navigation, and precision engineering.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180 (approximately 0.01745) to get radians. For example, 180° = π radians ≈ 3.14159 radians, and 90° = π/2 radians ≈ 1.5708 radians. Radians are the standard unit in mathematics and physics, while degrees are more intuitive for everyday use.
What is a gradian?
A gradian (also called a gon or grad) divides a right angle into 100 parts, making a full circle 400 gradians. This system is used primarily in surveying and civil engineering in some European countries because it simplifies percentage-of-slope calculations.