Central Angle Calculator
Calculate Using Arc Length
Calculate Using Sector Area
Calculate Using Chord Length
Results
Formulas Used
- Arc Length: θ = (L/r) × (180/π)
- Sector Area: θ = (2A/r²) × (180/π)
- Chord Length: θ = 2arcsin(c/2r) × (180/π)
Where:
θ = central angle in degrees
r = radius
L = arc length
A = sector area
c = chord length
Central Angle
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degrees
Arc Length
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units
Sector Area
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square units
Chord Length
-
units
About Central Angles
A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) extend to the circumference. Key properties:
- The central angle is twice any inscribed angle that subtends the same arc
- The central angle is proportional to the arc length
- The central angle determines the sector area
- The central angle can be used to find the chord length