Winkelumrechner (Grad, Radiant, Gon, Umdrehungen)

Degrees divide a full circle into 360 equal parts, a convention dating back to ancient Babylonian mathematics. Radians measure angles based on the radius of a circle — one radian is the angle where the arc length equals the radius. A full circle is 2π radians (approximately 6.2832). Radians are the standard unit in mathematics and physics because they simplify calculus and trigonometric formulas. To convert: degrees = radians × (180/π).

Gradians (also called gon or grade) divide a full circle into 400 equal parts, making a right angle exactly 100 gradians. This system was introduced during the French Revolution as part of the metric system and is primarily used in surveying, mining, and some European engineering applications. The even division makes certain calculations simpler: a right angle is 100 grad, a straight angle is 200 grad, and a full rotation is 400 grad.

A turn (also called a revolution or full rotation) represents one complete circle. It is the simplest angle unit conceptually: 1 turn equals 360 degrees, 2π radians, or 400 gradians. Turns are useful in engineering for describing rotational speed (revolutions per minute) and in programming for animation and circular motion calculations where thinking in fractions of a full circle is more intuitive than degrees or radians.

The unit circle is a circle with radius 1 centered at the origin. For any angle measured from the positive x-axis, the x-coordinate of the point where the terminal ray intersects the circle equals the cosine of that angle, and the y-coordinate equals the sine. The tangent equals sine divided by cosine. This geometric relationship is fundamental to trigonometry and makes the unit circle the most intuitive way to visualize how trig functions change with angle.