Area of a Circular Sector Calculator

A = ½ r² θ (radians) or A = πr² × (θ/360) (degrees).

Inputs

Result

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How to use this calculator

  • Enter the radius.
  • Enter the central angle in degrees or radians.
  • Read sector area and arc length.

About this calculator

A sector is a "slice" of a circle bounded by two radii and an arc. The area is a fraction of the full circle proportional to the central angle. In radians the formula is A = ½r²θ; in degrees it's A = πr² × (θ/360). Arc length is r × θ (radians).

Frequently asked

Why does the formula change with the unit?+
The radian formula ½r²θ works because radian = arc/radius is dimensionless. Degrees need a conversion factor (π/180).
What is the area of a semicircle?+
Half of πr² = ½πr². A 180° sector.
How does sector area relate to a pie chart?+
A pie slice IS a sector. The slice for a 25% category has angle 90° and area ¼ × πr².
Can the angle exceed 360°?+
Mathematically yes — a 720° angle would have twice the area of the full circle. In practice, restrict to 0-360°.
What is the arc length for the sector?+
For radian angle θ, arc length = r × θ. For degrees, arc = πr × θ/180.

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