Arc Length and Sector Area Calculator (Free Step-by-Step)
Use this free arc length and sector area calculator to analyze any circular sector. Enter the radius and the central angle (in degrees or radians) and get the arc length, the sector area, the chord, and the sector perimeter — with a labeled diagram and clear steps.
The formulas
With the central angle θ in radians: arc length is s = r θ and sector area is A = ½ r² θ. If your angle is in degrees, convert first with θ(rad) = θ(deg) × π/180.
How to use the calculator
- Pick degrees or radians.
- Enter the radius and central angle.
- Press Solve for the arc length, area, chord, and perimeter.
Related: the Circle Calculator and all of our free math calculators.
Frequently asked questions
Do I need radians?
You can enter either; the calculator converts to radians internally because s = rθ and A = ½r²θ require radians.
What is the chord length?
The straight-line distance across the arc, equal to 2r·sin(θ/2). The calculator reports it alongside the arc length.
Is it free?
Yes — it runs in your browser with no sign-up.
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