Winkelunits

Winkelunits are the units used to measure the size of an angle. The most common Winkelunits are degrees, radians, grads (also called gons or gradians), and turns. Each unit provides a different scale for expressing the same angular size, and they are related by simple arithmetic conversions.

Degrees: A full circle contains 360 degrees. Each degree is subdivided into 60 arcminutes and 60 arcseconds. Degrees are widely used in everyday life, navigation, cartography, and many engineering disciplines.

Radians: The radian is the SI unit for plane angles. By definition, a radian is the angle subtending an arc equal in length to the circle’s radius. A full circle has 2π radians. Conversions: degrees to radians multiply by π/180; radians to degrees multiply by 180/π. The radian is preferred in mathematical formulas and most physics calculations.

Grads and turns: The grad (gon) subdivides the circle into 400 units; 1 grad = 0.9 degrees, and 1 degree = 10/9 grads. A full circle is 400 grads. A turn (or revolution) equals 360 degrees or 2π radians and is sometimes used in computing to denote a complete cycle.

Usage and standards: The radian is the official SI unit for angles; degrees remain common in everyday contexts and many applied fields. Grads are used in some surveying and historical European contexts, while turns appear in computer science and certain engineering domains. In practice, selecting a Winkelunit depends on the field, with conversions available between all units.