The relationship
Formula
A = ½r²θ · s = rθ · P = 2r + s
For a radius of 8 cm and an angle of 90°: area ≈ 50.2655 cm², arc ≈ 12.5664 cm, perimeter ≈ 28.5664 cm.
Slices & sweeps
Sector Area, Arc Length & Perimeter Calculator
A sector is the slice enclosed by two radii and their connecting arc. Enter its radius and angle to calculate all three useful measurements together.
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INPUT
Measure a circular sector
Area, curved edge and full perimeter together.
RESULT
Calculated instantly
Sector area50.2655 cm²
Arc length12.5664 cm
Perimeter28.5664 cmArc plus both radii
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Straight answers
Common questions
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc. A segment is bounded by a chord and an arc.
Does sector perimeter include both radii?
Yes. Sector perimeter is the arc length plus the two straight radii.
How do I calculate a semicircle?
Use a central angle of 180°. The calculated sector area will be half the area of the full circle.