123 123Calculator

Central Angle Calculator

Calculate the central angle of a circle with ease using the central angle calculator. Enter arc length and radius to get accurate results instantly.

Clear
Central angle95.492966°1.66666667 radians
In radians1.66666667
Fraction of the circle26.5258%
Sector area30
Full circumference37.699112
More than a full turn?No

The rule

θ = arc ÷ radius (radians)

Degrees and radians

A full turn is 360° or 2π radians, so:

radians = degrees × π/180 and degrees = radians × 180/π

Degrees are convenient because 360 divides so many ways. Radians are the natural choice in mathematics because arc length becomes simply rθ and the calculus of sine and cosine comes out clean — derivatives pick up stray factors of π/180 in degrees.

Names worth knowing

  • Acute — under 90°. Right — exactly 90°. Obtuse — between 90° and 180°.
  • Straight — 180°. Reflex — over 180°.
  • Complementary pairs add to 90°; supplementary pairs add to 180°.