Browser-local angle arithmetic

Central Angle Calculator

Solve a circle’s central angle from arc length and radius or sector area and radius.

Calculate

Enter values and calculate.

Formula and method

Arc mode rearranges s = rθ to θ = s ÷ r. Sector mode rearranges A = ½r²θ to θ = 2A ÷ r². θ is calculated in radians and also converted to degrees.

Worked example

Arc length π with radius 1 gives θ = π radians = 180°. Sector area π with radius 1 gives 2π radians = 360°.

Limits and ownership boundary

Inputs must use compatible length or squared-length units. This classroom V1 accepts zero through one full revolution. Existing Arc Length and Sector Area calculators retain forward-solving ownership.

Method source

OpenStax Precalculus 2e: Angles.