Keskikulman

Keskikulman, the Finnish term for central angle, is a geometric concept defined as the angle formed at the center of a circle by two radii drawn to points on the circle. The central angle subtends an arc of the circle and determines both the length of that arc and the area of the corresponding sector.

In a circle with radius R, the central angle θ is most commonly measured in radians, with the arc length s related by s = Rθ. When θ is expressed in degrees, the arc length is s = (θ/360) · 2πR. The size of a central angle also directly yields the area of the sector it bounds: A = (1/2)R^2θ in radians, or A = (θ_deg/360) · πR^2 in degrees.

A key geometric property is that an inscribed angle subtending the same arc is half the central angle, meaning inscribed angles are half as large as the central angle that subtends the same arc.

In three-dimensional contexts, a central angle can be defined on a sphere as the angle between two radii drawn from the center to points on the sphere, indicating the same angular separation as on a circle.

Keskikulman plays a fundamental role in trigonometry, circle geometry, and applications such as orbital mechanics, computer graphics, and navigation. It is closely related to related concepts like radii, chords, arcs, and sectors, and is foundational to calculations involving arc lengths and areas in circular figures. The term derives from keski- meaning center and kulma meaning angle in Finnish.