Online Calculators > Math Calculators > Central Angle Calculator

Central Angle Calculator

Central angle calculator calculates the central angle of the arc base on the arc length and radius or diameters.

Central Angle of a Circle Calculator

Radius or     Diameter
Arc Length
Central Angle(θ)
arc length

Central Angle Formula

To calculate the central angle θ of the arc,
we need to know the radius or diameter, and the arc length of the arc.

The central angle formula is

θ = L / r

θ = radians
L = arc length
r = radius

To calculate the central angle in degrees,

θ = L x 180 / πr


For example, to calculate the central angle with an arc length of 22, and a radius of 10,
the calculation result in radians is:
θ = 22 / 10 = 2.2

To convert radians to degrees:
θ = 2.2 x 180 / π = 126°

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